Quantification of Aromaticity Based on Interaction Coordinates: A New

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Quantification of Aromaticity Based on Interaction Coordinates: A New Proposal Sarvesh Kumar Pandey, Dhivya Manogaran, Sadasivam Manogaran, and Henry F. Schaefer J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 13 Apr 2016 Downloaded from http://pubs.acs.org on April 13, 2016

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The Journal of Physical Chemistry

Revised Manuscript Manuscript ID jp-2016-00240s.R1

Quantification of Aromaticity Based on Interaction Coordinates: A New Proposal Sarvesh Kumar Pandey1, Dhivya Manogaran1 Sadasivam Manogaran*,1,2 and Henry F. Schaefer III*,2 1

Department of Chemistry, Indian Institute of Technology, Kanpur 208 016, India

2

Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia, 30602, USA

Author for correspondence, 1E-mail: [email protected], [email protected] 1 Phone: +91 512 259 7700

ACS Paragon Plus Environment

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Abstract Attempts to establish degrees of aromaticity in molecules are legion. In the present study, we begin with a fictitious fragment arising from only those atoms contributing to the aromatic ring and having a force field projected from the original system. For example, in benzene, we adopt a fictitious C6 fragment with a force field projected from the full benzene force field. When one bond or angle is stretched and kept fixed, followed by a partial optimization for all other internal coordinates, structures change from their respective equilibria. These changes are the responses of all other internal coordinates for constraining the bond or angle by unit displacements and relaxing the forces on all other internal coordinates. The "interaction coordinate" derived from the redundant internal coordinate compliance constants measures how a bond (its electron density) responds for constrained optimization when another bond or angle is stretched by a specified unit (its electron density is perturbed by a finite amount). The sum of interaction coordinates (responses) of all bonded neighbours for all internal coordinates of the fictitious fragment is a measure of the strength of the σ and π electron interactions leading to aromatic stability. This sum, based on interaction coordinates, appears to be successful as an aromaticity index for a range of chemical systems. Since the concept involves analysing a fragment rather than the whole molecule, this idea is more general and is likely to lead to new insights.


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1.

Introduction

Concepts like valency, bond order, aromaticity are extensively used in the chemistry literature although quantification of these concepts is difficult if not impossible. In this article, we focus on the quantification of aromaticity. Although several attempts have been made in this direction from the inception of aromaticity in 1855,1,2 the degree of success has not been entirely satisfactory.3 Using experimental and theoretical methods Katritzky4,5 and Jug5-7 tried various formulations for the quantification of aromaticity. For this purpose, the energy, structure and magnetic criteria are primarily used. Using the energy difference between an aromatic cyclic system and its corresponding suitable reference system (usually acyclic olefins or conjugated unsaturated analogues), the "resonance energy (RE)",8 is defined and extended to "an Aromatic Stabilization Energy (ASE)" based on homodesmotic reactions.9 The energy criteria lead to difficulties, including selecting the suitable nonaromatic reference compound and a correct value of the heat of formation from the different values given by different authors for the same compound.4 The cyclic CC bond lengths in aromatic systems fall between the single and double bonds, and Krygowski used this structural information, in his "Harmonic Oscillator Model of Aromaticity (HOMA)" index.10,11 The HOMA index based on the geometry criterion has achieved partial success, but the definition of the reference single and double bond lengths limits its applicability. From the early days of NMR, the induced ring current in the presence of an applied magnetic field in benzene and other aromatic systems, the NMR chemical shifts,12 and


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magnetic susceptibility(∆)13 values were often used to infer aromatic systems. Schleyer and coworkers extended these magnetic criteria to the "Nucleus Independent Chemical Shift (NICS)"14 which is often thought to be a better criterion and is widely used as aromaticity index (AI). The reference compounds required for the other methods are not required for NICS. However, NICS has its own limitations.15,16 There are several other methods reported in the literature based on variations of one of these energetic, structural or magnetic criteria, but these may be less satisfactory and not widely used.15

