Review pubs.acs.org/CR
Aromaticity from the Viewpoint of Molecular Geometry: Application to Planar Systems Tadeusz M. Krygowski,*,† Halina Szatylowicz,*,‡ Olga A. Stasyuk,‡ Justyna Dominikowska,§ and Marcin Palusiak§ †
Department of Chemistry, Warsaw University, Pasteura 1, 02-093 Warsaw, Poland Faculty of Chemistry, Warsaw University of Technology, Noakowskiego 3, 00-664 Warsaw, Poland § Department of Theoretical and Structural Chemistry, Faculty of Chemistry, University of Łódź, Pomorska 163/165, 90-236 Łódź, Poland ‡
3.9. Heat of Formation from Atoms Estimated from Molecular Geometry, HtFfA (1995) 3.10. Separation of HOMA into the Two Components EN and GEO (1996) 3.11. Harmonic Oscillator Model of Electron Delocalization, HOMED (2007) 3.12. New HOMA Index Parametrization for πElectron Heterocycles: The HOMHED Index (2012) 4. Applications of the Geometry-Based Aromaticity Indices 4.1. Global and Local Aromaticity of π-Electron Hydrocarbons 4.2. Aromatic Character of Hetero-π-electron Systems 4.3. Effect of Substituents on the Aromaticity of π-Electron Systems 4.4. Relationships between Tautomerism, HBonding, and Aromaticity 4.5. Aromaticity of Metal Complexes and Chelate Rings 4.6. Testing New Aromaticity Parameters 5. Quantitative Molecular Orbital Picture of Aromatic Bond Delocalization 6. General Problems and Conclusions Author Information Corresponding Authors Notes Biographies Acknowledgments Dedication Abbreviations References
CONTENTS 1. Introduction 2. How Important Is the Concept of Aromaticity? 3. Chronological Review of the Geometry-Based Aromaticity Indices 3.1. The Julg concept Aj (1967) 3.2. The Harmonic Oscillator Model of Aromaticity, HOMA (1972) 3.3. The Sum of the Bond Orders Differences as Aromaticity Index ∑ΔN (1974) 3.4. Harmonic Oscillator Stabilization Energy, HOSE (1981) 3.5. Bird’s Aromaticity Indices I5 and I6 (1985) 3.6. Pozharskii Criterion of Aromaticity, APoz (1985), and Its Modifications (2001) 3.7. Gilli’s Characteristics of π-Electron Delocalization in H-Bonded quasi-Aromatic Rings (1989) 3.7.1. Grabowski’s Modification of Gilli’s Parameter 3.8. Extensions and Modifications of the Harmonic Oscillator Model of Aromaticity, HOMA (1993) 3.8.1. Modification of HOMA for π-Electron Systems with BN Bonds 3.8.2. Parameters of HOMA for π-Electron Systems with CSe Bonds 3.8.3. Calculation of the HOMA Model Parameters for the BC Bond 3.8.4. Calculation of the HOMA Model Parameters for the BB Bond (2012)
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1. INTRODUCTION Following the history of organic chemistry, studies on relations between chemical (and later physicochemical) properties and the structure of chemical species in question are the heart of scientific investigation in this field.1,2 Undoubtedly, aromaticity belongs to one of the most important “collective” characteristics of molecules. Historical aspects of aromaticity concept
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Figure 1. The number of scientific papers, appearing per day, in which the indicated term appears in title, abstract, or keywords (asterisk denotes any adequate ending, i.e., s, ed, ing, ity, or nothing). Data taken from ref 37.
evolution are presented in a monograph by Neus,3 whereas the most important key developments are presented in Table 1 of the review paper of Schleyer and co-workers4 and in Table 1 of Balaban’s book chapter.5 Molecular geometry is of fundamental importance for any profound interpretation of molecular properties. This was elegantly pointed out by Roald Hoffmann6 and triggered intensive research in this direction. Experimental and theoretical methods enabling the determination of molecular geometry, developed since the mid-20th century, have provided numerical confirmation of the above-mentioned statement. Geometry-based aspects of aromaticity are the main subject of this Review. A definition of aromaticity is one of the important problems that is frequently discussed. In principle, definition is a formal passage describing the meaning of a word or a phrase. One possible way to define a term, to which it is difficult to attribute a strict, unequivocal definition, is to construct a collection of properties or features, which have to be exhibited/observed by a given object to accept that the term is understandable in the frame of fulfilling these conditions. This is the case for a socalled enumerative definition of a concept or term. Thus, the classical way4,7−16 to define aromaticity is the manifestation of the following features in cyclic, π-conjugated compounds: (i) a reduced bond-length alternation as compared to their acyclic unsaturated analogues, (ii) an enhanced stability as compared to their acyclic unsaturated analogues, (iii) a tendency to retain their π-electron structure (preference of substitution over addition) in chemical reactions, (iv) the induction of a diatropic ring current by an external magnetic field. According to the 520 Tetrahedron Report,15 if the π-electron cyclic system follows all four of these criteria, the system is fully aromatic. If only some of these criteria are fulfilled, the system is considered partly aromatic. However, an important problem associated with the above definition of aromaticity is that the mentioned criteria can in general not be applied universally in a consistent manner. In many cases, finding an appropriate point of reference is problematic. Let us consider a few examples. Values of the aromatic stabilization energy (ASE) depend dramatically on the reference systems in virtual reactions.17−19 A similar situation is encountered in the case of the estimation of the magnetic susceptibility exaltation. Nucleus-independent chemical shifts (NICS, NICS(1), NICS(1)zz) (for an
exhaustive review, see ref 4) are, as a magnetic property, dependent on the molecular size20 and work only for individual rings. Nevertheless, a number of attempts have been made to arrive at a summation of individual NICS values and, thus, to reproduce the magnetic susceptibility exaltation.21 Likewise, it is practically impossible to deduce differences in aromaticity from trends in reactivity, unless one considers structurally similar reaction series, for example, benzenoid hydrocarbons.22 Geometry-based indices, such as HOMA23,24 and Bird’s25,26 I5 or I6, depend on the chosen reference as well. This issue will be the subject of deeper discussion in the subsequent parts of this Review. There are a great number of papers dealing with the question to what degree the various indices of aromaticity or other molecular characteristics are mutually interrelated.16,27−34 The conclusion of these papers is that aromaticity is a multidimensional phenomenon; that is, aromaticity indices do not necessarily refer to the same aspects of aromaticity. Or, to put it in a different way, aromaticity indices do not always speak in one voice. Therefore, one may wonder whether studies on aromaticity are useful at all. The question is answered by the important statement below: “Classification and theory are not ends in themselves. If they generate new experimental work, new compounds, new processes, new methods - they are good; if they are sterile they are bad.”35
2. HOW IMPORTANT IS THE CONCEPT OF AROMATICITY? According to McWeeny, there are many notions in chemical laboratories and scientific discussions that can be named “primitive patterns of understanding”,36 terms that are understood rather intuitively, but that are very frequently used in every day practice in chemistry and related fields. One can consider the following as these kinds of terms: solvent effects, substituent effects, hydrogen bonds, Lewis acidity or basicity, along with many others including aromaticity. Attempts to define aromaticity and finding its most typical features have led to a great number of works in this direction. The histogram in Figure 1 shows how frequently these terms are used in practice. Thus, it can be seen that papers dedicated to the topic of aromaticity appear on average ∼30 times per day! Moreover, aromaticity belongs to one of the four most commonly used terms in organic chemistry, along with conformation, Hbonding, and polymerization. Encouraged by these results, we 6384
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intend to present recent achievements in the field of π-electron systems related to the problem of aromaticity. Because, in the past decade, two issues of Chemical Reviews38 were devoted to aromaticity and π-electron delocalization, in this Review, we mainly concentrate on results that were published after 2001 and were not discussed in the issue Chem. Rev. 2005, 111.
3.2. The Harmonic Oscillator Model of Aromaticity, HOMA (1972)
The next step was done by modifying the Julg idea. The mean bond length in the expression for variance was replaced by a conceptual quantity, the optimal bond length, Ropt (in the original paper the bond length was denoted by d), which is assumed to be realized in a fully aromatic system.23 The HOMA model is based on the assumption that the harmonic oscillator energy of extension or compression of a bond depends on the force constants, which, in turn, are dependent on the bond lengths. The optimal bond length Ropt is the length of a bond for which equal energy inputs are required to extend it to the length of the single bond or to compress it to the length of the double bond. The CC bond lengths in ethane (RC−C = 1.524 Å) and ethene (RCC = 1.334 Å)53 were taken as reference values, assuming the relation between force constants for double and single bonds to be 2:1.54,55 Thus, the formula for Ropt is
3. CHRONOLOGICAL REVIEW OF THE GEOMETRY-BASED AROMATICITY INDICES Before presenting the aromaticity indices based on molecular geometry, it is necessary to mention some specific features of this kind of indicator. They may be applied not only to an entire molecule, as in the case of ASE,17 magnetic susceptibility, or its exaltation,20 but also to any fragment of either cyclic or noncyclic π-electron systems. Moreover, the HOMA can be successfully applied to any π-electron fragment contained in a larger molecular entity.39−41 Magnetism-based NICS indicators4,42,43 can be applied to individual rings. Note, however, that they depend on the size of the ring in question. In almost all of the cases considered, the geometry-based indices describe the degree of π-electron or double-bond delocalization. It should also be mentioned that there is a long-time disputation on the nature of equalization of bond lengths in aromatic systems,44−51 but, in this Review, we mostly accept a traditional view that equalization of bond lengths is associated with πelectron delocalization. However, we also present a more recent approach, which shows that π electrons follow the σ system in its tendency to equalize bond lengths in aromatic rings. Geometry-based aromaticity indices, like other indices resulting from criteria (i)−(iv), are mostly used for three purposes: (a) estimation of the aromatic character of a given molecule in comparison to other molecules,
R opt = (R C − C + 2R CC)/3 = 1.397 Å
which is in good agreement with the experimental value obtained for benzene: 1.398 Å (X-ray measurement at 10 K).56 The formula for HOMA is as follows: α HOMA = 1 − n
∑ (R opt − R i)2 i
(3)
3.3. The Sum of the Bond Orders Differences as Aromaticity Index ∑ΔN (1974)
The next attempt of a quantitative description of aromaticity was made by Fringuelli et al.57 These authors proposed to use the bond orders instead of the bond lengths, because the bond between different atoms can have the same length, but may differ by bond order. The bond orders N were calculated by applying the Gordy equation:58 N = a ·R−2 − b
3.1. The Julg concept Aj (1967)
(4)
where a and b denote constants (see Table 1). The values obtained by Fringuelli et al.57 slightly differ from those of Gordy because more recently determined bond lengths (R) were used. The sum of the bond order differences in a ring, ∑ΔN, was taken as a measure of its aromaticity. The smaller ΣΔN value indicates more aromatic system (for benzene ∑ΔN = 0). The authors established the following order of decreasing aromaticity: benzene > thiophene > selenophene > tellurophene > furan. However, this index does not allow a comparison of the aromaticity of heterocycles differing by size.
The first quantitative approach to the definition of aromaticity based upon geometry was used by Julg et al.7 who constructed a normalized function of the CC-bond lengths variance in a perimeter of carbocyclic π-electron systems: 2 ⎛ Ri ⎞ ∑ ⎜1 − ⎟ R av ⎠ i=1 ⎝
n
where α = 98.89 is an empirical normalization constant, chosen to give HOMA = 0 for a model nonaromatic system and HOMA = 1 for a system where all bonds are equal to Ropt = 1.397 Å, n is the number of CC bonds taken into summation, Ropt is the optimal aromatic bond length, and Ri are the experimental or computed bond lengths.
(b) testing new numerical characteristics of aromaticity by statistical analyses of similarity to typical aromaticity indices, (c) studies of the changes in aromaticity due to intra- or intermolecular perturbation (H-bonding, substituent effects, solvent effects, etc.). References to all of these applications will be provided when reviewing all indices of aromaticity in the subsequent text.
225 Aj = 1 − n
(2)
n
(1)
where n is the number of peripheral bonds of length Ri, and Rav is the mean value of all bond lengths (in the original paper, the bond length was denoted by d). The constant 225, which results from the condition of normalization, was chosen such that Aj assumes the value zero in the case of Kekulé’s benzene structure. For any system with all bonds of the same length, Aj = 1. The approach was extended to also include hetero-πelectron systems in 1971.8 In some cases, Aj was applied for hetero-π-electron systems taking into account only CC bonds.52
3.4. Harmonic Oscillator Stabilization Energy, HOSE (1981)
It is well-known from elementary spectroscopy54 that the squared change of the geometric parameter of the vibration, (ΔP)2, multiplied by the appropriate force constant, k, gives the energy of deformation associated with this vibration, E = k· (ΔP)2. This is a foundation for the concept of harmonic oscillator stabilization energy (HOSE),61−63 which is the 6385
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Table 1. Values of Constants a and b Used in the Calculation of Bond Orders According to Equation 4 type of bond
a
b
ref
BB BC BN
9.12 8.05 7.15 7.72 6.75 6.80 11.79 7.366 6.48 6.941 13.54 5.75 5.315 11.9 11.250 15.24 21.41 5.28 6.132 4.98 4.634 10.53 13.31 4.73 17.05 19.30
1.94 2.11 2.10 2.16 2.14 1.71 4.48 2.115 2.00 2.205 3.02 1.85 1.616 2.59 2.400 3.09 3.81 1.41 1.916 1.45 1.165 2.50 2.86 1.22 5.58 3.46
58 58 58 59 58 58 59 60 58 60 25 58 60 58 60 57 57 58 60 58 60 25 25 58 25 25
BO CC
CN CP CO CS CSe CTe NN NO NS NSe OO OS SS
formal single and double bonds in the ith canonical structure, respectively. As a result of deformation, the N1 bonds corresponding to single bonds in the ith canonical structure are lengthened, whereas the N2 bonds corresponding to double bonds in the canonical structure are shortened to the bond lengths Rs0 and Rd0, respectively. The force constants kr for the first-row elements in the periodic table, which concerns CC, CN, and CO bonds, are assumed to fulfill an empirical relation: k r = a + bR r
using constants a and b listed in Table 2. For longer bonds (e.g., CS), the force constants are obtained from the formula:66 log k r = 2.15 − 6.60 log R r
HOSEtot = ∑i Ci HOSEi
CC CNa COa CSb
Rs0/Å
Rd0/Å
a·105/(dyn cm−1)
b·1013/(dyn cm−2)
1.467 1.474 1.428 1.820
1.349 1.274 1.209 1.610
44.39 43.18 52.35
−26.02 −25.73 −32.88
Ci = (HOSEi)−1 /∑j (HOSEj)−1
3.5. Bird’s Aromaticity Indices I5 and I6 (1985)
The following formula for HOSE was proposed:61
Bird,25,70,71 using basically the same idea as Julg et al.,7 replaced the bond lengths, R, by the Gordy bond orders,58 eq 4. These modifications led to the following formulas for the coefficient of variation of the bond order and the aromaticity index in a heterocyclic ring:
HOSEi = −Edef N2
⎤
∑ (R r″ − R d0)2 kr ⎥ r=1
(9)
The summation in eqs 8 and 9 runs over all canonical structures taken into consideration. There are many applications of the HOSE concept; two of these showed advantages of this model. For alternant hydrocarbons, HOSEtot was found to be in a good correlation with the RE values obtained by Hess and Schaad67 (correlation coefficient −0.991). Application of this concept to the estimation of the canonical structure weights was also successful. Benzenoid hydrocarbons can be given here as an instructive example. The values of the Ci parameter (eq 9) agree with the weights determined by Randic.68 Recently, it has been shown that contributions of the canonical structures of 18 benzenoid hydrocarbons estimated by the use of the HOSE model are in perfect agreement (cc = 0.997) with the contributions obtained by the graph-topological approach.69
a Details of the choice of Rs0 and Rd0 in ref 63. bDetails of the choice of Rs0 and Rd0 and calculation kr in ref 66; see also eq 7.
⎡ N1 = 301.15⎢∑ (R r′ − R s0)2 k r + ⎢⎣ r = 1
(8)
(ii) The contribution Ci of the ith canonical structure in a description of the real molecule is inversely proportional to its destabilization energy, that is, the energy by which the ith canonical structure is less stable than the real molecule:
Table 2. Constants Used in the HOSE Model64 a
(7)
When the geometry of a π-electron molecule is known, it is possible to calculate the value of HOSE (i.e., the energy by which the real molecule is more stable than the ith canonical form) by using the data listed in Table 2 and applying eqs 6 and 7. Usually, several canonical structures are possible for a given molecule; each of them may have a different HOSE value. From the chemical intuition and ideas of valence bond theory, the following two assumptions were made:63,64 (i) All of the most important canonical structures have to be taken into consideration in the estimation of the HOSEtot for a given molecule, here:
method that allows for estimation of the resonance energy (RE) and the contributions of particular canonical structures in the description of a π-electron system. This method is based on the following assumptions:64 “Deformation of bond lengths (due to inter- or intramolecular interactions in π-electron systems) from some values taken as references may be approximately described in terms of harmonic potentials... Other deformations (e.g., angular) are of less importance and are not taken into consideration in this model.” The reference values for CC bond were taken as lengths of single and double bonds in buta-1,3-diene.65 Appropriate data are shown in Table 2.
type of bond
(6)
⎥⎦
(5)
V=
where Rr′ and Rr″ denote the lengths of π bonds in the real molecule, whereas N1 and N2 are the numbers of corresponding 6386
100 Nav
1 n
n
∑ (Ni − Nav)2 i=1
(10)
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(11)
In eq 10, Ni is the individual bond order, Nav denotes the mean bond order, and n is the number of bonds. In the case of a fully delocalized heterocyclic ring, V = 0, whereas for a localized Kekulé structure with alternating single and double bonds, this value depends on the type of heterocyclic ring under consideration. Thus, in eq 11, one has the constant Vk = 33.3 for a six-membered heterocyclic ring, whereas for a fivemembered ring Vk = 35. Because the value of the aromaticity index I depends on ring size, a subscript was added. Thus, I5, I6, I5,6, and I5,5 denote the Bird index for five-membered,25,72 sixmembered,70,72 five- and six-membered, or five- and fivemembered rings fused together,73 respectively.
Figure 2. The H-bonded quasi-aromatic ring with Rn bonds used in the definition of Q parameter; arrows denote direction of bond length changes.
in RAHB formation was pointed out already in the first paper on RAHB.75 It was demonstrated there that the strength of RAHB is directly linked with the structural properties of the quasi-aromatic ring. To measure the relation between the Hbond strength and the resonance effect acting along the CO and CC bonds, the parameter Q was introduced as follows:
3.6. Pozharskii Criterion of Aromaticity, APoz (1985), and Its Modifications (2001)
In 1985, Pozharskii74 proposed a criterion of aromaticity (APoz, denoted in original paper by ΔN̅ ), which is the average fluctuation of the bond orders in a given cycle: APoz = ΔN̅ =
∑ ΔN n
Q = q1 + q2
where q1 = R1−R4 and q2 = R2−R3, whereas R-values denote the distances between covalently bonded heavy atoms within the quasi-aromatic ring (in the original paper, the bond length was denoted by d). See Figure 2 for graphics with the original notation of bonds in the quasi-aromatic ring under consideration. It was demonstrated that the O···O distance in the H-bridge and the Q parameter are interrelated and that the shortest O··· O distances, thus the strongest H-bonds, are observed for Q close to 0 (see Figure 3 for a graphical presentation of the relation between Q and, e.g., dO···O distance).
(12)
∑ ΔN = ∑ |Ni − Nj| i,j
(13)
where N denotes the bond order and n the number of bonds. For benzene, APoz = 0, whereas for cyclopentadiene, APoz = 0.49. These values can be expressed as a percentage, where the scale starts from cyclopentadiene (as 0%) and ends with benzene (as 100%). In 2001, Kotelevskii and Prezhdo60 proposed a modification of the Pozharskii index by dividing APoz by the mean bond order: APoz,KP = 100APoz (Nav)−1%
(15)
(14)
Moreover, these authors paid more attention to the selection of an appropriate reference data (source of the structural data) and derived the a and b values of the Gordy equation (eq 4); see Table 1. This index allows using both the experimental and the theoretical bond lengths. It can also be applied for the estimation of the aromaticity of individual rings in polycyclic systems. However, the Pozharskii structural index has a major disadvantage: it is not applicable to planar antiaromatic systems or for the evaluation of aromaticity of highly symmetric systems, such as 1,3,5-triazines, where a significant equalization of bonds takes place in a cyclic conjugated system.
Figure 3. A graphical scheme of the RAHB model proposed by Gilli et al.75 Reprinted with permission from ref 75. Copyright 1989 American Chemical Society.
The Q parameter equals zero for fully delocalized systems and ±0.320 for a fully localized system. Alternatively, Q can be expressed as a coupling parameter:75,76 λ = (1 − |Q | /Q 0)
3.7. Gilli’s Characteristics of π-Electron Delocalization in H-Bonded quasi-Aromatic Rings (1989)
(16)
where Q0 corresponds to the value obtained for a fully localized system, that is, 0.320. In such a case, λ adopts values in the range between 0 and 1 (0 for fully localized and 1 for fully delocalized quasi-aromatic ring). It is also worth mentioning that the bond lengths Rn in quasiaromatic rings are in direct relationship between themselves and that a linear relationship between q1 and q2 parameters was found for a set of data obtained through a search in CSD.77 The similarity between Q and some aromaticity indices introduced in section 3 is obvious; thus, one should expect that the resonance in a RAHB-bonded quasi-aromatic ring may be
If in a six-membered aromatic ring three subsequent sp2 carbons are replaced by a X−H···Y unit (where X, Y are N, O or other proton-donor−acceptor centers), then a system with intramolecular H-bond is formed, which can be classified as a quasi-aromatic ring (see Figure 2). In line with Gilli’s concept of resonance-assisted hydrogen bonding (RAHB),75 the resonance in this type of quasiaromatic ring may be understood as the π-electron delocalization in this part of the system, which is built up of heavy atoms containing π-electrons. The importance of the structural aspect 6387
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Later, it was shown that the Δrp parameter correlates well with HOMA,78 Gilli’s λ parameter,91 and also with several energetic and electron-density-based measures of RAHB strength.89
quantified with the use of aromaticity indices. Of course, there are some limitations, resulting from definitions of individual indices. For instance, in the case of HOMA, there are no reference data for bonds with H atoms, which is natural, because HOMA was originally designed for aromatic cyclic systems built from non-H atoms. However, HOMA values can be estimated for the sequence of OCCCO bonds, which, in fact, are π-electron conjugated. It appears that HOMA and Q are well correlated. This was shown for malonaldehyde and its Li+- and BeH+-bonded analogues.78,79 Since the publication of the first paper on RAHB in 1989, this concept has been systematically developed on the basis of both experimental and theoretical methods.80−87 Recently, the topic of RAHB was summarized in a book by Gilli and Gilli, which was entirely devoted to the theory of hydrogen bonding.88 3.7.1. Grabowski’s Modification of Gilli’s Parameter. Another structural parameter designed as a measure of πelectron resonance (delocalization) in H-bonded quasiaromatic rings was introduced by Grabowski in 2003.89 According to that author, the influence of H-bonding on the structure of a quasi-aromatic ring can be concluded from the comparison between the closed and open conformers of the system, for instance, the enol of malonaldehyde (see Figure 4).90
3.8. Extensions and Modifications of the Harmonic Oscillator Model of Aromaticity, HOMA (1993)
The modification of HOMA24 presented in 1993 relies on two important changes: (i) the model is extended to hetero-πelectron systems with the following bonds, CN, CO, CP, CS, NN, NO, and (ii) the calculation of Ropt is based on the CC bond lengths in buta-1,3-diene (taken from the electron diffraction data), 1.467 and 1.349 Å for single and double bonds, respectively.65 In the earlier versions of HOMA, CC bond lengths in ethane and ethene were taken for the calculations, yielding Ropt = 1.397 Å. These modifications resulted in a change in the normalization constant, which for this optimal bond length is α = 257.7. The motivation leading to the introduction of this change was a consequence of the fact that the reference systems for the estimation of RE were acyclic olefins45,92,93 (for a recent review, see Cyranski17). Therefore, taking into account the reference bond lengths, Rs and Rd for single and double bonds, respectively, the HOMA parameters were obtained as follows: R opt = (R s + wR d)/(1 + w)
(20)
α = 2[(R s + R opt)2 + (R d + R opt)2 ]−1
(21)
where w denotes the ratio of force constants for the double and single bonds, and, as previously, it was assumed that w = 2.54,55 HOMA can be expressed as follows: Figure 4. Open and closed forms of malonaldehyde system.
HOMA = 1 −
The direct comparison of total energies of the open and the closed forms of the system depicted in Figure 4 may provide information on stabilizing energy resulting from the H-bond formation (although it is not the H-bond energy itself). Following this idea, structural changes associated with the transformation of the open form to the closed one may also provide information on the consequences of the H-bond formation on the quasi-aromatic ring structure. Thus, q1 and q2 values from Gilli’s Q parameter definition can be obtained for both closed and open forms of the system presented in Figure 4. Therefore, for the open conformation, we have q1o = R3o − R 2 o
and
q1o = R 4 o − R1o
and
q1c = R 4 c − R1c
(17)
(18)
where R values correspond to covalent bond lengths in OCCCO sequence (in the original paper, the bond length was denoted by d and the bond length differences as Δd; the above notation is consistent with Figure 2). On that basis, the following parameter can be defined as a measure of resonance in a given quasi-aromatic ring: Δrp = 1/2[(q1o − q1c)/q1o + (q2 o − q2 c)/q2 o]
n
n
∑ (R opt,j − R j ,i)2 i
(22)
where subscript j denotes the type of the bond: CC, CN, CO, CP, CS, NN, NO, etc. This idea, however, could not be applied as a general rule, and parameters of HOMA (shown in Table 3) originate from the two kinds of the above-mentioned models, or even from a mixture of them. For instance, Ropt could be obtained from single and double bonds of the same molecule with some πelectron delocalization; for example, in the case with CC bonds taken from buta-1,3-diene or CO bonds taken from the monomer of formic acid, large values of the normalization constant α are observed (257.7 and 157.38 for CC and CO bonds, respectively). If the reference bond lengths are taken from two different molecules, then lower values of the normalization constants are obtained. Taking the data for CC from ethane and ethene, for CS from S(CH3)2 and H2CS, and for CN from H2N−CH3 and HNCH2, yields the following values of α: 98.89, 94.09, and 93.52, respectively. This inconsistency of the HOMA model and the differences in the α values must always be taken into consideration when aromaticity is quantified using this approach. Differences between various definitions of Ropt and consequently of the α normalization constant will be thoroughly discussed in subsequent parts of this Review. Andrzejak et al.94 pointed out that the theoretical method and the basis set used for estimation of HOMA constants should be the same as that used for geometry optimization of a given system. Their analysis was carried out for 25 systems and various advanced quantum-chemical models.
and similarly for the closed form: q1c = R3c − R 2 c
αj
(19)
Δrp equals 0 if there is no difference between the closed and the open conformations, in other words, if the formation of the intramolecular H-bond does not cause any further π-electron delocalization. 6388
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Table 3. Reference Bond Lengths Rs and Rd, and Appropriate Ropt and α Values Used in the HOMA and Its Components Calculation type of bond (ref system used) a
BB BBwa BCexpb BCtheob BCtheo/wb BNc CCd CNe COf CPg CSh CSei NNj NOk
Rs/Å
Rd/Å
Ropt/Å
α
c
ref
1.6474 1.6474 1.5472 1.5542 1.5542 1.564 1.467 1.465 1.367 1.814 1.807 1.959 1.420 1.415
1.5260 1.5260 1.3616 1.3796 1.3766 1.363 1.349 1.269 1.217 1.640 1.611 1.7591 1.254 1.164
1.5665 1.5693 1.4235 1.4378 1.4386 1.402 1.388 1.334 1.265 1.698 1.677 1.8217 1.309 1.248
244.147 250.544 104.507 118.009 118.618 72.03 257.7 93.52 157.38 118.91 94.09 84.9144 130.33 57.21
0.1752 0.1750 0.2678 0.2520 0.2520
95 95 96 96 96 59 24 24 24 24 24 97 24 24
0.1702l 0.2828l 0.2164l 0.2510l 0.2828l 0.2970 0.2395l 0.3621l
3.8.3. Calculation of the HOMA Model Parameters for the BC Bond. More recently,96 HOMA parameters enabling application of this model to π-electron systems containing BC bonds have been introduced. The basic parameters of HOMA (i.e., Ropt, α) were estimated in three ways: (i) from experimental BC single and double bonds, (ii) from optimized geometries of the model molecules containing this bond, and (iii) the same as (ii) but assuming the ratio of force constants, w, of the double to single bond, not as 2:1 (as in the original HOMA approach23), but using the ratio w = 1.9615, which resulted from some theoretical calculations. Additionally, to make possible the separation of HOMA into EN and GEO terms,98 the c parameter was provided. Differences between the final results of HOMA calculated for 10 model molecules containing BC bonds are usually much smaller than 5%. The values obtained for HOMA parameters for the three procedures mentioned above are presented in Table 3. 3.8.4. Calculation of the HOMA Model Parameters for the BB Bond (2012). The same group95 also introduced HOMA parameters for BB bonds. They were obtained in two ways: (i) within the approximation according to which w = 2 and (ii) from the estimated force constants ratio. The new parameters for BB bonds and those obtained earlier for BC bonds96 could be applied to 19 π-electron systems, indicating an important effect of the replacement of CC bonds by BB ones, particularly in cases when the BB bond was not located in the perimeter of the molecule.
a
H2B−BH2 and HBBH. bH3C−BH2 and H2CBH. cH3B−NH3 and (isoPr)2NBC(SiMe3)2, H3B−NH3 and H2BNH2. dButa1,3-diene. eH2N−CH3 and HNCH2. fHCOOH monomer. gH2C P−CH3 . h S(CH 3 ) 2 and H 2 CS. i H3 C−SeH and H 2 CSe. j (CH3)2CN−N(CH3)2 and H3C−NN−CH3. kCH3−O−NO. l Taken from ref 98.
3.8.1. Modification of HOMA for π-Electron Systems with BN Bonds. This modification relies on the method used for the optimal bond length calculation. For example, w = 2, used in eq 20, can be considered a rather crude approximation of the ratio of the force constants estimated for single and double bonds. In the case of BN bonds, this simplified approach is even less appropriate due to the polarity of these bonds. Therefore, a more sophisticated method had to be applied.59 Ab initio calculations for ethane, ethene, BH3NH3, and BH2NH2 were used to obtain force constants for the stretching motion of C−C, CC, B−N, and BN bonds. Calculations were based upon the single point energies for five geometries: stretched by 0.01 and 0.005 Å, the optimal geometry, and compressed by 0.005 and 0.01 Å, for which the curvature (i.e., force constants) was calculated from the parabolic approximation of the Morse curve. The obtained ratio of w for BN bonds amounts to 4.2. The results obtained for BN bond are Rs = 1.564 Å, Rd = 1.363 Å, leading to Ropt = 1.402 Å and α = 72.03. Application of these HOMA parameters gave for 15 systems with BN bonds acceptable agreement with the data obtained by means of the Bird I6 index.25,70 3.8.2. Parameters of HOMA for π-Electron Systems with CSe Bonds. Zborowski and Proniewicz97 obtained the HOMA index parameters enabling the description of aromaticity in systems with CSe bonds. Reference lengths of single and double bonds were taken from the experimental geometry of CH3SeH99 and CH2Se,100 respectively. Following the procedure of Madura et al.,59 the value of w = 1.79 was obtained, which is quite close to 2.0. In the case of CC and CO bonds, the corresponding values were 2.22 and 2.60, respectively. For this reason, the carbon−selenium bond was included in the group of bonds for which the approximation w = 2 is valid. The obtained values of the HOMA parameters are given in Table 3.
3.9. Heat of Formation from Atoms Estimated from Molecular Geometry, HtFfA (1995)
Pauling established a well-known formula101 relating the bond length R(N) to its bond order N: R(N ) − R(1) = −c ln(N )
(23)
where c is an empirical constant and R(1) is a standard “single bond” length (in the original paper, a term “bond number” was used and denoted by n). This concept was successfully applied in structural chemistry.102,103 Combining eq 23 with another empirical rule: E(N ) = E(1)N p
(24)
relating bond energy E(N) to the bond order N with an empirical constant p,104 the result is E(N ) = E(1) exp{α[R(1) − R(N )]}
(25)
where E(1) and E(N) are bond energies for bond orders 1 and N, respectively, and α = p/c. Assuming for CC bonds, R(1) = 1.533 Å,105 R(2) = 1.337 Å,106 E(1) = 94.66 kcal/mol,107 E(2) = 132.91 kcal/mol,107 and taking into consideration an appropriate assumption [E(C−H) = 100.53 kcal/mol]107 and corrections29 (to fit calorimetric data), the final formula for the heat of formation from atoms (HtFfA) can be expressed as follows:29 HtFfA = −100.53N − 87.99 ∑i = 1n exp{2.255 (1.533 − R i)}
(26)
Comparison of the data calculated from eq 26 with thermochemical data108 for nine benzenoid hydrocarbons showed that the HtFfA values were obtained with an error less than 1%. 6389
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are (i) the normalization constant, and (ii) the reference systems. The normalization constant for HOMED is the same as for HOMA, eq 21, in the case of systems with an even number of bonds. For systems with an odd number of bonds, the normalization constant can be determined using the formulas:
Exner and Schleyer, in a critical analysis of theoretical bond energies,109 demonstrated that the dependence of bond energies on bond lengths is exponential, in line with the model introduced earlier.29 3.10. Separation of HOMA into the Two Components EN and GEO (1996)
Formula 3 can be analytically converted into:110 HOMA = 1 −
1 n
α=
∑ α(R opt − R i)2 = 1 − EN − GEO
for systems with i+1 single bonds and i double bonds, and
where EN and GEO are defined as 1 n
(33)
i
(27)
GEO =
2i + 1 (i + 1)(R opt − R s)2 + i(R opt − R d)2
∑ α(R av − R i)2 i
α= (28)
(29)
Component GEO represents a decrease of aromaticity due to an increase of the bond length alternation, whereas EN reflects an increase of the average bond length in a given structure. Note that the increase of EN (i.e., elongation of mean bond length) denotes a decrease of aromaticity, because the value of HOMA diminishes. The separation carried out in this way works only for carbocyclic systems. To apply the above separation of HOMA for systems with heteroatoms,98 one must use the Pauling concept of the bond order,101 eq 23. The value of constant c in eq 23 can be estimated taking into account bond lengths for typical single, Rs, and double, Rd, bonds with bond order N = 1 and 2, respectively:
c = [(R s − R d)/ln 2]
(30)
Table 4. Reference Bond Lengths Applied in HOMED Procedure113a
Therefore, for any bond, its bond order can be calculated using eq 23 and the appropriate parameters (Rs and c): N = exp[(R s − RN )/c]
(34)
for systems that consist of i single and i+1 double bonds; Rs and Rd are the single and double bond lengths in the reference systems, respectively. As reference systems for single bonds, the simplest saturated compounds were chosen. Thus, for single CC, CN, and CO bonds, the reference systems are ethane, methylamine, and methanol, respectively. The same procedure was applied to unsaturated molecules to determine the reference double bond lengths. The reference systems for the double CC, CN, and CO bond lengths are ethene, methylimine, and formaldehyde, respectively. In the case of the optimal bond lengths, benzene, 1,3,5-triazine, and protonated carbonic acid were chosen as the systems with “complete” delocalization. Raczynska et al.113 emphasized that the reference systems should be optimized at the same level of theory as the systems under consideration, which assures the cancellation of computational errors. Reference bond lengths and normalization constants used in the HOMED procedure at the B3LYP/6-311+G(d,p) level of theory are reported in Tables 4 and 5, respectively.
and EN = α(R opt − R av)2
i(R opt
2i + 1 − R s) + (i + 1)(R opt − R d)2 2
(31)
The optimal bond order, Nopt, can be evaluated using eq 31 for RN = Ropt. It was found that Nopt has practically the same value for all bonds taken into consideration (in the range between 1.584 and 1.602); therefore, Nopt = 1.590 was proposed for all bonds. Finally, replacing bond lengths by the respective bond orders in eqs 27, 28, and 29, the formulas enabling the separation of HOMA into its energetic and geometric terms for heterosystems were introduced.98 The values of constant c for particular bonds are reported in Table 3.
a
type of bond
Rs/Å
Rd/Å
Ropt/Å
CC CN CO
1.5300 1.4658 1.4238
1.3288 1.2670 1.2017
1.3943 1.3342 1.2811
Calculated at B3LYP/6-311+G(d,p) level of theory.