The inverse of the force constant matrix(F) (Hessian) is the compliance constant matrix(C)17 and the reciprocals of the diagonal compliance matrix elements are the relaxed force constants (RFCs).18,19 In the literature,20 it has been shown that the RFC of a bond is a measure of bond strength interaction. Hence, if we add the RFCs of all the ring bonds of the force field it should be a measure of aromaticity. But the sum of RFCs of all the bonds or the sum of RFCs of all the internal coordinates (bonds + angles) of the aromatic ring, does not correspond to the expected aromaticity order of furan < pyrrole < thiophene.21 Because of the electronegativity and size differences between C and S, the RFC value of the C-S bond is very low. Typical values for AI for furan, pyrrole and thiophene based on RFCs in the projected force field (vide infra) are given in the supplementary information (Table S1). Since the RFC is a measure of bond strength20 (related to bond order), RFCs may be used in the place of bondlengths to get a HOMA like value,22 but they will have the same limitations as


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HOMA. Cremer has reported a study of the aromaticity of anthracene and phenanthrene using RFCs.23

Hence, we experimented with the interaction coordinate (IC), first introduced by Jones,19 (i)k = Cik/Ckk24 (vide infra), which is defined as a ratio between related compliance matrix elements. If the delocalization in the aromatic system is more extensive, for constraining a bond by unit displacement from the equilibrium geometry, it requires more energy. So the response of the other internal coordinates will be greater for constrained optimization and is proportional to the effective delocalization and hence related to the aromatic stabilization. The IC is a measure of the response of a bond (its electron density) for constrained optimization when another bond or angle is stretched by one unit (its electron density is perturbed by a measured amount).24 Since the electron density of a bond gets adjusted according to the electronegativity of the atoms in the bond or bond angle, the ICs are likely to include the differences between the electronegativity, mass, and size of the bonded atoms in terms of the compliance matrix elements. Several repeated trials for many molecules made it clear that the full molecular force field, when used, is unlikely to give the correct answer for the AI. This leads us to consider the possibility of the aromatic fragment as a fictitious system containing only the ring atoms, having the force field projected from the full force field of the original system. The ICs, when combined with the idea of a fictitious aromatic fragment, appear to give more meaningful results. In this manuscript, we describe how the index based on ICs of the


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fictitious systems involving only the atoms contributing to the aromatic ring(s) satisfactorily predicts the order of aromaticity for several types of homo and heteronuclear systems. The subject of nonaromatic and antiaromatic systems will not be discussed here. However typical values for three simple linear conjugated systems, butadiene, hexatriene, and octatetraene, are included in this work for the sake of comparison.

2. Methodology Although present day technology permits direct computation of compliance constants and the related ICs,25 it is much more convenient to calculate these quantities using Wilson's B matrix formalism.26 The cartesian force constants are usually obtained from any standard electronic structure program, such as Gaussian09.27 The procedure for converting the cartesian force constant matrix to the redundant internal compliance matrix has been described in the literature.25,28 The methodology is briefly given here. The potential energy in different coordinate systems is given by 2V = XTFxX = RTFRR = sT Fs s

(1)

where X is cartesian, R is internal and s is local coordinate column matrix. They are related by R = BX and s = UR where B is Wilson's B-matrix26 and U is the internal to local coordinate transformation matrix. Rearranging we get s = UR = U(BX) or X = (UB)-1s. Substituting this in the potential energy expression we obtain


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2V = XTFxX = [(UB)-1s]TFx[(UB)-1s] = sT Fs s

(2)

Fs = [(UB)-1]TFx[(UB)-1]

(3)

which gives

Also we have 2V = sT Fs s = (UR)TFs(UR) = RTUTFsUR = RTFRR giving UTFsU = FR or UUTFsUUT = UFRUT. Because UUT = E, Fs = UFRUT. Inverting both sides, we get (Fs) -1 = (UT) -1(FR)-1U-1 or UTCsU = CR. The Cs and CR are the compliance matrices. Hence we obtain UTCsU = CR

(4)

To find (UB)-1, we use (UB)-1(UB) = E. Right multiplying by M-1(UB)T, we see (UB)-1(UB)M-1(UB)T = M-1(UB)T. Because (UB)M-1(UB)T = Gs, we get (UB)-1 = M-1(UB)T (Gs)-1

(5)

Since there is no redundancy in the local coordinates, (Gs)-1 is well defined. Hence, we can find (UB)-1. Using (UB)-1 and Fx (obtained from Gaussian09) in equation 3 we get Fs. Since there is no redundancy in Fs, (Fs)-1 exists and hence (Fs)-1 = (Cs) may be computed. Now equation 4 may be used to get CR. Since all elements of the compliance matrix in internal coordinates are known, we can compute all ICs using (i)k = Cik/Ckk.24 The transformation matrix U can be obtained by diagonalizing the redundant internal G matrix and choosing the non-zero eigenvectors as its rows.25 We do not use the complete valence internal coordinate basis of the parent molecule in the force field conversion. We use only the in-plane valence internal coordinates of the aromatic fragment in the conversion of the cartesian to the local coordinate force constant matrix and hence, the final local force field and the redundant internal compliance field are


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projected from the full molecular force field as the force field corresponding to the aromatic fragment.

Unlike the value of a regular force constant, the value of the compliance constant of a given coordinate does not depend on what other coordinates are used to define the molecular system.17,24 Also, as described by Decius,17 Cyvin29 and in our earlier paper,25 the computation of the internal compliance matrix is not a problem when the coordinates are redundant. Hence, the redundancy does not pose any problem. In the present work, we used the B3LYP/cc-pVTZ method with the keywords fopt = tight and int = ultrafine unless mentioned otherwise. We have observed that sometimes two different starting geometries for the same method and basis set give IC values differing in the third decimal. Using fopt = tight solved this problem. In this research, all ICs are evaluated using computer programs developed in IIT-Kanpur based on UMAT.30

A. Compliance Constants Since the AI calculation involves ICs, (i)k = Cik/Ckk,24 it is good to understand the meaning of ICs, and hence a brief outline is given here. This is essential to follow the broad argument. A detailed discussion is available elsewhere.24,25 The purpose of explaining the direct calculation is to provide a physical interpretation for the interaction displacement coordinates. It is easier to compute them by inverting the F matrix in nonredundant local coordinates and converting them to a redundant compliance matrix in internal coordinates25,28 as


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explained in the last section. It is possible to compute the compliance constants by direct electronic structure methods without calculating the full Hessian using Cik = RiRk/(2V) and Ckk = Rk2/(2V), as described in the literature.24,25 Consider water as an example. It has three internal coordinates r1, r2, and θ. Structurally optimize the water molecule and let this energy correspond to Ve = 0. The equilibrium internal coordinates are re1, re2, and θe. Now we increase re1 by 0.01Å (or any small increment that will give a suitable energy increase) and, keeping it fixed, we do a partial optimization for all coordinates except r1. Now the force is only on the coordinate r1 (fk), and all other coordinates (here r2 and θ) have zero forces (fi = 0 when i ≠ k). Since this is a non-equilibrium situation, the energy of the partially optimized structure will be higher than the fully optimized structure. The increase in energy is V - Ve = V – 0 = V The increase (r1 - re1) is Rk (here 0.01Å), and then Ckk = R2k/(2V). If r2 is the coordinate i after partial optimization, the change (r2 - re2) is Ri, then Cik = RiRk/(2V). To relate the compliance constants to the angle θ, increase the angle by one degree (or any suitable small value) and keeping it fixed do a partial optimization. Then (θ - θe) = 1×(π/180) radians = Rk.

B. Aromaticity Index Based on Interaction Coordinates (AIBIC) The interaction coordinate (i)k = Cik/Ckk24 is the relative displacement of coordinate i if the energy is minimized with coordinate k constrained in a displaced configuration. Let us consider four atoms A-B-C-D connected by


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three adjacent bonds A-B, B-C and C-D which we call internal coordinates i, j and k. Let us calculate the ICs (i)j and (k)j. If we stretch the bond (weaken) B-C by a unit displacement, these two ICs tell us how the bonds A-B and C-D respond to this stretching of B-C due to constrained optimization. In the aromatic systems studied in this research, these two ICs decrease (bonds becomes stronger). The extent of the responses (here decrease) depends on the nature of the electron density in the three bonds. This is because during constrained optimization the electron density of all bonds gets adjusted so that the forces on these bonds become zero except on the constrained bond. This means that the responses are a measure of the interaction of electrons in the bonds A-B and C-D (relaxed bonds) with the electrons in bond B-C (constrained bond). Assuming that the responses are due to σ and π electrons in the given bond, the sum of the responses for all the internal coordinates in an aromatic fragment should measure its stability due to σ and π electron interactions, and hence measure its aromaticity.