HOMED can be used for both acyclic and cyclic π-electron systems.113 In the former case, where only σ−π delocalization is possible, HOMED values lie in the range from 0.0 to 0.4, which proves weak delocalization. For heteroallyl systems, where n−π conjugation occurs, HOMED values are between 0.4 and 0.8, suggesting moderate delocalization in these systems. Moreover, HOMED values obtained at different levels of theory are comparable even if the method/basis set is changed leading to different α values and bond lengths.113
3.11. Harmonic Oscillator Model of Electron Delocalization, HOMED (2007)
HOMED111−113 is a measure of all resonance effects (any type of π-electron delocalization). It is based on the HOMA concept and is defined by the following expression: α HOMED = 1 − ∑ (R opt − R i)2 (32) n
3.12. New HOMA Index Parametrization for π-Electron Heterocycles: The HOMHED Index (2012)
Very recently, the idea of using experimental bond lengths for evaluating HOMA index parameters resurfaced and was applied to π-electron systems with CC, CN, CO, CS, NN, NO, and NS bonds.114 The experimental bond lengths used for the estimation of new HOMA parameters (Rs, Rd, Ropt, and α) were taken from the X-ray and neutron diffraction databases115
where α is a normalization constant, n is the number of bonds forming a system, Ropt is the optimal bond length, and Ri is the ith bond length. The HOMED formula, eq 32, is thus the same as for HOMA, eq 3. The two main differences between HOMA and HOMED 6390
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Table 5. Normalization Constants Values for Even and Odd Numbers of Bonds in the Rings Obtained on the Basis of the Bond Lengths from Table 4a α2i
a
α3
α5
α7
type of bond
is+id
2s+1d
1s+2d
3s+2d
2s+3d
4s+3d
3s+4d
CC CN CO
88.09 91.60 75.00
72.96 73.90 63.79
111.13 113.85 90.83
78.34 113.85 67.84
100.76 103.77 83.84
80.90 84.52 69.74
96.68 99.97 81.10
Subscripts s and d denote single and double bonds, respectively.113
as mean values for a given type of bond. The resulting parameters are shown in Table 6.
shown in Scheme 1. Allylic conjugation (a) is more favorable than benzylic conjugation (b), which was documented by
Table 6. Parameters for HOMHED Index114
Scheme 1. Possible Protonation Sites in Naphthalene
type of bond
Rs/Å
Rd/Å
Ropt/Å
α
CC CN CO CS NN NO NS
1.530 1.484 1.426 1.819 1.454 1.463 1.765
1.316 1.271 1.210 1.559 1.240 1.218 1.541
1.387 1.339 1.282 1.672 1.311 1.300 1.616
78.6 87.4 77.2 74.4 78.6 60.0 71.7
numerical values of σr+; by analogy to the Hammett substituent constants, 121 these quantities were named as position constants.122 Local and global aromaticity can be considered only for polycyclic π-electron systems. The former characterizes the aromaticity of a particular ring of the system, whereas global aromaticity refers to the system as a whole. In a somewhat limited way, the problem of global and local aromaticity has been discussed for a long time. Dependence of HOMA for the whole molecules of linear and kinked acenes on the ASE (based on the Cohen−Benson group additivity values123) gave good correlation (cc = 0.989) for 11 molecules. Moreover, for kinked hydrocarbons, a good relationship was obtained for local aromaticity, that is, between NICS and HOMA (cc = 0.994) for 14 rings.124 Schleyer et al.125 concluded, on the basis of the analyses made for seven linear acenes and applying NICS, HOMA, and energetic parameters, that RE per π-electron is nearly constant. The problem has also been discussed more recently leading to the conclusion that kinked acenes are more stable than straight ones.126,127 A qualitative picture of the aromatic character of a particular ring in a molecule of polycyclic benzenoid hydrocarbon is offered by so-called Clar rules. These rules classify rings according to their π-electron structure into aromatic sextets, empty rings, migrating rings, and those with localized double bonds.128,129 The aromaticity indices may successfully serve for a quantitative description of these four classes of rings. Application of HOMA allows one to clearly distinguish Clar’s sextets (HOMA very high, close to 1.00) and two kinds of rings: empty ones and those with a localized double bond, which have low values of HOMA.130 This can also be done, in a potentially clearer way, using EN and GEO terms.110 Vijayalakshmi and Suresh131 applied molecular electrostatic potential132 to describe Clar’s classification of benzenoid hydrocarbons. The Clar rules in terms of magnetic properties were thoroughly discussed in the review by Gomes and Mallion.133 Recently, correlations between topological ring currents,134 π-electron partitions, and six-center delocalization indices in benzenoid hydrocarbons in relation to the Clar rules have been shown.135 The concept of Clar’s sextet was also applied to some two- and three-dimensional aromatic
The HOMHED parameters were compared to those for HOMED113 and HOMA (1993),24 and applied for 16 molecular systems with the bonds listed in Table 6. A significant difference between HOMA (1993) and HOMHED was observed for systems with CO and CN bonds. HOMHED values for oxazoles and pyrimidine were 0.654 and 0.995,114 respectively. The difference in aromaticity between these compounds, as judged from the HOMHED parameters, seems lower than expected. This is due to the difference in the model bonds applied for estimation of Ropt and α in HOMA (1993) and in HOMHED. For HOMA (1993), the reference systems for CC, CO, and CN bonds are buta-1,3-diene, monomers of HCOOH, and amidine, respectively, thus systems with resonance effect. In the case of Frizzo and Martins’ approach,114 similarly to the case of HOMED,113 single bonds (Rs) contain atoms with sp3 hybridization and hence are dramatically longer, leading to a much smaller α value.
4. APPLICATIONS OF THE GEOMETRY-BASED AROMATICITY INDICES 4.1. Global and Local Aromaticity of π-Electron Hydrocarbons
At the very beginning, aromaticity was strongly related to reactivity: aromatic compounds not only were considered as less reactive, but also as undergoing substitution rather than addition reactions. However, any chemical reaction usually takes place regioselectively, that is, at a particular position of the molecule. In polycyclic molecular systems, reactive rings could be identified, for example, those containing positions 9,10 in anthracene or phenenthrene. The two other rings in these compounds are much less reactive. These observations were experimentally documented by estimation of the basicity of particular positions in benzenoid hydrocarbons.116−119 Protonation results in the formation of the positively charged moieties, differing in a kind of delocalization. Hence, its basicity depends on the position of the protonated site and can be used as a quantitative measure of the ability of the π-electron compensation in the remaining part of the molecule,120 as 6391
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Table 7. Geometry-Based Aromaticity Indices Applied to Five-Membered Heterocyclesa
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Table 7. continued
6393
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Table 7. continued
a
Hydrogen atoms connected to the carbon atoms are omitted for clarity. *For MW geometry. **For MP2 geometry.
systems.136 Topological methods combined with the application of graph theory137,138 allow mathematically based grounds of the Clar rules to be found.139 Among all aromaticity characteristics, ASE and RE describe only the global properties of the molecules in question. Energetic characteristics of single rings are possible, but the models that enable this are directly based on molecular geometry.29,140 Estimations of bond energy, ASE, and strain in IPR fullerenes based on geometrical data141 gave results for C60 that were comparable with the recent computation data by Schleyer and co-workers.142 Magnetic characteristics describe either whole molecule properties, as, for example, magnetic exaltation or magnetic anisotropy (for review, see ref 20), or local properties, such as Schleyer’s NICSs (for review, see ref 4). Recently, an attempt was made to relate the sum of NICSvalues of all individual rings in π-electron hydrocarbons to their magnetic susceptibility exaltation.21 Some of the aromaticity indices based on molecular geometry are the only ones in which the frame of the same model may be used for the description of both the aromatic character of the whole molecule as well as any of its fragments. HOMA was the first numerical measure used for aromaticity estimation in pentagons and hexagons building the fullerenes C60 and C70.143 On the basis of experimental geometry,144 the HOMA values for pentagons and hexagons are estimated to be 0.10 and 0.55, respectively. For the whole molecule, HOMA = 0.38, which is in line with a small ring current measured experimentally for the whole molecule.145 Gas-phase diffraction data provide only slightly different geometry,146 which changes insignificantly the HOMA parameters in the direction of lower values (pentagons, hexagons, and the whole molecule have HOMA values equal to 0.35, −0.26, and 0.14, respectively). For the geometry of Cs salt of C60,147 the values of HOMA for pentagons, hexagons, and the whole molecule are 0.25, 0.13, or 0.10 and 0.17, respectively. Negative charging of C60 equalizes the aromaticity of the particular components and decreases the aromaticity of the whole molecule. In the case of the C70 complex with sulfur (C70S8),148 there are three symmetrically independent hexagons and two pentagons. The HOMA for the whole molecule is 0.39; for hexagons this is 0.40, 0.54, or 0.76, whereas for pentagons it is 0.23 or −0.09. The geometry-based method of energy estimation140 allowed the energy of C60 formation to be obtained with good agreement with experimental149 and various theoretical determinations.150,151 Additive local aromaticity (ALA) indices (defined as the sum of local aromaticities of all rings) were calculated for a large number of of fullerenes and their anionic derivatives.152 It was shown that the global geometry-based aromaticity index ALA
depended on the number of pentalenene units in the systems studied. Aromaticity patterns in graphene nanoribbons were investigated by the mean bond length (MBL) in the ring as a geometry-based local aromaticity descriptor.153,154 Cyclooctatetraene (COT) is an interesting π-electron crownshaped system, which is considered nonaromatic.42,155 The question posed is as follows: Is COT antiaromatic when it is planarized? Klärner showed many examples156 where some derivatives of COT due to substitution are nearly planar, but it was still found to show a strongly localized structure,157 as was previously reported for, for example, 9,10-diphenylbicyclo[6.2.1]decapentaene.158 Theoretical planarization by pairwise bending CCH angles but maintaining D2d symmetry led to a π-electron structure with a partial equalization of CC bonds (HOMA went up to ca. 0.5), but magnetic characteristics by NICS or magnetic susceptibility did not change in line with HOMA.159 Very recently, similar conclusions were drawn for the inner eight-membered ring in bicalicene.160 In section 4.5, this problem is also discussed for metal complexes with COT. Even at room temperature, planar molecules like benzene or cyclic heteroaromatic systems exist in various forms of deformation due to oscillation. Recently, analyses were undertaken demonstrating how much thermal ring flexibilities affect the aromaticity of benzene,161 nucleic acid bases, and other heteroaromatic compounds.162 In both studies, not only were many geometry-based aromaticity indices used, but also some magnetism-based parameters. Substantial support for the resolution of this problem comes also from Car−Parinello molecular dynamics study of the dynamic nonplanarity of benzene.163 The problem presented above is of great importance, because the π-electron molecules may significantly change their π-electron structure due to thermal flexibility, and hence their reactivity may be altered. This is evidently dependent on the temperature. 4.2. Aromatic Character of Hetero-π-electron Systems
Heterocyclic compounds play a significant role in biochemistry, life processes, and modern materials chemistry, including that organic electronics−heterocycles are essential constituents of living cells (DNA and RNA), coenzymes, vitamins, pharmaceuticals, and low and high molecular weight organic semiconductors.164−166 In addition to their importance in the applied sciences, they are also very fascinating subjects of basic research because of their largely diversified chemical, physical, and biological properties. One of the most important characteristics of heterocycles is their aromaticity; its quantitative assessment has been reviewed twice in Chemical Reviews in 200132 and 2004,167 and more recently in book chapters.5,168 In particular, collections of NICS’s values for more than 350 hetero-π-electron systems can be found in ref 4, 6394
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Table 8. Geometry-Based Aromaticity Indices Applied to Six-Membered Heterocyclesa
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Table 8. continued
Hydrogen atoms connected to the carbon atoms are omitted for clarity. *Experimentally not observed; investigated quantum chemically. **Considered as planar systems.
a
phosphole (aromatic systems), was investigated by Cyranski et al.;33 see Table 7. Energetic, magnetic, and geometry-based criteria were used for this purpose. Taking into consideration all of the studied systems, statistically significant correlations among the various aromaticity indices were found; the indices used allow for a rough division of conjugated cyclic compounds into aromatic, nonaromatic, and antiaromatic groups. However, within any one of these groups, the indices are not correlated. This is summarized by the following statement: “In practical applications energetic, geometric and magnetic descriptors of aromaticity (even if optimally chosen) do not speak with the same voice.”33 For a wide range of structural data, both experimental (MW, X-ray) and theoretical, Kotelevskii and Prezdho60 obtained Bird’s (I5) and Pozharskii’s (APoz and APozKP) indices; in Table 7 are presented their values for MW or MP2/6-31G* geometry. To eliminate discrepancies between conventional I5 and APoz, three improvements were proposed: (i) recalibration of the Gordy relationship, eq 4, from the experimental bond lengths (see Table 1); (ii) MW geometry of cyclopentadiene as a unified reference structure; and (iii) normalization of APoz by the mean bond order, APozKP. Several regularities in the aromaticity of azoles as a function of chemical structure and environment were specified using the refined indices: (i) the heterocycles with oxygen are less aromatic that their N−R analogues; (ii) values of aromaticity indices increase with the number of α aza substitutions, whereas it decreases for β aza derivatives; and (iii) if both α and β aza substitutions are present, the effect of the latter (β) substitution dominates in oxazole series. Protonation may also have an influence on the ring πelectron structure. Imidazole (3-azapyrrole) anion is more aromatic (HOMA = 0.92, APoz = 68.76) than its neutral (see
and critical comparisons of various aromaticity indices are presented in ref 17. Geometry-based aromaticity indices of five- and sixmembered heterocycles (published since 2000) are shown in Tables 7 and 8. As can be seen from these data, the HOMA index was most often used. Therefore, this index can be considered a suitable tool for comparing the aromaticity of various heterocycles. However, it should be noted that the newest indices such as HOMED111−113 and HOMHED,114 in addition to π−π interactions that are inherently associated with aromaticity, take into account other types of π-electron delocalization like n−π, for example. This is clearly visible for five-membered systems, where mixed n−π and π−π conjugations are possible. Such a mixture leads to nonequivalent resonance structures with or without charge separation.113 For these systems, the HOMED index indicates a significantly higher aromaticity as compared to HOMA (see Table 7). For six-membered rings, where π−π conjugation leads to equivalent resonance structures without charge separation, HOMED values indicate their aromatic character in line with HOMA (Table 8). However, in the case of pyranyl cation and its Nderivatives, where the positive charge can be placed on different atoms and the resonance structures are not equivalent, HOMED index follows the resonance effects and classifies such systems as less aromatic than equivalents that are not charged.113 For five-membered monoheterocycles, the order of decreasing HOMA agrees with that reported by Fringuelli et al.57 (thiophene > selenophene > tellurophene > furan, see section 3.3). In the latter case, the sum of the differences of the bond orders of the ring (∑ΔN) was used as a measure of aromaticity. Aromaticity of a set of 75 five-membered π-electron systems, aza and phospha derivatives of furan, thiophene, pyrrole, and 6396
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Table 7) and protonated forms (HOMA = 0.90, APoz = 53.46).169 The sulfur-containing heterocyclic compounds are more aromatic than their oxygen analogues33,114,170 (see Table 7). The studies of the effect of aza-substitution on azole aromaticity showed clear relationships between the HOMA index and the number of nitrogen atoms at positions 2,5 and 3,4 of the ring.174 The same rule works for NICS and ASE indices. Aza-derivatives of pyrrole, furan, and thiophene all gave similar relationships. All three indices suggest that pyrazole is more aromatic than imidazole. In the case of pyrrole and azapyrroles, the following relation was found:174
pyromeconic acid (3-hydroxy-4H-pyran-4-one), maltol (3hydroxy-2-methyl-4H-pyran-4-one), and ethylmaltol (3-hydroxy-2-ethyl-4H-pyran-4-one) were chosen as the objects of these investigations. It was found that the aromaticity of the pyran ring increases in the following order: anion < neutral molecule < cation, which is consistent with the previously obtained HOSE data.184 This trend is also preserved for their thio derivatives.185 No influence of aliphatic substituents on the pyran ring aromaticity was found.183 Intermolecular H-bonds can also be considered a factor influencing aromaticity. For example, the interactions between pyrylium cation and water molecules (computational studies) cause a slight decrease in the aromaticity of the ring, which is most visible in its complex with three water molecules.179 More pronounced reduction in aromaticity of this heterocycle was evidenced when the experimental (X-ray) structure of its substituted pyrylium salts was considered.186 Boron derivatives differ in their properties from other heterocycles. They are interesting compounds showing among other features bioactivity. For this reason, they have been the subject of significant research interest involving new synthetic routes and profound physicochemical characterization.187−189 The aromaticity of these compounds varies to a more significant extent than in their carbon and nitrogen counterparts.96 Aromaticity, expressed both by HOMA and by NICS, of naphthalene endo substituted (a carbon atom replaced by a heteroatom) with boron atoms was found to be strongly dependent on the position of these atoms in the ring; such dependence was not observed for nitrogenated naphthalene derivatives.96 In boron-containing compounds, the insertion of the boron− boron bond usually leads to a decrease of aromaticity in comparison to their parent hydrocarbons, as evidenced by the HOMA indices obtained.95 Nevertheless, borabenzene (derived from benzene by replacing one CH moiety by a B atom) is highly reactive and exists in a form of zwitterionic products with neutral Lewis bases (e.g., pyridine), where the boron has a negative formal charge.190,191 A stable form of borabenzene is the boratabenzene anion (C5H6B−). Its aromatic ring acts as a strong π-donating ligand, similar to the cyclopentadienide anion, forming sandwich π-complexes with metals.5,192,193 Cyclic borazine [(−BH−NH−)3] (see Table 8) and its derivatives exhibit less aromatic character, expressed by HOMA and Bird’s indices, in comparison to their benzene analogues.59 Moreover, they are less sensitive to chemical and topological effects from the environment of the ring in question. Recently, NICS, HOMA, PDI, and FLU parameters were used to study aromaticity of endo B and/or N substituted benzene, pyrene, chrysene, triphenylene, and tetracene molecules.194 Six-membered rings containing B and N atoms in all cases were found to be less aromatic than their carbon analogues. Additionally, the global and local aromaticity in tetracyclic polyaromatic hydrocarbon derivatives was found to be dependent on the heteroatoms’ positions in the molecules. A geometric criterion (HOMA index) was used to study the effect of thermal ring flexibilities on its aromaticity in pyrimidine and purine derivatives.162 The ring deformability was defined as the averaged change of bond angles or dihedral angles constituting the ring, which yielded a 1.5 kcal/mol increase of the system energy. The molecular structures adopted during such vibrations at room temperature can lead to a significant HOMA heterogeneity that increases with decreasing aromatic character of the ring. However, the average