Let us consider the C6 fragment of benzene. This fictitious fragment is completely described by six CC bonds and six CCC angles, a total of 12 internal coordinates. Since planarity is one of the requirements for aromaticity, we considered only in-plane internal coordinates. We stretch each bond one after another by a unit displacement and measure the response of the immediate neighbours to the constrained optimization. Immediate neighbours will have the maximum responses and have minimum contamination from responses due to


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other sources. Each CC bond has two CC bonds as neighbours and we add 6x2 = 12 responses by summing the 12 ICs for the six bonds. For each CCC angle, we measure the responses of the two CC bonds containing the angle. Here again, we add 6x2 = 12 responses for the six angles. The sum of the 24 responses from the 12 internal coordinates (six bonds and six angles) measures the response of the aromatic fragment for a small measured perturbation in its internal coordinates after constrained optimization. This sum is a measure of the aromatic stability of the C6 fragment and hence an aromaticity index based on interaction coordinates (AIBIC). If we have polycyclic structures, some of the bonds are shared by more than one ring. When such a common bond is stretched, all connected bonds will respond, and these extra responses from the bonds of the neighbouring rings have to be added with appropriate weight factors.

The comparison of the aromaticity indices is easier if we normalize the AI relative to a reference substance. If we choose benzene as a reference compound, the normalized aromaticity index (NAI) of the system is given by NAI = [(AI)system-(AI)benzene]/(AI)benzene. The NAI is positive if the AI is greater than that of benzene and negative if it is less aromatic when benzene has a zero value.


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C.

Origin of Aromaticity

The origin of aromaticity is a highly controversial issue. Whether the aromatic stability is due only to π-electron overlap or whether σ electrons also contribute to the stability (in addition to π-electron overlap) is not a settled issue.7,31,32 The success of simple Hückel theory in the early days contributed to the notion of σ and π electron separability and aromaticity due to π-electron overlap. However, it should be remembered that Hückel theory has several approximations and its extension to hetero systems involves arbitrary parametrization.33 The bonds and angles (internal coordinates) infer only the total electron density (σ + π) around the bonds and angles. Hence, from the AIBIC values, it appears that σ electron contribution also plays a role in the aromatic stability. Similar views have expressed by other authors from different perspectives.31,34

3. Results and Discussion We have looked at the AIs of methyl and fluorine substituted benzenes, fluorine substituted borazines, a few five and six membered heterocyclic systems, some mono and polycyclic aromatic systems, and some larger equilibrium structures containing distorted benzene and naphthalene as their constituents. The results are very encouraging and there is an overall agreement with the published literature.


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A.

Fluorinated Benzenes

The values calculated for the AI using the present method (AIBIC) for the different fluorinated benzenes are given in Table 1. Wu et al.35 studied different fluorine substituted benzenes (C6FnH(6-n), n = 1-6) using localized molecular orbital NICS(0)πzz and their results are also given in Table 1, along with those of Kaipio et al.36 for NICS(0)zz. There is qualitative agreement between NICS(0)πzz (ring) and the AIBIC values. Fluorination of benzene changes its aromaticity to a very small extent. As we increase the number of fluorines, the aromaticity decreases until we reach trifluoro and then increases, making hexafluorobenzene as aromatic as benzene, with AIBIC values of 4.85 and 4.84, respectively. Generally, substitutions at the ortho and para positions are more aromatic than those at meta. The order of aromaticity based on AIBIC is for disubstitution 1,2 > 1,4 > 1,3; for trisubstitution 1,2,3 > 1,2,4 > 1,3,5; and for tetrasubstitution 1,2,3,4 > 1,2,4,5 > 1,2,3,5. Due to the electronegativity of fluorine, the carbons bonded to fluorine have partial positive charges and the carbons containing hydrogens have partial negative charges. The charge alteration decreases the effective overlap (i.e. bonds are elongated) to some extent and the aromaticity decreases.

B.

Methyl Substituted Benzenes

It is possible to have several conformations (of different point groups) for each of the methyl substituted benzenes. Since one of our goals is to study the variation of aromaticity with the number of methyl groups, we selected the first


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conformation which gave all positive vibrational frequencies in each case. It is very unlikely that the final results will change because of conformational changes of the methyl groups. The final aromaticity indices are given in Table 2 along with available NICS(0) and NICS(1) values.37 The substitution of the methyl

group(s)

lowers

the

D6h

symmetry

of

benzene

including

hexamethylbenzene. This acts as a perturbation to the π electron delocalization, reducing the aromaticity of the C6 ring. The aromaticity order given by the AIBIC is: 1,2 > 1,3 > 1,4 (di); 1,2,3 > 1,2,4 > 1,3,5 (tri); 1,2,3,4 > 1,2,3,5 > 1,2,4,5 (tetra). From the values in Table 2, it appears that when immediate neighbours are substituted the AI is higher. The agreement with NICS(1) is better than NICS(0). The decrease in aromaticity as the number of methyl group increases is in general agreement with earlier studies.37,38

C.

Six Membered Heterocyclic Systems

An important aim of the present work is to understand the effect of adding nitrogen atoms by replacing C-H groups of six-membered heterocyclic systems in succession. Previous studies of this question are available in the literature.15,39 In general, we find the inductive effect due to the higher electronegativity of nitrogen assisted by the resonance effect due to its lone pair. The nitrogen lone pair in the six-membered ring is in the plane of the molecule. As a result, when we have adjacent nitrogen atoms, electron lone pair repulsion also has to be taken into account. The computed results are given in Table 3 along with the available NICS literature values. From the table, it is clear that neighbouring


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nitrogens lead to increased aromaticity. The aromaticity order predicted by AIBIC is: in diazines, 1,2 > 1,3 > 1,4; in triazine, 1,2,3 > 1,2,4 > 1,3,5; and in tetrazine, 1,2,3,4 > 1,2,3,5 > 1,2,4,5. This result is in agreement with the NICS(0)πzz values for diazines and triazines and with NICS(0) for triazines and tetrazines.

D.

Five Membered Heterocyclic Systems

The aromaticity literature for five-membered heterocyclic systems is extensive.21,37,40,41 and most of this literature agree with the aromaticity order thiophene > pyrrole > furan.21 The aromaticity order according to AIBIC is pyrrole > imidazole > pyrazole (set 1); triazole123-1H > triazole124-4H > triazole123-2H > triazole124-1H (set 2); tetrazole-1H > tetrazole-2H (set 3); isoxazole > oxazole (set 4), as given in Table 4. In the above list, triazole123-1H means that the nitrogen atoms are at positions 1,2,3 and the hydrogen atom is at position 1 and similarly for others. In general, the aromaticity order seems to depend on the property from which it is based and we observe considerable variations in the earlier reports.37,40,41

E.

Fluorinated Borazines

Borazine is isoelectronic with benzene and has six π-electrons justifying the name 'inorganic benzene'. The nitrogens have lone pair electrons while boron is electron deficient, having empty p-orbitals. As a result, nitrogen can donate p electrons to boron forming a π bond and leading to six π-electron aromaticity.


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The aromaticity of borazine is discussed in the literature without consistent answers. Several authors agree that borazine is aromatic but much less aromatic than benzene.42-45 The property used to calculate the aromaticity appears to determine its magnitude. If we replace a hydrogen atom of boron by a fluorine atom, because of the electronegativity of fluorine the boron will draw more electron density from nitrogen, thus increasing the aromaticity. This was clearly observed in the results given in Table 5. B-trifluoroborazine has the highest aromaticity followed by B-difluoroborazine and B-monofluoroborazine, as expected. Replacing N-H by N-F will decrease the aromaticity because it will hinder the donation of electron density to boron. Consistent with this, Ntrifluoroborazine has the lowest aromaticity. The other mixed substituted borazines have values which represent a balance of these two opposing effects. The excellent agreement between the AIBIC values and the expected aromaticity order validates its reliability.

F.

Mono and Polycyclic Aromatic Systems

Some of these systems have been earlier studied by NICS and diamagnetic susceptibility measurements.46,47 In C8H82- we have ten π-electrons while all the other monocyclic ring systems have six. For the ionic species, the charges and sizes of the rings are different. Ignoring all effects (such as charge, size and the number of π electrons), for monocyclic rings the AIBIC aromaticity order is C8H82+ > C8H82- > C7H7+ > C6H6 > C5H5-. For polycyclic rings, two neighbouring rings may share one or more bonds. This has to be taken into


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account when adding the ICs to get the final value of AIBIC. For bonds which belong to a single ring, the ICs of all neighbours have to be added, even when some of them belong to the neighbouring rings. For each common bond, the ICs of all neighbours are added with half of the contribution to the AIBIC for each ring. In all molecules studied here, the inner rings are less aromatic than the outer rings. This was observed in the results presented in Table 6. Details are given in the supplementary information.