HOMA = 0.889(± 0.015) + 0.044( ± 0.009)N2;5 − 0.015(± 0.009)N3;4
(35)
where N2;5 denotes the number of nitrogen atoms at positions 2 and/or 5, and N3;4 indicates the number of nitrogen atoms at positions 3 and/or 4 of the ring. Therefore, the isomer with nitrogen atoms at positions 2 and 5 is the most aromatic. The presence of nitrogen atoms at positions 2 and/or 5 increases aromaticity, whereas their presence at positions 3 and/or 4 leads to its decrease. For furan and oxazoles, a similar relationship was found:174 HOMA = 0.367(± 0.033) + 0.148( ± 0.021)N2;5 − 0.058(± 0.021)N3;4
(36)
The above equations were formulated on the basis of data taken from the paper by Cyranski et al.33 Analysis of the effects of N-substituents on the aromaticity of 1,2-azoles (pyrazoles) and 1,3-azoles (imidazoles) has shown that their aromaticity is significantly less influenced by Nsubstitutions in comparison with the C-substituted benzene counterparts.171 The aromaticity of six-membered heterocycles containing nitrogen atom(s), as measured by geometric (Table 8), magnetic,180 and electronic181 indices, is similar to that of benzene. Therefore, it is not surprising that establishing their aromaticity sequence may fail, because the variation of the aromaticity indices is very small. The same applies to aza derivatives of naphthalene and indole (magnetic and electronic indices show aromaticity lowering with increasing number of nitrogen atoms in the ring, whereas HOMA values suggest the opposite trend).182 The aromaticities of hexazine (N6, HOMED = 1.000) and its protonated form (N6H+, HOMED = 0.994)178 are similar; the same was observed for pyridine and pyridinium cation.176 Recently, the aromaticities of six-membered monoheterocycles (C5H5X) with IV−VI group heteroatoms (X = SiH, GeH, N, P, As, O+, S+, and Se+) were analyzed using different aromaticity indices based on structural (Bird’s index, see Table 8), magnetic, energetic, and electronic properties of the ring.34 The obtained indices indicated significant aromaticity of all of the heterocycles studied. Although a decrease in aromaticity was observed with increasing atomic number of the heteroatom (except in the case of the pyrylium cation), considerable inconsistency between the different indices was found. Similar inconsistency was also observed in the case of heterocycles with two heteroatoms (C4H4X2, where X = O, S, Se; see Table 8).97 HOMA, I6, and NICS parameters were used to study aromaticity of the pyran ring in hydroxypyrones and their cations and anions.183 Biologically active compounds such as 6397
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Table 9. HOMA Indices for Five- and Six-Membered Heterocycles of Nucleobase Monomers and Their Stacked Complexes202 base or bases pair X···Y
HOMA(5) X
HOMA(6) X
A A···A A···C A···T A···U C C···C G G···A G···C G···G G···T G···U T T···C T···T U U···C U···T U···U
0.8910 0.8940 0.8998 0.8976 0.8960
0.9906 0.9951 0.9941 0.9892 0.9902 0.7233 0.7471 0.7541 0.7774 0.7784 0.8006 0.7744 0.7893 0.5378 0.6131 0.5706 0.5700 0.6358 0.5965 0.6178
0.8956 0.9131 0.8906 0.9054 0.9031 0.9042
values of the index obtained for such fluctuations almost perfectly match HOMA values of the molecule in its ground state. Deformation of the benzene ring also influences its aromaticity to a small extent,195 but significant reduction of the π-electron delocalization in the ring was found for 2,4,6trinitroaniline derivatives with bulky substituents.196 The fusion of pyrimidine and imidazole moieties into purine units decreases aromaticity of both rings, as documented by HOMA and NICS values.197 Many biologically important compounds are derivatives of purine; the most widely known examples are adenine and guanine. Box and Jean-Mary were the first to investigate the role of aromaticity in the structure of DNA.198 Later, Cyranski et al.199 analyzed the π-electron delocalization in nucleobases constituting DNA and RNA using the geometry model of aromaticity HOMA and magnetic index NICS. The aromatic character of the bases differs significantly, as shown by the HOMA ranges: from 0.466 for thymine to 0.917 for adenine (based on B3LYP/6-311+G** calculations). The substituents attached to the six-membered ring via a double bond CX (X = N or O) were identified as the main source of these differences. Moreover, H-bonds involving C O groups in Watson−Crick pairs cause an increase in the aromatic character of the rings. Aromaticity, expressed by HOMA and NICS, decreases in the following sequence: adenine (A) > guanine (G) > cytosine (C) > uracil (U) > thymine (T). Almost the same order was found by Cysewski,200 who used the same indices. Moreover, HOMA values calculated for geometries estimated in the presence of water suggest a slight increase of aromaticity. A significant impact of protonation on the aromatic character was also noticed.200 Protonation of adenine decreases the aromaticity of both rings, whereas the aromaticity increases in derivatives of guanine and pyrimidines, as compared to neutral bases. A hybrid QM/MM approach was used to study the influence of the environment on the aromatic character of nucleobases and amino acids.201 It was also documented that experimental geometries of protein and DNA crystals, determined from Xray measurements with extra fine resolution (≤1.0 Å) and provided by the PDB database, are not sufficient for the direct
HOMA(5) Y
HOMA(6) Y
0.7125
0.9904 0.7509 0.5667 0.5976 0.7518
0.9033 0.8983
0.9913 0.7529 0.8078 0.6138 0.6584 0.8408 0.5725 0.7592 0.5756 0.6048
estimation of the HOMA index. Three consequences of the interactions with the environment in structural and magnetic indices of aromaticity could be identified: (i) broad ranges of HOMA or NICS values for different conformations of the nearest neighborhood, (ii) a significant difference in the obtained indices values and their means as compared to the analogue parameters in the isolated monomers, and (iii) a most significant increase of aromaticity for the pyrimidine rings of guanine, thymine, and cytosine. The same trend was also observed for all amino acids inside proteins, but it was much smaller. Moreover, similar changes of HOMA and NICS distributions were found for explicit water solutions of nucleobases and amino acids. It is well-known that hydrogen bonding and stacking interactions are responsible for the stabilization of the threedimensional structure of the DNA double helix. The effect of noncovalent stacking interactions on ring aromaticity has been studied for 15-stacked complexes of the five nucleic acid bases (adenine, guanine, cytosine, thymine, and uracil).202 For this purpose, HOMA and four electronic indices were used. A new generation DFT method, MPWB1K hybrid meta density functional,203,204 was applied to obtain the structures of the monomer and stacked complexes. The trend of aromaticity for the isolated bases agrees with the above-mentioned results199,200 and those obtained by Huertas et al.205 (A > C > G > U > T). For stacking complexes, the aromaticity variability of the imidazole ring is lower than in the case of a pyrimidine ring (see Table 9). Therefore, it can be postulated that the imidazole ring is considerably less involved in the stacking interaction. Moreover, some authors state96,202 that the stacking interaction reduces the aromatic character of the nucleobase fragments. This conclusion was based on electronic indices. However, HOMA index suggests an increase of the aromatic character of pyrimidine ring in stacked systems (see Table 9). Good compatibility between different indices (ring moieties with more negative NICS values also have larger HOMA and PDI measures and lower FLU indices) was found in the investigation of the influence of the benzene ring insertion/ addition to the natural nucleic acid bases on local aromaticity of 6398
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the so-called size-expanded benzo-fused derivatives.205 Components of Watson−Crick pairs (adenine, cytosine, guanine, and thymine) were expanded by the insertion or addition of a benzene ring in purine (adenine, guanine) and pyrimidine (cytosine, thymine) derivatives, respectively. The indices of aromaticity were determined using the molecular geometries obtained from a full geometry optimization of natural and expanded monomers and their H-bonded complexes at the BH and HLYP/cc-pVTZ level. HOMA and electronic indices (FLU and PDI) showed almost the same order of aromaticity for different rings in natural and benzo-fused bases. The insertion or addition of a benzene ring decreases the aromaticity of both heterocyclic rings and the added benzene ring. Hydrogen bonding does not have a large effect on the local aromaticity of the bases. Noticeable changes are restricted to the sixmembered rings that participate directly in the H-bond interaction. Very recently, the HOMA index was used to study the aromaticity of poly(thiaheterohelicene), a novel helical polymer composed of fused benzothiophene rings.206 For this purpose, their short chain models (oligomers) abbreviated as Oligo-Th and Oligo-mSp (see Scheme 2) formed by n repeating units
into account. In this case, only bonds of the same type should be considered.208 4.3. Effect of Substituents on the Aromaticity of π-Electron Systems
As stated above, π-electron delocalization is one of the most significant properties of all aromatic systems. Because πelectrons are distributed mostly above and below the molecular plane, they contribute to the delocalization and, thus, are considered to be more movable than, for example, σ-electrons. Because of this property, π-electrons are often considered as the medium along which different parts of the molecule may interact (communicate) between themselves. The phenomenon known as the substituent effect, one of the most important issues in organic chemistry, has its origin in this type of interactions.209−211 This section is devoted to the review of recent developments in the substituent effect analysis, with the structural aspects emphasized in the foreground. It has been generally accepted that the benzene ring is considered an archetype of aromatic species. An unsubstituted benzene ring is considered fully aromatic, because it fulfills all of the criteria of aromaticity (see Introduction, where an enumerative definition of aromaticity is given). However, the aromatic character of the benzene ring in phenol or nitrobenzene differs from that of unsubstituted benzene. Actually, the degree of π-electron delocalization decreases due to the presence of substituents. This decrease in aromaticity is relatively small, less than 1%,212 as shown by the HOMA index. However, it has a crucial impact on the properties of the molecule, including the properties of the benzene ring itself, changing its chemical reactivity, activating specific sites, etc.,213 or even influencing its ability of H-bonding formation.214 What is more, when both NO2 and OH groups are introduced into a benzene ring via substitution, as in para-nitrophenol, the decrease in aromaticity is even larger than would be expected assuming an additive effect of the substituents.215 Thus, interactions between substituents of cooperative or competitive character through the benzene ring (or more generally πconjugated system) are also possible. The cooperative effect, being stronger and imposing a larger difference in electronwithdrawing and electron-donating properties of the substituents attached to the ring (or generally benzene-like πelectron system), can be explained in part by the contribution from the quinone-like canonical structure.210,215 In 2005−2006, the subject of substituent effects was thoroughly reviewed in comprehensive papers.210,211 For this reason, in this Review, we focus only on the data, which have appeared in the past seven years. In all analyses, structural indices of aromaticity are used as a criterion of π-electron delocalization. The effect of substitution on the aromaticity of cyclopentadiene and its cationic (dehydrogenated) and anionic (deprotonated) form was investigated with the use of neural networks by Alonso and Herradon.216 They found that the aromaticity of a cyclopentadiene ring and cyclopentadienyl anion ring decreases upon substitution, irrespective of the electronic character of the substituent. As a consequence, both rings become less stable. This seems to be typical for aromatic systems, which retain their fully delocalized structure and recognize substitution as a kind of perturbation leading to a decrease in their stability. As could be expected for anionic species, electron-donating substituents destabilize the substituted ring in a more effective way than electron-withdrawing
Scheme 2
were considered; the number of monomers varied from 1 to 8. A decrease of aromaticity with increasing n was documented.206 Good agreement was found between their helical structure obtained by DFT calculations and available experimental data. To illustrate the influence of the number of repeating units on the aromaticity of oligomers, average values of HOMA were calculated by considering the whole system, benzene and thiophene rings (HOMAall, HOMA6, and HOMA5, respectively). For Oligo-Th, the aromaticity index was found practically independent of n (HOMAall ranges from 0.57 for n = 8 to 0.60 for n = 1). Furthermore, an individual thiophene ring in the oligomer was characterized by lower aromaticity (HOMA = 0.236 for n = 8 and HOMA = 0.265 for n = 1). Much greater aromaticity variability was found for Oligo-mSp where HOMAall decreases from 0.48 (n = 1) to 0.11 (n = 8). Deeper inspection of HOMA6 and HOMA5 indices indicates that this variation is mainly caused by the loss of aromaticity of the thiophene rings with the increasing size of the molecule. Additionally, it was found that ionization also reduces aromaticity, particularly in the case of Oligo-mSp. For macromolecular compounds, the bond length alternation (BLA) index is the most popular, as judged from the available data.207 This index is expressed as the sum of the absolute values of the deviations of the particular bond lengths from the average bond lengths divided by the number of bonds taken 6399
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substituent active region was found.221−223 Note that, in that work, the substituent active region was defined as a fragment of the molecule consisting of a substituted carbon atom and all of the atoms belonging to the substituent group. It is also worth mentioning here the very recent studies on the substituent effect in the benzodiazepinone system,224 a chemical species that is of wide interest because of its medical applications.225 Karpinska et al.224 performed a detailed analysis of the intramolecular factors influencing structural changes in C7-substituted 1,3-dihydrobenzo[e][1,4]diazepin-2-ones (see Figure 5).
ones. In the case of cyclopentadiene cation, the substitution results in a reduction of the antiaromatic character of the ring (by means of an increase of delocalization). Thus, in this case, the substitution leads to partial stabilization of the ring with respect to its unsubstituted form. Again, as expected, this effect has been found to be stronger in the case of electronwithdrawing substituents. In their study, Alonso and Herradon216 used several measures of π-electron delocalization, including ASE, three types of NICS index, magnetic susceptibility exaltation (Λ), and HOMA, as a structural measure of aromaticity. The values of aromaticity indices calculated by these authors differed significantly. Correlations between them, obtained for each type of ring, turned out to be poor. This was interpreted as an indication of the somewhat multidimensional character of aromaticity in cyclopentadiene and its charged analogues.27,31,33 Interestingly, the structural index HOMA correlates quite well with NICS (but not NICS(1) and NICS(1)zz) in the case of substituted cyclopentadienyl anion (cc = −0.943); however, this relation was not observed for neutral and cationic counterparts. This may perhaps be surprising, because both NICS and HOMA were originally designed for neutral species. However, the anionic cyclopentadiene ring reveals a more aromatic character in general (it is a 4n+2 Hückel-type system) than its neutral and cationic forms; thus, a better interrelation between aromaticity indices observed for more aromatic species should, in fact, be expected. In that light, it should be more surprising that, for the set of investigated systems, the HOMA index indicates that a neutral cyclopentadiene ring and its substituted derivatives are more aromatic than their anionic counterparts. Also, in the case of imidazole ring and its substituted derivatives, it was found that the anionic form is more aromatic than its parent neutral form.169 This conclusion was built on the basis of several different criteria, including the structural index HOMA. However, no explanation was given by the authors regarding why the electron-withdrawing substituents increased the degree of π-electron delocalization within the neutral ring, while electron-donating ones decreased the aromatic character of this ring. If the anionic form of imidazole ring was more aromatic, then an increase of the π-electron charge within the neutral imidazole ring should perhaps also lead to an increase in aromaticity. As shown by results from numerical data collected by authors,169 such a relation is not fulfilled in the case of imidazole, and it was left with no comment. The same research group previously studied different tetrazole derivatives217 and came to generally similar conclusions. However, in the case of these compounds, the position of protonated N atom(s) in the neutral and cationic ring was decisive, leading to a more aromatic or less aromatic ring with respect to its anionic counterpart. More recently,218 a comparison of the substituent effect in tetrazole and benzene was performed by means of natural bond orbital (NBO) analysis,219 including the pEDA parameter220 (for definition see, section 4.6). A straight relation between pz orbital populations on atoms within the ring and the pEDA was found, with evident exception for meta-carbon atoms in benzene and N4 atom in tetrazole. The relation between pEDA and σ + p substituent constant was also found. Considering the NBO approach as a tool in the analysis of the substituent effect, it is worth mentioning the recent report in which a clear relation between Hammett substituent constants and NBO-based populations of the so-called
Figure 5. Tautomers of C7-substituted benzo[1,4]diazepinone systems (a, N1H tautomer; b, N4H tautomer); R = NMe2, NH2, OH, SH, F, Cl, Br, Me, Ph, CN, COOH, NO2, CHO, NO, and BH2.
It was observed that the position of the N−H group in the seven-membered ring strongly influences the aromatic character of the whole molecule. The N1H tautomer was found to be more stable than the N4H one (by at least 17 kcal/ mol in the gas phase); details concerning their aromaticity can be found in section 4.4. The influence of substituents in position 7 on the aromaticity of the benzodiazepinone system was also discussed, but no direct relation between the electrondonating/withdrawing properties of X and aromaticity of individual rings was found. The only exception was the seven-membered ring in the N4H tautomer in which an increase of delocalization due to more pronounced electrondonating properties of the substituent was reported. In the case of the N1H tautomer, the only straight relation was found for the GEO component of HOMA. Interestingly enough, the benzene ring shows much worse correlations between aromaticity measures and substituent properties, despite the fact that it was directly substituted. Usually, the substituent effect is considered in the context of the presence and position of the given substituent (with respect to a specific center). However, not only is the presence or position of the given substituent of importance, but also its spatial arrangement with respect to the substituted ring. The nitro group can be taken here as an excellent example. If it is attached to the planar benzene ring, it may rotate along the N− C bond under some conditions. This aspect was recently investigated by Dobrowolski et al.226 for para-nitrophenol and para-nitrophenolate. The nitro group conjugates most effectively with the benzene π-electron system, when it is in planar conformation with respect to the plane of the ring. Any distortion leads to lowering in π-conjugation and results in a weaker substituent effect. Dobrowolski et al.226 had shown the direct relation between the distortion angle and HOMA values (an increase of the distortion leads to higher HOMA values), as well as between the distortion angle and substituent effect stabilization energy (SESE).227 The latter parameter was estimated as an energetic balance of the hypothetical reaction shown in Figure 6. It was also shown by numerical means that, in the case of planar orientation of NO2 with respect to the benzene ring, the estimated substituent constant includes both inductive and 6400
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more effective way. Such conjugation paths were determined for naphthalene229 and later also for ortho-benzoquinone39 and 1,2- and 2,3-naphtoquinones.40 Similar studies on the substituent effect in molecules consisting of two aromatic rings were also performed for diazanaphthalenes.230 It was found there that the presence of electron-withdrawing substituents in the position adjacent to the position of N atom in the hetero ring may in some cases lead to an increase in aromaticity (with respect to the unsubstituted compound). According to the HOMA values,230 the increase of aromaticity in the substituted ring is usually connected to a decrease of aromaticity of the second, unsubstituted, ring in the heteroderivative of naphthalene. This can most probably be explained in the framework of Clar’s aromaticity concept,128,129 according to which in naphthalene there is a migrating sextet of π-electrons, which, in some cases, may be localized on one of the two rings, for example, by the specific substitution.231,232 Most often, substitution of an aromatic system leads to a decrease of aromaticity, but usually only by a small degree, as was already mentioned at the beginning of this section. However, when more than one substituent is involved in such intramolecular interactions, the reduction of aromaticity can be very drastic, even leading to the nonaromatic character of the substituted ring. Nitroaniline233 and its overcrowded analogues196,234 can be taken here as instructive examples. It was demonstrated for 1,3,5-trinitro-2,4,6-triamino-benzene that the HOMA value estimated for the benzene ring is only about 0.2.233 When hydrogens in amino-groups are substituted with larger molecular fragments, the decrease in aromaticity can be even stronger, not only due to the substituent effect influencing the π-electron system directly, but also due to steric interactions leading to out-of-plane deformation of the benzene ring.196 Note that in the case of 1,3,5-trinitro-2,4,6-triamino-benzene and its derivatives, the effect of intramolecular H-bonding has to be taken into account, which cooperates with the substituent effect leading to an additional decrease of aromaticity in the benzene ring.232,235−237 In benzene derivatives and other aromatic compounds, the delocalized π-electron structure is considered as the one containing relatively more movable electrons (delocalized), which may more easily contribute to the transfer of charge between particular substituents, interacting along the substituted ring. On the other hand, it can be easily concluded that the substituent effect leads to a decrease of aromatic delocalization. Because this delocalization is the property that is directly responsible for the extra stabilization of a given (aromatic) system, the substituent effect should perhaps be considered as a kind of perturbation, which is competitive with aromaticity. Such a point of view was formulated on the basis of reactions defining the Hammett constants.238 Quoting the authors’ main conclusion: “it may be stated that similarly to the resistance of benzene (and most typical aromatic systems) in chemical reactions to change their π-electron structure, i.e. to maintain the π-electron delocalization, the substituent effect as a kind of perturbation meets similar resistance to change the πelectron delocalization in the ring.” It follows from this conclusion that the aromatic ring, although acting as a medium in interaction (communication) between the substituents, may also, in some way, limit this interaction due to its tendency of keeping aromatic character. This conclusion implies the next: nonaromatic π-conjugated system should be a better medium in communication between the substituents than its aromatic
Figure 6. The homodesmotic reaction used for SESE estimation by Dobrowolski et al.;226 X = OH, O− and Y = CONH2, CHO, COOH, COCH 3, COCl, CN, NO2, NO.
resonance effects (large σp− value). However, when a nonplanar orientation is forced on the NO2 group, the estimated substituent constant reflects more inductive effect and less resonance effect with respect to the planar orientation. In the case of perpendicular orientation, the estimated constant corresponds to inductive contribution only (the estimated σp− value was only one-half of that estimated for the planar orientation). As was previously mentioned, the presence of two substituents may lead to interactions between them through the π-electron delocalized system. The strength of these interactions strongly depends on the mutual positions of such substituents. For instance, in benzene ring substitutions, paraand meta-positions drastically differ, being much more effective in the former one.228 For larger systems, such as naphthalene, the problem becomes even more complicated. Recently, the substituent effect in disubstituted naphthalene was thoroughly investigated, and it was shown that the number of CC bonds linking substituents determines the strength of their mutual interaction.229 More effective interactions between substituents are observed for quinone-type substitutions, being analogues to the para-substitution in benzene, which is schematically illustrated in Figure 7a. In this structure, formal charges are
Figure 7. Single- (a) and double- (b) charge-separated structures in disubstituted benzene. A stands for electron-accepting substituents and D for electron-donating ones.
located on the substituents (e.g., single-charge separated structure). When double charge-separated structures are the only ones that allow locating formal charges on both substituents, the communication between substituents is much less effective, as shown in Figure 7b for the metasubstitution. Thus, it can be stated that there are special conjugation paths along which substituents may interact in a 6401
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conclusion was also confirmed by the use of NBO analysis, including pz orbital populations of atoms belonging to the given ring.244,245 Generally, it can be concluded that the impact of the substituent effect on the π-electron structure significantly depends not only on the type of the substituent, but also on the type of π-electron structure itself. Classifying π-electron systems in the context of the Hückel rule, it can be said that: (i) 4n+2 systems are rather resistant to the substituent effect (they are aromatic and they try to keep their aromatic character), (ii) 4n antiaromatic (sometimes, as in the case of COT in its tub-shaped conformation−nonaromatic) or olefinic πelectron systems are significantly sensitive to the substituent effect, (iii) 4n+1 systems are more sensitive to this effect as compared to 4n+2 ones, but this sensitivity strongly depends on the type of substituent. The multidimensional character of aromaticity has been postulated since the 1980s.27,28,31,33,246 For this reason, the use of different aromaticity measures defined on different basic properties of aromatic systems was also recommended.195,247,248 On the other hand, there are various indices, even in groups of measures defined strictly on one given basic property of the aromatic system (e.g., geometry, energy, etc.), and it is not obvious which should really be included in the set of aromaticity measures used for the set of systems under investigation. For instance, the agreement in indications of different aromaticity measures used for monosubstituted benzene derivatives was recently investigated by means of HOMA and Bird’s I6, as structural indices of aromaticity, the set of six NICS indices, and the value of energy connected with out-of-plane deformation, which was suggested as a potential energy-based measure of π-electron delocalization.249 It was found that, in general, all of the indices used in this study were very poorly correlated, if at all. Interestingly, even in the group of NICS indices, interrelations were rather poor, perhaps with one exception for which the best correlation coefficient was 0.92. Such a significant discrepancy is rather surprising, particularly taking into account the relatively homogeneous group of the investigated systems. Cysewski et al.250 performed a more comprehensive statistical analysis for the collection of data obtained with several aromaticity measures applied for a set of monosubstituted benzene, pentafulvene, and heptafulvene rings (in total, 63 compounds were investigated in three groups, 21 systems for each kind of substituted ring). The use of Principal Component Analysis (PCA) suggests that, for these systems, the initial set of 32 aromaticity measures can be reduced just to three: FLU,251 pEDA,220 and RCP(∇2ρ) (the Laplacian of electron density measured in the ring critical point according to quantum theory of atoms in molecules, QTAIM),252,253 which cover 99% of population variance. It was also shown that these three measures are independent from each other. Interestingly, none of them are based on the geometrical properties. In the case of the seven structural indices taken into account, it was shown that they are very well intercorrelated, which was illustrated by the collection of correlation coefficients being in the range of absolute values from 0.92 to 1.00. For other type indices, such correlations were significantly worse. It is also worth mentioning that structural indices were in good agreement with energy-based measures. This fulfills an intuitive
counterpart. In fact, this was later confirmed numerically for 1,4-disubstituted cyclohexa-1,3-diene and benzene.239 These findings are important for two reasons: First, they clearly define the relation between the two most important aspects of chemistry, the aromaticity and the substituent effect; second, it fully justifies the analysis of the substituent effect for nonaromatic and even noncyclic conjugated systems. Later, a detailed analysis of the substituent effect in 1,4-disubstituted cyclohexa-1,3-diene showed that the communication between the substituent is ca. 10 times more effective in comparison with its aromatic analogue, benzene, in this system, as estimated by the use of HOMA index.41 Therefore, the substituent effect can also be considered for nonaromatic systems. The analysis of the substituent effect in mono- and disubstituted 1,3,5,7-COT can be taken here as a good example.240 In this compound, the most favorable for the substituent effect is the 1,4-conjugation path, which corresponds to para-substitution in benzene analogues. In the case of 1,3- and 1,5-substitution, the interaction between the substituents is significantly reduced, similar to the case of meta-substitution in benzene. What is particularly worth pointing out is the fact that, as distinct to aromatic species, the substitution in COT leads to an increase of the degree of delocalization. The stronger is the communication between the substituents, the more delocalized are the bonds along the path linking these substituents. This is actually opposite to that which was observed for aromatic rings.240 Note that COT, being a 4n-type Hückel system, is fully localized in its natural unsubstituted form with a HOMA value of about −0.2. After substitution, the HOMA value in 1-nitroso-4-hydroxy-COT is around 0.01. Thus, the difference is about 0.2, which may seem to be relatively small. However, the same kind of structural modification estimated for benzene and para-nitrosophenol results in a HOMA difference of 0.04,212 which proves that aromatic systems are more resistant to the substituent effect than are nonaromatic compounds. In that light, an interesting case is fulvene. This compound is isoelectronic with benzene, however, with the ring of 4n+1 Hückel-type. Distinct from its better known aromatic counterpart, fulvene is much less stable, both kinetically and thermodynamically.241,242 Recently, a detailed analysis of the substitution in C6 position of fulvene was performed.243 It was demonstrated that both electron-donating and electron-withdrawing substitutions always lead to an increase in aromaticity of the five-membered fulvene ring. This is schematically illustrated in Figure 8.
Figure 8. Substituent effect in fulvene, X = B(OH)2, BH2, CC−, CCH, CF3, CH2−, CH3, CHCH2, CHO, Cl, CMe3, CN, COCH3, CONH2, COO−, COOH, F, H, Li, NH−, NH2, NH3+, NMe2, NO, NO2, O−, OCH3, OH, SiH3, and SiMe3.
What is particularly interesting, depending on the substituent, is that the fulvene ring may reflect a full spectrum of πelectron delocalization, from partially antiaromatic (or significantly localized) to significantly aromatic, which is reflected by the HOMA values, which range from −0.2 to 0.8. This shows drastically higher sensitivity for the substituent effect in the case of a fulvene ring, when compared to benzene. Such a 6402
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the lone electron pairs of neighboring heteroatoms and the repulsions of the neighboring groups should also be taken into account.113 A comparison of several indices of aromaticity (structural: HOMA, Pozharskii, APoz, Bird, I5, and electronic−minimum bond order in the ring,271 BOmin) for tautomers of 5-substituted NH-triazoles and tetrazoles has shown that, for all of these cases, the most stable tautomer corresponds to the maximum values of these indices (HOMA > 0.95, APoz > 74%, I5 > 83%, BOmin > 1.49), except for the BH2 derivative of tetrazole and nitro-1,2,4-triazole.172,173,269 Moreover, the ionic forms of tetrazoles were also considered172 (Figure 9). The highest
expectation that the two most fundamental properties of the molecular system, that is, the energy and the geometry, are both mutually interdependent. 4.4. Relationships between Tautomerism, H-Bonding, and Aromaticity
Many chemical compounds exist in the form of tautomers, which differ in their structure and stability and are always involved in some kind of tautomeric equilibria. These equilibria are, in turn, responsible for the unique physicochemical properties and biological activity of tautomeric compounds. In recent decades, the most significant interest has been directed to the investigation of factors influencing the tautomerism, as well as to the explanation of the mechanism of the tautomerism, particularly in biochemical reactions. Tautomerism also plays a crucial role in biological activity of drugs.254,255 Tautomeric preferences depend on many factors, among which π-electron delocalization is an important one. An excellent review concerning tautomeric equilibria and their relation with π-electron delocalization was published by Raczynska et al.256 The general scheme of tautomerism, according to the IUPAC recommendation,257 can be written as a chemical reaction in which tautomers are readily interconvertible: GX−ZY ⇌ XZ−YG
where the atoms connecting to X, Y, Z groups are typically any of C, H, O, or S, and the G group plays a role of the leaving group that carries away or not the bonding electron pair during tautomerization. In this Review, mainly aromatic systems in which several kinds of tautomeric equilibria are possible will be considered. Among the main types of this phenomenon, valence, anionotropic, and cationotropic tautomerisms should be distinguished. Investigation of the valence tautomeric interconversion in terms of aromaticity was performed mostly by means of NICS and NBO analyses.258−261 The aromaticity of the tautomers involved in anionotropic equilibria262 (the migrating group moves with its electron pair) is not characterized. This kind of tautomerism is known mainly for acyclic compounds (migration of any group Cl, Br, I, OH, NH2, or NO2), but examples for cyclic and even aromatic systems exist.263 The most important for life sciences, the largest and most often studied tautomerism phenomena, are the prototropic equilibria, which are particular cases of cationotropy.263 The prototropic equilibria for cyclic compounds can be divided into two main types: (i) annular and (ii) side chain tautomerisms. In the first case, the atom or atomic group is exchanged between carbon and heteroatoms in the ring, whereas in the second, the exchange takes place between the ring and a side-chain atom.264 The annular type of tautomerism was studied mainly for nitrogen-containing heterocycles: pyrrole,113 imidazole,265 purine,197,266 1-deazapurines,267,268 C-nitro triazoles,269 tetrazoles,172,173 4-aminopyrimidine,270 and benzodiazepinones.224 For molecules without an exo group (pyrrole, imidazole, purine), the π-electron delocalization plays a primary role in the tautomeric preference, and the HOMED aromaticity index correlates well with the relative energies of tautomers.113 For more complex systems, with several heteroatoms and various substituents and functional groups, the equilibrium of tautomerization depends strongly on the electron effects of functional groups and their intramolecular interactions with the remaining part of the molecule. In addition, the repulsions of
Figure 9. Prototropy of tetrazole derivatives, R = H, CH3, CMe3, Ph, Cl, CF3, NO2.
aromaticity characterizes substituted tetrazolate anions (APoz > 85%), whereas the lowest is found for the 1,4-H,H+ form (the range of variability of APoz is 55−60%). It should also be noted that, for all tetrazoles, the 2H tautomer is more stable than its 1H counterpart and the aromaticity of the ring slightly depends on the nature of the substituent. Similar results were obtained for planar triazoleporphyrazines.272 The aromaticity increases in the sequence a < b < c (see Figure 10) with increasing stability of the tautomer. The values of HOMA for the whole molecule and NICS in the center of the macrocycle correlate fairly well and are similar to those obtained for free base porphyrin for the most stable tautomer (0.666 and −16.5 ppm, respectively).273 However, for weakly conjugated systems, such as hemiporphyrazine, the HOMA index for internal cross shows high values (0.7−0.9), although from X-ray investigations it is known that hemiporphyrazine has a nonplanar equilibrium structure, and, as a result, its inner macrocycle is nonaromatic.274,275 In this case, NICS values are more appropriate, because they are positive for internal cross and quite well describe the loss of aromaticity in comparison with porphyrazine. Conformational preferences and N-fusion reaction of [22]- and [24]pentaphyrins were investigated using DFT computation. Additionally, the analysis was supported by the studies of the relationship between aromaticity and molecular topology.276 Energetic, magnetic, and geometry-based indices were used for this purpose. Continuing the discussion of nitrogen-containing cyclic compounds, the benzodiazepinone systems should be noted, in which the equilibrium between N1H and N4H tautomeric forms is possible (Figure 5). For the more stable N1H tautomer, HOMA values for the benzene ring are greater than 0.88, while for the diazepinone ring, HOMA values are negative 6403
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Figure 10. Tautomers of triazoleporphyrazine and HOMA values for whole molecules. Data taken from ref 272.
Figure 11. Example of equilibrium in 1,3-dihydroxyaryl-2-aldehydes (aryl = naphthalene) and HOMA indices.
correlation between the π-electron delocalization, the dipole moment, and the stability of tautomers. Therefore, aromaticity and solvent polarity are secondary factors dictating the tautomeric preference. In this case, the stability of the functional groups is a dominant factor. For hydroxyquinolines, the most stable is an OH tautomer, except for 2- and 4-hydroxyquinolines. The sum of HOMA values of individual rings correlates with the stability of tautomers and was applied for the analysis of Kekulé/nonKekulé structural properties in these compounds.289,290 For monohydroxyarenes, the total HOMA index can be negative for the keto forms and is always positive for the enol forms. In all cases, the aromatic enol forms are strongly favored. An exception is 9-anthrol and other meso-hydroxyacenes, in which the keto form is favored.291 The tautomeric equilibria induced by RAHB H-bonding (see Figure 3) should be considered separately. RAHB can be divided into homonuclear and heteronuclear types.88 The former is most often limited to the O−H···O and N−H···N bridges. β-Diketones are typical oxygen-containing compounds exhibiting homonuclear RAHB; among them, malonaldehyde derivatives are the most frequently studied.256,292 In solution and in the gas phase, malonaldehyde exists in the cis-enolone form with intramolecular hydrogen bonding leading to a quasiaromatic ring. For such quasi-aromatic rings with substituents located at position 1(3) or 2, various aromaticity indices were applied.235 It was found that the quasi-aromatic ring is more aromatic (HOMA > 0.9) and the H-bond is stronger in the transition state than in the ground state. Additionally, for the 1(3)-substituted derivatives, the more stable tautomer is characterized by a weaker H-bond and lower aromaticity. This was discussed and explained by means of the substituent effect. In the study of the equilibria in 1,3-dihydroxyaryl-2aldehydes (naphthalene derivative presented in Figure 11), it was found that the systems with a straight-line topology are relatively less stable than those showing a kinked-like structure.236 Moreover, the position of the extra quasi-aromatic ring influences both the strength of the H-bonding and the local aromaticity of the polyaromatic skeleton. Tautomer b has
(∼ −0.35). It shows us that the seven-membered ring is antiaromatic. At the same time, in the N4H tautomer, the diazepinone ring retains the antiaromaticity, whereas the benzene ring loses its own aromaticity (HOMA < 0.35). Apparently, this is the main reason for the preference of the N1H tautomer.224 Recently, much attention has been paid not only to neutral molecules, but also to their radical ions. Among the studied molecules and their radicals are phenol,277 aniline,278 imidazole,265 4-aminopyrimidine,270 purine,266,279 uracil,280 and adenine.281,282 The investigations of the presence of tautomers in different redox forms in the tautomeric mixture facilitate the understanding of biochemical processes in living organisms. For all cases, the neutral and oxidized molecules behave in a similar manner. Aromaticity is the main factor that dictates the tautomeric preference. However, the reduced forms demonstrate the reverse correlation. The order of tautomer stability is changed, and the least aromatic form becomes the dominant tautomer. The reasons for this deviation are not yet understood.278 The next and the most prevalent types of tautomerism in heteroaromatic compounds are side-chain equilibria, particularly the keto−enol tautomerism. This type of equilibrium was studied in different molecules, such as phenols,277,283 their azaderivatives,284−288 hydroxyquinolines289,290 and other monohydroxy aromatic compounds.291 When going from phenol to its aza-derivatives (where carbon atoms are replaced by N-aza groups in various positions of the ring), the preference of OH tautomer changes to the NH form. This trend is maintained, even if the number of nitrogen atoms in the ring and the number of exo OH groups increase. We can see the domination of poly-NH tautomers instead of the more aromatic poly-OH form. HOMED values are equal to 0.60 and 0.92 for rings of the corresponding uracil tautomers;284 HOMA values are equal to 0.737 and 0.998 for cyanuric acid ones.287 The HOMED index decreases with increasing numbers of nitrogen atoms in the ring when going from OH through NH to CH tautomer. The ranges of the HOMED index for these kinds of tautomers are 0.74−1.00, 0.16−0.76, and −0.66 to 0.47, respectively.284 It has also been found that there is no 6404
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Figure 12. Tautomeric equilibria in the compounds with N−H···N bridge.
a relatively stronger hydrogen bond and is more stable than tautomer c (Figure 11). A loss of aromaticity of the adjacent ring is observed because π-electrons from this ring participate in the formation of the quasi-aromatic ring. It should be noted that most indices of aromaticity (HOMA, PDI, FLU, SCI, KSCI) correlate with each other, except for NICS indices. Another example of homonuclear RAHB (N−H···N bridge) is the tautomerism in di(2-pyridyl)-methane and its benzoannulated derivatives (Figure 12). It was shown that, in all cases except that of the phenanthydin-6-yl derivative, tautomer a, without protonated pyridine rings and H-bonding, is the most stable. In these tautomers, the HOMA index for the pyridine ring amounts to 0.99. In other cases, HOMA values decrease to 0.71, reaching ca. 0.87 in the transition state. This is caused by the electron transfer to the quasi-aromatic ring (HOMA > 0.74 for all studied systems). As in the previous case, good correlation among all of the aromaticity indices used was observed, except for NICS indices for quasi-aromatic rings.293 A comparative analysis between homonuclear and heteronuclear RAHB in terms of tautomerism was performed by Zubatyuk et al.294,295 These authors investigated a series of nitrogen-containing heterocyclic molecules, which can form an intramolecular H-bond with N, O, or S atoms, and thus can exist in two tautomeric forms (NH and XH) (Figure 13). It was
Figure 14. Scheme of alkyl (a) and aryl (b) Schiff bases.
the proton located almost at the midpoint of the hydrogen bridge; moreover, these interactions can be regarded as lowbarrier hydrogen bonds (LBHB).300 In aryl Schiff bases studied in the gas phase, the OH form is dominant, unlike in the case of alkyl ones. However, in the solid state and solution, either both tautomers exist in almost equal proportions or the NH tautomer is preferred.256 The tautomerism of Schiff bases can be affected by many intra- and intermolecular factors (π-electron delocalization, intramolecular hydrogen bond, and effect of substituent, polarity of the solvent, temperature). Recently, it was documented that an increase in π-electron delocalization in the chelate ring (quasi-aromatic ring, Figure 16, ring B) is associated with a decrease of π-electron delocalization in the adjacent aromatic ring (Figure 16, ring A) and consequently its increase in the distant aromatic ring (Figure 16, ring C).296−300 Similar trends were observed for aryl-300 and alkyl-296 Schiff bases (Figures 17 and 18, respectively). The theoretical study of the tautomeric equilibria and proton transfer process in Schiff bases was supplemented by experimental investigations (X-ray diffraction, UV−vis, FT-IR, and NMR spectroscopy).297,300,303,304 Moreover, for (E)-2ethoxy-6-[(2-methoxyphenylimino)methyl] phenol, the influence of temperature on the proton transfer phenomenon was studied.300 The crystal and molecular structures were determined at 296 and 100 K (X-ray measurements); the results obtained confirmed the coexistence of OH and NH tautomers at 296 K, whereas the OH form dominated at 100 K (DFT calculations in the gas phase predict this form as more stable than the NH one). The influence of temperature on the aromaticity of individual rings was observed. It was found that the charge transfer from the phenol ring to the pseudoaromatic chelate ring increases with increasing temperature, whereas the π-electron transfer from chelate ring to the phenyl ring decreases under the same conditions. In a general case, it can be concluded that neither aromaticity nor a hydrogen bond can be considered the absolute criterion allowing the tautomeric preferences for Schiff bases to be determined, and they should always be considered together.302 An interesting case of tautomeric equilibrium with competing RAHB in 1,3-dicarbonyl compounds was discussed using the 2(pyridin-2-yl) and 2-(quinolin-2-yl) derivatives as an instructive example305,306 (Figure 19). The most stable tautomer is always enaminone (form d), which exhibits the most effective
Figure 13. Tautomerism in N-containing heterocycles, (a) NH tautomers and (b) XH tautomers (X = O, NH, and S).
concluded that tautomeric preferences depend on two factors: aromaticity of the heterocycle and relative proton affinities of two heteroatoms participating in the H-bond. These results demonstrate that the N−H···N bond is the strongest for NH tautomers, while heteronuclear hydrogen bonds are stronger than homonuclear ones for XH tautomers due to the change in proton affinities of the nitrogen atom in the ring. Among systems with heteronuclear RAHB alkyl296 and aryl,79,297−304 Schiff bases were the most frequently studied. In their quasi-aromatic rings, a proton transfer from the hydroxyl group to the imine group, through the O−H···N and O···H−N hydrogen bonds, takes place (Figure 14). In these compounds, π-electron delocalization was investigated by HOMA, HOSE, and other structural aromaticity indices, as well as in rare cases by NICS index, QTAIM, and NBO parameters. Two forms of tautomers exist for Schiff bases: enolimine (socalled OH-form) and enaminone (NH-form); see Figure 15. The transfer from one tautomeric form to the other goes through a transition state, which is stabilized by the hydrogen bond. The strongest intramolecular H-bonds were observed for 6405
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Figure 15. Tautomeric equilibrium in o-hydroxy Schiff bases.
Figure 16. Description of the ring types in Schiff base (A, phenol ring; B, chelate ring; C, phenyl ring).
delocalization and the strongest hydrogen bond. The HOMA values for the pyridine ring in the enaminone tautomers of pyridine and quinoline derivatives are in the range of 0.86−0.90 and 0.64−0.76, respectively. When considering 1,5-bis-substituted derivatives of pentane2,4-dione, the symmetric dienol (for pyridin-2-yl derivatives, Figure 20a) and dienaminone (for quinolin-2-yl derivatives, Figure 20b) forms were found to be the most stable. However, simple correlations between the aromaticity, strength of hydrogen bond, and stability of tautomers were not observed.307,308 Nevertheless, for all cases, the relatively high aromaticity of quasi-aromatic rings, which are formed by intramolecular hydrogen bonds (HOMA > 0.5), shows that these bonds are of RAHB type. Derivatives of 1,2-diketones with such substituents as pyridines or quinolines can exist in numerous tautomeric forms due to the formation of intramolecular hydrogen bonding.309−311 The most stable of these are presented in Figure 21: enol/enaminone and dienol forms, a and b, respectively. According to the theoretical results, tautomer a predominates in vacuum and in chloroform solution. The aromaticity, in combination with hydrogen bonds, is responsible for this preference. As can be seen from the HOMA values, the right part of tautomer a follows the topology of a phenanthrene-type fragment with a less aromatic inner ring. Tautomer b contains
Figure 18. Scatter plot of HOMA index versus the OH bond distance, d(OH), for the chelate chain of alkyl Schiff bases; ○, □, and △ correspond to the OH, transition state, and HN forms, respectively. Reprinted with permission from ref 296. Copyright 2012 Springer Science and Business Media.
only a naphthalene-like fragment,311 with the quasi-aromatic ring of relatively lower aromaticity, as compared to the case of a tautomer. The aromaticity indices can be applied not only for typically aromatic systems. For example, the tautomerization of chalcocyclopentadienes (CpXH, X = O, S, Se, Te; see Figure 22) was investigated by means of several indices including magnetic (NICS), structural (HOMA), and electronic (FLU) ones.312 These compounds can exist in a form of three isomers: 1-, 2-, or 5-substituted. Two rotamers are possible for 1- and 2derivatives, leading to the keto−enol tautomeric equilibrium. According to theoretical estimations, independent of the nature of heteroatom, asymmetric 2-cyclopenten-1-one (b in Figure 22) is the most stable. For 5-substituted 1,3-cyclopentadienes, an increase of stability and aromaticity is observed when going from O to Te: HOMA is equal to 0.13 for the O-derivative,
Figure 17. Dependence of HOMA values of the adjacent rings involving proton transfer (a) and anisole ring (b) against the scan coordinate d(O− H). Reprinted with permission from ref 300. Copyright 2010 Springer Science and Business Media. 6406
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Figure 19. Tautomeric equilibrium in 2-(quinolin-2-yl) derivatives of 1,3-diketones.
Figure 20. Tautomeric equilibrium in 1,5-bis(pyridin-2-yl)pentane-2,4-dione.
Figure 21. Preferred tautomers for derivatives of 1,2-diketones and their HOMA values. Data taken from ref 311.
Figure 22. Possible tautomeric form in chalcocyclopentadienes (X = O, S, Se, and Te).
Figure 24. Preferred tautomeric structure of the nucleobases with numbering of atoms.
whereas it amounts to 0.39 for the Te one. This effect is connected by a decrease in electronegativity of the heteroatom and a change of the electron donation from the C−X bond to the five-membered ring. However, these derivatives are the least stable tautomers, except for the Te ones.312 For diaza-substituted cyclopentadienes with extra heteroatoms (O or S) in the ring (Figure 23), similar trends are
despite the fact that CH tautomers are also present in tautomeric mixtures. In addition, adenine can participate in amino−imino equilibrium, thymine and uracil in keto−enol ones, and guanine and cytosine combine both tautomerism types. The data from earlier research on tautomerism in nucleic acid bases are collected and discussed in two reviews.256,313 For adenine, 14 possible tautomers are known: 12 “classical” and 2 unusual zwitterion-like structures (Figure 25).314 The
Figure 23. Tautomeric equilibrium of diaza-substituted cyclopentadiene derivatives (X = O, S; Y = O, S).
observed.170 The oxo and thione tautomers are more stable than the hydroxyl and thiol ones. Aromaticity is not a key factor of tautomeric preferences in these compounds because the stabilization due to the carbonyl or thiocarbonyl functional group has a greater effect. On the basis of the values of the HOMA index, it can be concluded that sulfur-containing compounds are more aromatic than their oxygen analogues.170 An increase in aromaticity when oxygen is replaced by sulfur is also found for thiosubstituted maltol (3-hydroxy-2-methyl-4H-pyran-4-one), which prefer the tautomers with the enol group.185 The prototropic tautomeric equilibria in nucleobases (Figure 24) have been subject of intensive studies for a long time. Recently, experimental techniques have been improved, and the tautomeric mixtures have been reinvestigated. The annular tautomerism is common to all nucleobases, but only NH and OH tautomers have been considered to date,
Figure 25. Rotamers for zwitterionic form of adenine.
9H-amino tautomer is more stable in all phases. In the gas phase, the energy gap between the canonical 9H-structure and the less preferred 7H- and 3H-tautomers is about 7.5 kcal/mol, while this gap is reduced to 2.5 kcal/mol in water, but the order of stability is retained; 7H- and 3H-tautomers are energetically very close.314−316 Theoretical results are in agreement with experimental data.317−320 It is also found that the 9H,1H+ form of adenine (9H adenine protonated at the position N1) dominates in water along with the 9H and 7H ones.321−323 Among all nucleic acid bases, guanine has the largest number of tautomers, 36 including rotamers.324 According to theoretical and experimental results, two keto−amino forms (7H and 9H) are dominant in the gas phase.325−327 Two enol forms of 9H 6407
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tautomer stabilities for this molecule.341,342 The same conclusion can be drawn for uracil and 2-imidazolone.342 In this case, HOMED values are larger for the OH forms and lower for the CH tautomers. The HOMED index was used not only to describe the πelectron delocalization in cyclic compounds, but also for the estimation of the delocalization changes in some acyclic tautomeric systems. Pyruvate and oxamate tautomers (lactate dehydrogenase substrate and inhibitor, respectively), their radicals,111 protonated forms, and adducts111,112 can be considered here as instructive examples. In the case of pyruvate and oxamate anions and radicals, HOMED values for the OCO fragment are close to 1. This indicates a very strong electron delocalization in this fragment. The situation for the CCO and NCO groups is different, where HOMED estimations depend on the tautomeric form of the system. The HOMED values are the lowest for σ−π conjugated systems. It should be stressed that for pyruvic and oxamic acid, the delocalization in the OCO fragment is weaker than in its deprotonated form.112 The most stable amide and iminol tautomers of oxamic acid were also investigated.344 HOMED values between 0.5 and 1.0 are typical of n−π conjugated fragments.344 The HOMED index was also discussed for keto−enol tautomers of neutral and ionized forms of pyruvic acid and acetaldehyde. In both cases, the enol form shows higher π-electron delocalization than the keto form. Ionization of the keto forms of both systems leads to a decrease in the π-electron delocalization, but for the enol forms, the delocalization is significantly increased in the anionic form. HOMED values for neutral and ionized species indicate that the enol forms exhibit, in general, a higher degree of delocalization than the keto tautomers.345,346 In summary, for simple molecules, aromaticity is the main factor determining the tautomeric preference in the mixture. The next but no less important factor is the intramolecular hydrogen bonding, which stabilizes a given tautomeric form. However, for complex systems there are more internal and external factors, which are decisive for the stability of the dominant tautomer.
guanine (cis and trans) are energetically very close to the 9H keto one. All four tautomers were observed experimentally.328 However, in aqueous solutions and for hydrated polycrystalline guanine, the 9H keto−amino tautomer is the most favored species.329,330 Cytosine, like adenine, has 14 possible tautomers. Results of theoretical calculations suggest that, in solid state as well as in aqueous solutions, only the canonical 1H keto−amino form is present.331 However, experimental studies have proven that two rotamers of the 2H enol form and the 1H keto−amino form are the most stable in the gas phase.332,333 Moreover, experiments on cytosine in Ar matrixes (and irradiated with monochromatic UV laser light) allowed the presence of keto−imino isomers to be identified in the tautomeric mixture.334,335 Investigations of thymine tautomers show that it can exist in the form of 13 tautomers/rotamers. The 1H,3H-diketo tautomer is the most stable in the gas phase, solution, and solid state, similar to uracil.336,337 It was proven experimentally that in the tautomeric mixture only one diketo form is present.338,339 Moreover, the replacement of O4 in thymine by Se does not change the tautomeric equilibrium.340 Although the tautomeric equilibria of nucleobases, their analogues, and derivatives have been widely studied, the influence of aromaticity on the preference and stability of their tautomers has not been studied in detail. The aromaticity of some nucleobase tautomers was estimated by Cyranski et al.199 The results showed that for such complex systems as nucleobases, there is no simple relation between the π-electron delocalization and the stability of tautomers. Recently, the four more stable tautomers of purine were investigated in terms of aromaticity and H-bonding.197 It was found that tautomeric preference and aromaticity decrease in the following order: 9H > 7H > 3H > 1H, resulting in a decrease of the HOMA values from 0.92 to 0.78. Moreover, the presence of intermolecular interaction by H-bonding does not change this sequence. The aromaticities of uracil and uric acid (product of the metabolic breakdown of purine nucleotides) tautomers were also estimated by HOMA and HOMED indices.280,284,285,341,342 Tautomeric equilibria of uracil are represented by 18 possible tautomers/rotamers, but theoretical and experimental investigations indicate that, among them, the 1H,3H-diketo form is the most stable.285,339,343 However, it was found that πelectrons are less delocalized in this form (HOMA for the ring is equal to 0.697) than in the case of rare dienol forms (HOMA values for the pyrimidine ring of these forms are greater than 0.990). In all of the remaining tautomers of uracil, the πelectrons are less delocalized. Among them, in CH tautomers, this delocalization is the least pronounced (HOMA values of the both types are lower than 0.5). Their aromaticity was estimated by HOMA and HOMED indices for pyrimidine ring and for the whole system;284,285 values of the latter index are given at the beginning of this section. It should be noted that aromaticity is not the main factor influencing stabilization of the diketo form. Other factors should also be taken into account, such as interactions between functional groups and their stability, which can affect the tautomeric preference as well. A similar trend is observed for the radical cation form of uracil, in contrast to its radical anion, which adopts the amide form.280 For different tautomers of uric acid, HOMED values are not larger than 0.9 for the six-membered ring and not larger than 0.7 for the 2-imidazolone fragment, as well as for the whole system. HOMED values are not directly connected with
4.5. Aromaticity of Metal Complexes and Chelate Rings
There are many possible types of interactions of metal atoms/ ions with aromatic systems. Here we present two of them: (i) Chelating systems in which metal ions M+ are involved in the interaction described by X−M+···Y where X,Y are N or O, and M+ is a metal cation. Formally, this kind of system is formed when three sequential CH units in an aromatic system are replaced by X−M···Y. These kinds of systems may be related to molecules in which H+ is replaced by a metal cation in the intramolecular Hbonding. Such rings are termed quasi-aromatic, because a substantial π-electron delocalization is observed for the chain of heavy atoms with π-electrons (XCCCY). In the case of H-bonded systems, this phenomenon was summarized by the Gilli RAHB concept of H-bonding.75 (ii) Through-space interactions between metal atoms/ions and π-electron rings leading usually to an increase of aromaticity of the ring in question. It was shown for malonaldehyde and its Li+ bonded analogue, as well as for the anionic form (after deprotonation),78 that the metal bonded complex always shows higher delocalization than the H-bonded neutral system and the deprotonated anion. This was demonstrated by means of 6408
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by means of aromaticity indices: HOMA, NICS, FLU, and PDI. It was shown that complexation of anions increased aromaticity of the ligand, and the chelato-aromatic ring effect stabilized the metal complexes.349 B3LYP/6-311++G** studies on the structural parameters and intramolecular H-bond in substituted (Z)-N-(thionitrosomethylene) thiohydroxylamine systems revealed a very good correlation between the hydrogen-bond energy and HOMA of the chelating chain.350 A good correlation was also found between HOMA and AIMparameters G and H energies estimated in the BCP of the hydrogen bond. If the quasi-aromatic ring may exhibit (quasi)aromatic characteristics, it should also behave in a manner similar to a typical aromatic ring. In fact, it was reported that the quasiaromatic ring may, in some situations, adopt the role of a typical aromatic ring influencing in this manner the properties of the polycyclic aromatic hydrocarbons (PAH), as if it acted as a benzene ring.351 Among the many cases presented, a good and the simplest example is the naphthalene derivative shown in Figure 27.
HOMA index for a series of Cl-substituted derivatives. Figure 26 shows a graphical interpretation of the obtained results.
Figure 26. HOMA values for variously substituted derivatives of Libonded malonaldehyde analogue (LiA), its anionic form (A−), and neutral malonaldehyde (HA). Reprinted with permission from ref 78. Copyright 2005 Springer Science and Business Media.
Later, ortho-hydroxy Shiff bases were investigated in the same context, and the H-bonded and deprotonated forms were compared to the metal-bonded forms in which the H+ center was replaced either by Li+ or by BH+ ones.79 Again, it was demonstrated that the metal-bonded quasi-aromatic rings were characterized by a relatively higher degree of delocalization than the H-bonded systems and anions. This was concluded on the basis of HOMA index and Q parameter introduced by Gilli et al.75 It is worth mentioning that a good correlation between HOMA and Gilli’s Q parameter (see section 3.7) was found for a large series of molecular systems. Because the discussed metal complexes systematically show higher delocalization than their anionic counterparts, the contribution of the metal center to the π-electron delocalization in Li-bonded quasi-aromatic rings could be considered important. In other words, it could be concluded that πelectrons in metal complexes are more delocalized than in isolated anions due to a contribution of the metal center to the cyclic aromatization. Nevertheless, when the induced ring currents in Li-bonded analogues of malonaldehyde were investigated,347 it was shown that, in fact, the Li-center does not contribute directly to the π-electron delocalization, but instead a relative increase of the delocalized character of the quasi-aromatic ring occurs due to electrostatic interactions between the malonaldehyde anion (or its analogue) and the metal cationic center. This conclusion was confirmed for a large group of chelate rings, containing transition metal centers, including Ni2+, Pt2+, Os2+, Rh3+, Ir3+.348 It was demonstrated that the NICS index calculated for the chelate rings indicates a rather small aromaticity of these rings. However, some important exceptions were found for which a significantly aromatic character of the quasi-aromatic ring was noticed. It was concluded on that basis that aromatic metal-bonded quasiaromatic rings can exist for certain specific metal centers and ligands. The complex of Ru2+ with o-benzoquinonediimine ligand is an example of that type. Also, it is worth mentioning that, for these complexes, a relatively good relation between NICS and HOMA (calculated for the organic fragment merely) was reported. Aromatic properties of 8-hydroxyquinoline, its cation, anion, and complexes with Mg2+ and Al3+ were studied
Figure 27. Example of metal complexes of PAHs with quasi-aromatic rings partially adopting the role of typical aromatic ring.
It was found that in system a, shown in Figure 27, the aromaticity is similar for the benzenoid rings II and III and close to that in naphthalene itself (see Table 10 for HOMA Table 10. HOMA Values Estimated for Individual Rings and quasi-Aromatic Rings in Systems Shown in Figure 27a system a b
type of quasi-aromatic ring
HOMA for I
HOMA for II
HOMA for III
H-bonded Li-bonded H-bonded Li-bonded
0.17 0.43 0.42 0.73
0.78 0.65 0.69 0.40
0.74 0.72 0.82 0.86
The ring numbering is consistent with that figure. HOMA values given for H- and Li-bonded analogues. Data taken form ref 351. a
values). However, in system b, there is a noticeable difference in the aromaticity of both benzene rings, with a more aromatic character of the ring III. Also, the quasi-aromatic ring in b was more aromatic than the same ring in a (Figure 27). Such differences in aromaticity of particular parts of the systems consisting of identical fragments but in different arrangements (purely topological differences) have been explained in view of the Clar aromatic sextet.128,129 The direct analogy of a to anthracene with all three benzenoid rings of relatively similar aromaticity degree (the Clar migrating sextet) and of b to phenanthrene with significantly more aromatic lateral rings (being the Clar localized sextets) allows the confirmation that 6409
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quasi-aromatic rings may in fact adopt the role of typical aromatic ring.291 It is worth noting that similar conclusions were drawn for H-bonded quasi-aromatic rings232,236 (also see data in Table 10). Another interesting example of the situation when the quasiaromatic ring adopts the role of a typical aromatic ring can be quoted here. It is generally known that aromatic rings may interact through the space forming the so-called stacking interactions (see, e.g., ref 352). It was reported that the chelate rings may form complexes via stacking interactions with benzenoid rings.353 Such intermolecular interactions were found in crystals of planar copper(II) complexes. Clear relations between geometric parameters characteristic of the stacking interactions were reported on the basis of CSD search.77 Unfortunately, in the paper by Tomic et al.,353 the aspects of stacking interactions with the contribution of chelate rings were not investigated in the context of the π-electron delocalization. It is also worth mentioning that, very recently, similar stacking interactions were reported for H-bonded chelate rings.354 As mentioned earlier, in metal-bonded malonaldehyde analogues, the aromatic character of the quasi-aromatic ring is not increased as a consequence of the direct orbital mixing, but rather owes it to the through-space stabilizing interaction between the organic moiety (anion) and the metal center (cation).347 The influence of the metal center on the aromaticity of π-type ligands was also investigated. It was reported that the metal center may in fact significantly change the degree of π-electron delocalization within the ligand. Fulvene, acting as a π-type ligand in lithium complexes, can be considered here as an instructive example.355 It was reported there that the fulvene moiety forms a stable complex with a formally neutral Li atom. The complexation energy is about 41 kcal/mol. What is interesting is that a clear increase of the aromatic character of the five-membered fulvene ring due to complexation was observed and documented by HOMA and other indices and by a strong diatropic ring current, visualized by ipsocentric calculations.356 The Li atom is a well-known electron-donating center, which, when interacting with fulvene, increases the electron population on p-type orbitals of the fulvene ring. Because this ring can be considered a 4n+1 πelectron cycle, its aromaticity should increase due to an increase in the charge within the ring leading to the magic 4n+2 number of the π-electrons. The changes in aromaticity expressed as a function of Li−fulvene ring distance clearly support this explanation. Later, the analogous complexes formed by fulvene and other metal centers (such as Be, Mg, Ca, Sr, and Ba) were investigated by means of computational approach.357 Again, a strong aromatization of the fulvene ring due to complexation was reported. Additionally, the population analysis made in the framework of NBO theory (NEDA358) indicates a 1.6−1.8 e charge flow from the metal centers to the fulvene ring, supporting the concept of aromatization of the ring by the change of the 4n+1 π-electron structure to a 4n+2 π-electron one. An interesting and closely related example is the COT ring, which is nonplanar in its ground-state conformation, but very often undergoes planarization when it acts as a π-type ligand, for example, in uranocene. Usually, such planarization is explained by aromatization of the antiaromatic ring due to a change from the 4n to the 4n+2 Hückel structure, as a result of charge transfer from the metal center to the COT ring.359−361 However, it was recently shown by means of CSD search and
quantum-chemical calculations that COT planarization in metal complexes is not necessarily connected with its aromatization.362 Also, the bond alternation parameter defined in that case as ΔR CC =
1 n
n
∑ |R̅ CC − R i| i=1
(37)
where RCC were the CC bond lengths in COT ring (in the original paper, the bond length was denoted by d), did not correlate with the HOMA aromaticity index. The lack of correlation with HOMA was also reported for geometry-based parameters describing the planarization of COT. Thus, the explanation of the planarization of COT due to charge transfer from the metal to the COT ring and the change of the πelectron structure from 4n to 4n+2 is not so obvious in that case. Theoretical studies performed for selected model systems allowed the conclusion to be drawn that the main factor affecting the COT geometry in its complexes with metals is the efficiency of the metal center−COT interaction. The aromatization in such cases, usually considered the effect of leading importance, in fact seems to be rather a background effect. Also, the interpretation of ring currents produced for COT leads to the same conclusion. The COT derivatives planarized in various ways clearly show that such planarization does not in fact lead to the presence of diatropic ring currents, which is characteristic of aromatic cycles.363,364 Later, this conclusion was supported by more detailed studies based on quantum-chemical calculations performed for COT2− anion.365 It was proven that COT2− is in fact an unstable virtual moiety, which should not be observable in experimental conditions. If a properly advanced quantum-chemistry model is used for the description of the COT dianion, it evolves to a neutral COT ring (tub-shaped, not planar), which interacts with two free electrons. 4.6. Testing New Aromaticity Parameters
As was already mentioned in the Introduction, aromaticity is one of the most important concepts in organic chemistry. Beginning with the original work by Katritzky et al.,27 it has also been demonstrated in several subsequent studies that aromaticity is a multidimensional property.16,31−33 Therefore, new attempts are still being reported in which the authors analyze the aromaticity term and propose some new, local and global (presumably more general and more universal), aromaticity measures. Their ability to describe π-electron delocalization changes is checked with the existing aromaticity indices used. Because mutual relations between different aromaticity parameters strongly depend on the selection of the molecules under investigation, the use of more than one index for comparisons is recommended.33 Below, several new indices are chronologically presented, which were tested using geometrical criteria of aromaticity. The main sources of new measures of aromaticity are various quantum chemistry approaches, enabling an increasingly better description of the electronic structure of a given system. Undoubtedly, the latter is closely related to the geometric structure of the molecule. In 2000, Giambiagi et al.366 proposed a multicenter index, Iring, involving the total (σ and π) electron population, as a measure of aromaticity. The index was an extension of the bond index IAB, proposed earlier by the same authors,367 who generalized the Wiberg bond index368 to nonorthogonal bases. Iring was applied to differentiate between aromaticities of 6410
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membered rings, ΔDI index was proposed, which is defined as the difference between delocalization indices for double and single CC bonds. Therefore, ΔDI is a measure of the deviation with respect to a bond equivalent system, and its value increases when the aromaticity is reduced. A good correlation between ΔDI and NICS values was observed, with the sole exception of the cyclopentadienyl cation. An undoubted advantage of all of the above-mentioned indices is the ability to use them as local aromaticity probes in large systems consisting of fused five- and six-membered rings, for example, fullerenes.372 In the case of benzenoid systems that are described by a superposition of Clar structures, PDI and HOMA parameters provide local aromaticity values that are fully consistent with Clar’s rule.231 Also in 2003, the delocalization index was used to define an aromaticity index, θ, which is similar to the geometric HOMA parameter. The delocalization index was applied as a measure of alternation in the delocalization of electrons within a ring of a given PAH.373,374 The θ index is based on delocalization of the Fermi hole density; therefore, it is also known as the Fermi hole density delocalization (FHDD) index. To calculate θ, it is necessary to use the delocalization indices (DIs) used to count the number of electron pairs shared between bonded atoms. It was shown that DI values can be interpreted as a measure of the bond order. An empirical normalization constant (equal to 2.4312)374 was chosen to give θ = 0 for cyclohexane. In benzene, θ is equal to 3.0170. This value originates from a reference value embracing the total electron delocalization between a carbon atom in the given molecule and all remaining C atoms in the ring.373 The proposed local aromaticity measure was correlated with HOMA and NICS. The θ index was found to show a similar trend as the independent measure of aromaticity provided by HOMA. The aromatic fluctuation index (FLU),251 describing the fluctuation of electronic charge between adjacent atoms in a given ring, was introduced in 2005. This new aromaticity measure is based on the fact that aromaticity is related to the cyclic delocalized circulation of π electrons; FLU measures weighted electron delocalization divergences with respect to typical aromatic molecules, which means that it requires the use of reference parameters; FLU is a dimensionless quantity, it can be applied to analyze both local and global aromaticity; its value is close to zero for aromatic systems and it differs from zero for nonaromatic ones. Matito et al.251 demonstrated that the FLU index and its π analogue, the FLUπ descriptor, are simple and efficient probes of aromaticity. For a series of 15 planar PAHs, FLU and FLUπ correlate well, with only a few exceptions, with other already existing independent local aromaticity parameters, such as HOMA, NICS, and PDI indices. In contrast to PDI, the FLU index can be applied to study the aromaticity of rings with any number of atoms. All of the above-mentioned indices were used to follow the changes of local aromaticity in a series of polyfluorene compounds with the increasing number of πstacked layers.375 The obtained values of HOMA, PDI, and FLU parameters indicate that the local aromaticity of the aromatic and nonaromatic rings of polyfluorenes remains unchanged when going from one to four layers of the π-stacked rings. Additionally, the obtained ASE values confirm the above characteristics. On the contrary, the calculated NICS values indicate a reduction of the aromaticity of π-stacked rings with a decreasing number of layers, whereas the opposite tendency was observed on the basis of experimental 1H NMR chemical shifts. Therefore, it can be concluded that the changes in local aromaticity in the superimposed aromatic rings indicated both
particular rings in cyclic conjugated hydrocarbons (both benzenoid and nonbenzenoid rings), azines, benzoazines, and heterocycles with five-membered rings. The values of Iring were compared to various different indices, among others, with HOMA and Bird’s aromaticity index IA. For benzene and naphthalene, Iring is equal to 0.0883 and 0.0499, whereas HOMA amounts to 0.990 and 0.777, respectively. The correlation between Iring and HOMA for all of the benzenoid hydrocarbons considered yields R2 = 0.7269. However, if coronene is excluded, R2 increases to 0.8216. In the case of fivemembered ring heterocycles, both Iring and Bird’s index I5 agree in assigning the lowest aromaticity to furan derivatives, in comparison with pyrrole and thiophene ones. The authors concluded that the multicenter bond index gives satisfactory values for monocyclic molecules and is quite suitable in distinguishing the relative aromaticity of different rings in polycyclic compounds. Recently, a normalized version of the Iring was proposed, and named ING, which was expected to be less dependent on the ring size than its unnormalized analogue.181 In 2001, Sadlej-Sosnowska,173 exploiting electronic properties evaluated on the basis of the NBO theory,369 introduced a new π-electron delocalization parameter as the root-mean square of π-electron density (pz) localized on the atoms of the five-membered tetrazole ring, abbreviated as SDn. The SDn values obtained were compared to HOMA, Bird’s I5, the minimum bond order in the ring (BOmin),271 NICS, and ASE aromaticity parameters. For two tautomeric forms of 10 tetrazole C5-substituted derivatives, the structural and electronic aromaticity indices were found to be well intercorrelated; for example, the correlation coefficient between HOMA and SDn is −0.820. Moreover, it was also stated that the electronic delocalization can be equally well described by two additional electronic parameters: the extent of the transfer of electron density from the pz orbital of one nitrogen to the rest of the π electron system (LP) and the population of the two antibonding π* orbitals (BD*); correlation coefficients of HOMA against LP and BD* amount to 0.973 and 0.902, respectively. Therefore, the information provided by the electronic parameters was found to be similar to that contained in the geometric aromaticity indices, excluding the case of tetrazole substituted with −BH2. The para-delocalization index, PDI,370 was introduced in 2003 as a new local aromaticity measure. It was defined as a mean value of all delocalization indices (DI) estimated for pararelated carbon atoms in a six-membered ring. The physical meaning of DI can be explained as the number of electron pairs shared by atoms A and B; its definition comes from the quantum theory of atoms in molecules (QTAIM).252,371 A comparison between PDI, HOMA, and NICS indices for planar PAHs was used as an indication of the usefulness of PDI as an aromaticity measure. Additionally, for planar polycyclic hydrocarbons, PDI values can be separated into σ and π contributions. The values of PDI and PDIπ obtained for sixmembered rings are in the range of 0.025−0.101 and 0.019− 0.093, respectively, whereas σ contributions (obtained as the difference between PDI and PDIπ) have been omitted as they are quite constant along the series (they amount to ca. 0.008 electrons). Benzene was found to be the most aromatic sixmembered ring of the studied series according to both HOMA and PDI indices. Moreover, these indices give almost the same order of aromaticity for the analyzed six-membered rings, with a few exceptions. The same applies to PDIπ. In the case of five6411
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by NICS and by 1H NMR are not real, but result from the coupling between the magnetic fields generated by the πstacked rings. In 2005, Bultinck et al.,376 following the work of Giambiagi et al.366 on Iring, proposed a new multicenter bond index (MCI).377 For benzenoid rings, this index is known as the six-center bond index (SCI). It was used for the quantitative characterization of aromaticity in PAHs. Their approach characterizes the extended delocalized bonding, which is generally considered one of the typical manifestations of aromaticity. For the studied set of benzenoid rings, a tight correlation between SCI and Iring parameters was found (R2 = 0.9991). The usefulness of SCI as a measure of aromaticity was confirmed by comparison with other previously reported aromaticity parameters: HOMA, NICS, and PDI. In the case of relation between SCI and NICS, the correlation was observed only within a narrow series of closely structurally related compounds. Therefore, the obtained results were found to be consistent with the orthogonality of structural and magnetic criteria of aromaticity.27 Additionally, the authors introduced a bond order index of aromaticity (BOIA) as a πelectron delocalization measure. In BOIA, which is closely related to HOMA, bond orders were used instead of bond lengths. Therefore, their mutual correlation is not surprising. Even better correlation was found between SCI and BOIA indices. Additionally, a normalized version of the MCI index, so-called INB, has recently been reported.181 Suresh and Koga,378 in 2006, proposed a new energetic scale of aromaticity, Earoma, for a large spectrum of organic molecules, which uses the energetics of radical-based isodesmic reactions. The Earoma values showed a good agreement with HOMA, NICS, MESP, 379 and ASE. The obtained correlation coefficients exceeded 0.91. It should be stressed that Earoma measures the global aromaticity; therefore, its comparison with NICS should be performed only for single ring systems. Some borderline cases of aromaticity, antiaromaticity, and nonaromaticity were also classified in the new aromaticity scale; Earoma allows the comparison of the aromaticity of molecules different from benzenoids. In 2007, QTAIM parameters at the ring critical point (RCP) were tested253 to describe the local aromaticity of carbocyclicand quasi-aromatic rings. For this purpose, a set of 33 benzenoid rings (characterized by varying aromaticity) and a set of 20 quasi-aromatic rings (formed by intramolecular hydrogen or lithium bonds) were taken into consideration. The parameters obtained were correlated with HOMA and NICS to check their usefulness to characterize aromaticity. A particularly good correlation was found for the density of the total electron energy at the RCP (HRCP); calculated correlation coefficients amounted to ca. 0.95. Therefore, HRCP was proposed as a new (and easy to estimate) quantitative characteristic of π-electron delocalization. In 2009, Oziminski and Dobrowolski220 proposed two independent substituent descriptors: σ and π electron-donor− acceptor (sEDA and pEDA, respectively), based on the natural population analysis approach. Subsequently, it was found that the pEDA index correlates with HOMA and NICS parameters;243,250,357,380 therefore, in some cases, it can be used to measure aromaticity changes. In 2010, Vijayalakshmi and Suresh131 used a topological feature of the molecular electrostatic potential (MESP) for a series of PAHs to study a relationship between π-electron distribution and Clar’s aromatic sextet theory. The MESP
values support Clar’s theory numerically; MESP maps provide its useful pictorial representations. Moreover, the MESP at the RCP (VRCP) for the π-region of each ring are found to be a good local measure of aromaticity; a linear correlation of VRCP with HOMA and HRCP was obtained. In the same year, Noorizadeh and Shakerzadeh381 introduced a new index of aromaticity, Shannon aromaticity (SA), based on the electron delocalization derived from the QTAIM theory, using the Shannon entropy concept in information theory. The SA was defined as the difference between the evaluated total Shannon entropy (anticipated for a fully aromatic molecule) and the expected maximum entropy for a given ring. Therefore, a more aromatic ring has a smaller SA value. The SA index was tested for a set of chosen compounds (including: fivemembered heterocyclic, monosubstituted benzenoid rings, nonbenzenoid systems, acenes, and others). The SA values obtained were compared to ASE, magnetic susceptibilities, NICS, HOMA, and PDI parameters. Good correlations were observed between SA and some earlier defined descriptors of aromaticity. For 70 mono-exo-cyclically tria-, penta-, and heptafulvene-substituted derivatives, the best correlation was observed between the SA and HOMA indices.382 Recently, in the case of aromatization of the pentafulvene ring by approaching alkali metal atoms, good mutual correlations were observed between SA, HOMA, and pEDA parameters.383 In 2011, Monza and co-workers384 defined a source function local aromaticity index (SFLAI), by using the source function (SF) tool to describe the electron density. The SF385 quantifies the influence of each atom in a system by determining the amount of electron density at a given point, regardless of the position of the atom with respect to this point (more or less remote). The SFLAI as a new measure of local aromaticity was tested by using HOMA, PDI,370 FHDD,373 and BOIA376 indices. An excellent correlation of SFLAI with FHDD373 (based on the delocalization indices) was found. A peculiar feature of the SFLAI index is its potential applicability to both theoretical and experimental electron densities. In 2012, the EL index was presented as a new aromaticity measure.386 Ellipticity of a bond, a quantity that numerically reflects to which extent a given chemical bond has elliptic crosssection (presumably of a more double character), and HOMAlike formula were used to define the EL parameter. The obtained EL values were compared to the other aromaticity indices calculated, such as HOMA, PDI, FLU, and NICS. It was shown that the indications of EL were in agreement with the indications of other indices and with general expectations. As the ellipticity is available from calculations based on oneelectron density function, the EL index can be applied to both theoretical and experimental data. In 2013, a new aromaticity index based on π-orbital energies was postulated.387 The values obtained for 14 molecular systems, including five- and six-membered heterocyclic πelectron rings as well as benzene, were compared to ASE and Bird’s I aromaticity parameters. However, a good agreement was found merely for the part of investigated systems. Very recently, in 2014, the aromatic delocalization index (AI) as a new approach to determine π-electron delocalization was presented for anthracene and phenanthrene.388 AI, a consecutive HOMA-like parameter, is based on experimental vibrational frequencies. Another approach describing the aromatic character of πelectron systems is based on natural resonance theory (NRT)389−391 and NBO theory.369 Weinhold and Landis369 6412
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aromaticity indices (stabilization energy, diamagnetic susceptibility, NICS, NICS(1), and HOMA) for five-membered heterocycles (103 molecules) were used. The trained Kohonen network was applied to classify three five-membered rings and five six-membered rings, that is, compounds that were not used for the training of the neural network. The SOM was found to be able to cluster an extensive data set into three classes: aromatic, nonaromatic, and antiaromatic. The weighted distance of the SOM allowed quantification of the degree of aromaticity associated with each molecule. Moreover, the relationships between different compounds are visualized on a two-dimensional map in a straightforward manner. The position of a compound in the map depends on its aromatic character; therefore, a new quantitative scale of aromaticity was established, based on Euclidean distances between neurons. Further, Alonso et al.177 successfully applied neural networks in the study of the substituent effect on the aromaticity for a set of pyrimidine derivatives with potential push−pull character. Moreover, the interplay between aromaticity, planarity, steric effect, and charge transfer properties of all substituted pyrimidine derivatives was demonstrated.
stressed that the NRT and NBO methods provide an optimal description of orbital composition or electron-density distributions based directly on the first-order density operator. NRT resonance weights, which allow one to determine resonancestructure contributions, and analysis of natural bond orders are frequently used to characterize the electron delocalization in molecules.34,179,392−396 Moreover, the latter can serve as a theoretical alternative to bond orders obtained by applying Gordy’s equation, eq 4. Very recently, NBO-based Bird’s indices (NBO-I6) were compared to I6 for heterocyclic analogues of benzene;34 only in the case of C5H5SiH was a dramatic difference found (the obtained values were 73.2 and 20.7, respectively). With the exception of the energy-based aromaticity parameters, all of the other new aromaticity indices presented above are based on the analysis of electron density. The use of state-of-the-art quantum mechanical calculations allows extracting information that is extremely helpful for the analysis of aromaticity. Many of the above-mentioned aromaticity indices are based on QTAIM and NBO descriptors. Therefore, it is worth mentioning that a complementary relationship between QTAIM and NBO bond characteristics was recently proven by explicit mathematical treatment, which resulted in a new analysis based on natural bond critical point (NBCP) properties.397 Electronic index development and applications based on the QTAIM theory, which are probably those that have been most widely used to discuss electron localization/ delocalization and aromaticity, were carefully reviewed in 2005.398 The last sentence of this work should be quoted here: “Without doubt, the quest for a universal index of aromaticity is likely to be among the main priorities during the coming years in the field of aromaticity.” A critical analysis of a large number of local aromaticity indices for the benzenoid rings in polyaromatic hydrocarbons was presented by Bultinck.247 The results obtained supported Clar’s hypothesis, and mutual correlations between some aromaticity parameters (mainly HOMA and electronic indices) were found. Feixas et al.,181 on the basis of the results obtained for a set of 10 indicators of aromaticity (structural, magnetic, and electronic indices were applied) for a series of 15 tested molecular systems, concluded that indices based on electron delocalization are the most accurate among those examined. As mentioned above (section 4.2), the aromaticity of sixmembered monoheterocycles34 (C5H5X, where X = CH, SiH, GeH, N, P, As, O+, S+, Se+) and diheterocycles97 (C4H4X2, where X = O, S, Se; these are antiaromatic when considered as planar) were analyzed by using electronic, structural (Table 8), and magnetic properties. In both cases, considerable inconsistency was found between the various indices. Because the different aromaticity properties do not lead to the same classification of compounds, a pattern taking into account the most widely accepted aromaticity parameters is necessary. Neural networks are computational tools that are able to detect nonlinear relationships between different parameters, having the capacity to order a large amount of input data and transform them into a graphical pattern of output data. Alonso and Herradon399 presented successful applications of Kohonen’s self-organizing maps (SOM) to classify organic compounds according to their aromatic character and showed a good correlation between the aromaticity of a compound and its placement in a particular neuron. As input data for the training of the network, various
5. QUANTITATIVE MOLECULAR ORBITAL PICTURE OF AROMATIC BOND DELOCALIZATION As pointed out repeatedly in this Review, aromaticity of compounds as well as the very concepts themselves have been the subject of many experimental and theoretical studies.13−15,33,38,400−404 The key characteristics of aromatic compounds are (i) a regular, delocalized structure involving CC bonds of almost equal length, each with partial doublebond character, (ii) enhanced thermodynamic stability, and (iii) reduced reactivity as compared to nonaromatic conjugated hydrocarbons. Here, we recall that antiaromatic compounds show exactly the opposite: (i) an irregular structure with alternating single and localized double CC bonds, (ii) reduced thermodynamic stability, and (iii) enhanced reactivity. Recently, in a quantitative Kohn−Sham molecular orbital (MO) study, Pierrefixe and Bickelhaupt addressed the question of why the antiaromatic 1,3-cyclobutadiene (a) and aromatic benzene (b) rings (see Scheme 3) have localized and Scheme 3
delocalized structures, respectively.51,405,406 Their MO model showed that the π-electron system never favors a symmetric, delocalized ring, in neither a nor b. The origin of this behavior can be easily understood from the well-known dependence of π overlapping carbon 2p atomic orbitals: the ⟨2pπ|2pπ⟩ overlap of two adjacent carbon atoms achieves its maximum value of 1.0 as the bond distance goes to zero. In practice, this situtation cannot be achieved, as the σ overlap that is involved in forming the CC σ-bond has an optimum around 1.5 Å, and goes down if the CC bond becomes shorter. In addition, a repulsive well is becoming dominant in σ-bonding due to Pauli repulsion between closed shells, initially between carbon 2s-derived orbitals. 6413
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Interestingly, the regular, symmetric structure of benzene appears to have the same cause as that of planar cyclohexane, the σ-electron system. Nevertheless, at first sight, the fact that it is the π system that decides if delocalization occurs or not may be somewhat counterintuitive. The mechanism behind this control is a qualitatively different geometry-dependence of the π overlap in a and in b; in both species, the topology of the π overlap pattern differs from the simple, archetypal situation that was encountered when two carbon atoms approach each other. In the aromatic species b, the localizing propensity of the πsystem emerges from a subtle interplay of counteracting overlap effects and is therefore not pronounced well enough to overcome the delocalizing σ-system. At variance, in the antiaromatic ring a, all π overlap effects unidirectional favor localization of the double bonds and can, in this way, overrule the σ-system.51,405,406 The above-presented work echoes earlier theoretical and experimental studies on aromaticity. Initially, Hückel ascribed the driving force for delocalization in benzene and other circularly conjugated 4n+2 π-electron species to the π-electron system.213,407,408 Note that this disagrees in a subtle, yet essential manner with the findings of Pierrefixe and Bickelhaupt.51,405,406 The latter points to a key role for the πelectrons in determining whether localization of the double bonds occurs, but they do so rather as a regulating factor, not as the driving force for this localization. In fact, evidence against the idea that benzene’s D6h symmetric structure originates from a delocalizing propensity of its π-electron system has been reported already since the late 1950s.409−417 Shaik, Hiberty, and co-workers44,47,418−423 showed, in terms of an elegant Valence Bond (VB) model, that it is the σ-system that enforces the delocalized D6h symmetric structure of b upon the π-system, which intrinsically strives for localized double bonds. These conclusions initiated a debate,424,425 but were eventually reconfirmed by others.51,405,406,426,427 This culminated in the quantitative MO model of aromaticity, proposed by Bickelhaupt, which not only nicely confirms the modern VB picture developed by Shaik and Hiberty, but also augments it with a causal electronic mechanism that explains the behavior of the πand σ-electronic systems a and b as well as the corresponding larger annulenes c and d,405 and in heteroaromatic and inorganic conjugated rings.406
(i) They may be applied not only to a molecule as a whole but also to a particular ring of a π-electron molecule, or even to any π-electron fragment of any molecule. (ii) In most cases, they exhibit very good mutual correlations with other types of indices, despite differences in the way of parametrization as well as in the choice of systems for estimation of the reference bond lengths. Usually, they correlate better with energetic measures of aromaticity than with magnetic ones. There are a few important conclusions, which should be pointed out. Although the substituents effect is, in classical organic chemistry, considered mainly an effect acting in substituted aromatic systems, it has recently been clearly shown that, on the contrary, this effect is much stronger in the case of nonaromatic conjugated systems (see section 4.3 for details). Therefore, this classical view on the substituent effect should perhaps be revised. For simple molecules, aromaticity is often a dominant factor deciding the preference in tautomeric equilibria. Another important factor is related to the H-bond interactions. In the case of more complex systems, there is no rule clearly indicating which of these two factors is dominant. Moreover, tautomerism is affected by other (internal and external) factors. The resonance effect in the quasi-aromatic rings of RAHB intramolecular H-bonded systems is well estimated by the HOMA index, in line with Gilli and Grabowski’s estimates of resonance. All of these parameters are well correlated with the strength of H-bonding. Moreover, quasi-aromatic rings when fused to polycyclic aromatic hydrocarbons may act as typical aromatic rings. Thus, they can mimic the benzene rings in PAHs or interact through stacking interactions. Furthermore, the mimicking effect increases for metal-bonded quasi-aromatic rings in which H-bonds have been replaced by metal bonds. New attempts to describe π-electron delocalization are still being reported. New aromaticity measures (local and global, presumably more general and more universal) are proposed and tested using geometrical indices. Molecular orbital study of bond delocalization shows that in aromatic rings π electrons follow the σ system in its tendency to equalize bond lengths.
6. GENERAL PROBLEMS AND CONCLUSIONS The definition of aromaticity is enumerative in nature. If all four classical criteria of aromaticity (see Introduction) are fulfilled, then the system is fully aromatic. If only some of them are fulfilled, the system is considered partly aromatic. The latter case is most frequently encountered. One of the most important problems in the application of geometry-based aromaticity indices is their limitation due to the necessity of a proper choice of parameters used as references for a given index. To some extent, problems may also arise from the (lack of) precision and accuracy of experimental and quantum-chemical structural data. Hence, numerical values of these indices should be understood as a quantitative representation of qualitative models. For a series of structurally similar systems, the estimated aromaticity indices become more reliable than in cases when structurally diversified compounds are taken into consideration. However, geometry-based aromaticity indices have substantial advantages over all other indices:
AUTHOR INFORMATION Corresponding Authors
*E-mail:
[email protected]. *E-mail:
[email protected]. Notes
The authors declare no competing financial interest. 6414
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Biographies
Olga A. Stasyuk received her M.Sc. degree in chemistry in 2007 from Omsk State University, Russia. In 2011 she started her Ph.D. research at the Warsaw University of Technology, Poland, under joint supervision of Professor Szatylowicz and Professor Krygowski. Her doctorate research is devoted to the investigation of tautomerism and intermolecular interactions of nucleobases by quantum-chemical methods.
Tadeusz Marek Krygowski was born in Poznań, Poland (1937), and received his M.Sc. degree at the Adam Mickiewicz University (Poznań, 1961). He then moved to the Department of Chemistry of the Warsaw University where he obtained his Ph.D. (1969) and D.Sc. (1973) degrees. In 1983 he was promoted to the position of a Professor of Chemistry. In 2008 he retired but continued his association with the University as an emeritus professor. In 2010 he received the Foundation of Polish Science prize, which is considered the most prestigious scientific award in Poland. In 2012 he became Doctor honoris causa of the Łódź University. His main research interests involve the studies of structural effects of intra- and intermolecular interactions, various phenomena associated with σ and π-electron delocalization, definition of aromaticity, and long-distance consequences of H-bonding. He is married to Maria Krygowska (mathematician) and the father of two daughters, Kinga and Aleksandra. His hobbies are national music and hiking on not too high mountains.
Justyna Dominikowska completed Interdisciplinary Science Studies at the University of Łódź (Poland) in 2010 graduating with Honors. Presently, she is a Ph.D. student of Professor Marcin Palusiak at the Faculty of Chemistry of the University of Łódź. Her scientific interests involve aromaticity and its measures, computational, and quantum chemistry. She is passionate about Tatra Mountains and the local dialect of that region.
Halina Szatylowicz, associate professor at the Department of Chemistry of the Warsaw University of Technology, obtained her Ph.D. in 1992 working under the supervision of Professor Henryk Buchowski. In 2009 she passed her habilitation thesis at the same university. For the past 12 years she has been closely collaborating Marcin Palusiak was born in Łódź, Poland (1974). After graduating in 2001 he received his M.Sc. Degree (in crystallography) at the Faculty of Physics and Chemistry of the University of Łódź. He completed his Ph.D. in structural chemistry in 2005 at the University of Łódź, working with professor Sławomir J. Grabowski. In 2009 he received
with Professor T. Marek Krygowski. Her research interests involve physical organic chemistry and more specifically studies on the effect of hydrogen bonding on the reactivity and supramolecular associations of organic molecules. 6415
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habilitation in the field of physical organic chemistry. His main research areas are chemical bonding, noncovalent interactions in solid state and gas phase, aromaticity, and related π-electron effects. He has authored or coauthored over 60 papers.
PCA PDB PDI pEDA QM/MM
ACKNOWLEDGMENTS We are deeply indebted to Professors Adam Pron from Warsaw University of Technology and F. Matthias Bickelhaupt from VU University Amsterdam, as well as to the Referees for their significant assistance in the formulation of the final form of this Review and Jarek Kucharczyk for preparing the graphical abstract. T.M.K., H.S., and O.A.S. gratefully acknowledge the Foundation for Polish Science for supporting this work under MPD/2010/4 project “Towards Advanced Functional Materials and Novel Devices - Joint UW and WUT International PhD Programme”. H.S. thanks Warsaw University of Technology for supporting this work. M.P. and J.D. acknowledge the financial support from the National Science Centre of Poland (Grant no. 2011/03/B/ST4/01351). J.D. acknowledges the financial support from University of Łódź Foundation (University of Łódź Foundation Award) and from the National Science Centre of Poland (Grant no. 2012/05/N/ST4/00203).
QTAIM RAHB RCP RE RNA SA SCI sEDA SESE SFLAI SOM VB
principal component analysis Protein Data Bank para-delocalization index π electron-donor−acceptor descriptor hybrid quantum mechanics/molecular mechanics method quantum theory of atoms in molecules resonance-assisted hydrogen bonding ring critical point resonance energy ribonucleic acids Shannon aromaticity six-center bond index σ electron-donor−acceptor descriptor substituent effect stabilization energy source function local aromaticity index Kohonen’s self-organizing maps valence bond
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DEDICATION Dedicated to our friend Professor Henryk Piekarski from the University of Łódź. ABBREVIATIONS AI aromatic delocalization index ALA additive local aromaticity ASE aromatic stabilization energy BLA bond length alternation BOIA bond order index of aromaticity cc correlation coefficient COT cyclooctatetraene CSD Cambridge Structural Database DFT density functional theory DI delocalization index DNA DNAs FHDD Fermi hole density delocalization FLU aromatic fluctuation index HOMA harmonic oscillator model of aromaticity HOMED harmonic oscillator model of electron delocalization HOMHED harmonic oscillator model for heterocycle electron delocalization HOSE harmonic oscillator stabilization energy HtFfA heat of formation from atoms IPR isolated pentagon rule LBHB low barrier hydrogen bond MBL mean bond length MCI multicenter bond index MESP molecular electrostatic potential MO molecular orbital MP2 Møller−Plesset second-order perturbation theory MW microwave spectroscopy NBCP natural bond critical point NBO natural bonding orbital method NRT natural resonance theory NICS nucleus independent chemical shifts NMR nuclear magnetic resonance PAH polycyclic aromatic hydrocarbon 6416
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