G.

Distorted Aromatic Systems

It may be of interest to know how the aromaticity changes if the aromatic systems are distorted from their most stable structure in the ground electronic state. The distortions can be of two types. The first is the distortion from equilibrium giving non-equilibrium structures. For example, in benzene, the normal D6h point group could be distorted to D3h by bond length alteration. This distortion takes the benzene to a non-equilibrium structure and lets the increase in energy from equilibrium be V1. To obtain the IC, (i)k of the distorted structure now we have to stretch Rk by a small amount, giving this new non-equilibrium benzene an energy V2 relative to equilibrium structure. The important point to be noted here is that V1 depends on the distortion D6h to D3h, and V2 depends on the distortion Rk. V1 and V2 may add or subtract depending on the nature of the distortion. For example, with D6h to D3h distortion, a given CC bond is elongated. Now for an Rk distortion when the same CC bond is stretched the two distortions add. On the other hand, in the D6h to D3h distortion a given CC bond


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is compressed, while under Rk distortion the same CC bond is stretched the two distortions subtract. Also, the relative values depend on how large or small V1 is. As a result, for a distorted non-equilibrium benzene, the sum of the two distortions is arbitrary, depending on the nature of distortions D6h to D3h and Rk for different k values. As a result, the calculated responses for Rk distortion for different Rk values will also be arbitrary and the AIBIC value will not be meaningful.

The second type of distortion is a distorted benzene when it is part of a large equilibrium structure. In this case, the aromaticity of the benzene ring is expected to decrease due to distortion and AIBIC is expected to give satisfactory results, because the larger system is an equilibrium structure. We have calculated the AIBIC values for distorted benzene and naphthalene which are parts of larger equilibrium structures reported in the references.48,49 The optimized structures of the larger molecules containing the distorted benzene and naphthalene as their constituents are shown in Figures 1 and 2. The aromaticity decreases as expected in the distorted benzene which is part of the larger system48 shown in Figure 1. It is very satisfying to see that the AI of the benzene rings in the distorted naphthalene vary according to their reactivity. In the larger equilibrium system containing the distorted naphthalene as a constituent as shown in Figure 2, the inner ring (AIBIC = 4.33) was found to be more reactive than the outer ring (AIBIC = 4.80).49 The final results for these systems are reported in Table 7.


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4. ICs of Linear Conjugated Systems It is of interest to see typical IC values of linear conjugated systems compared to those for aromatic systems. For this purpose, we included the calculated ICs of the linear conjugated systems, all trans butadiene, hexatriene and octatetraene. The sum of ICs for the bonds and angles of the carbon framework are 1.26, 2.32 and 3.32 for butadiene, hexatriene and octatetraene respectively. Since the number of π-electrons and the internal coordinates are different for these systems compared to the reference system (benzene), the AIBIC values are reported without normalization. Details are given in the supplementary information.

5. Conclusions Here we propose a new approach to the analysis of aromaticity. A fictitious aromatic fragment is constructed including only the atoms contributing to the aromatic ring(s) in the system. The internal coordinates (ICs) of the planar fragment are used to project its force field from the full molecular force field, and all the ICs are evaluated. The immediate bonded neighbour ICs of each bond and the ICs of the bonds contained in each of the bond angles are summed for all internal coordinates to get the Aromaticity Index Based on Interaction Coordinates (AIBIC). For polycyclic systems, the immediate neighbour ICs have to be added with proper weighs for the bonds shared between rings. The performance of AIBIC as an aromaticity index for fluorine substituted benzenes and borazines, methyl substituted benzenes, some five and six membered


19


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heterocyclic systems, some mono and polycyclic aromatic systems, and some larger equilibrium structures containing distorted benzene and naphthalene as their constituents, were studied and appears to give meaningful results. Since the concept involves analysing a fragment rather than the whole molecule, this idea is very general and can open up new directions for future research.


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Table 1 Aromaticity Index Based on Interaction Coordinates (AIBIC) for Six Membered Fluorine Substituted Benzenes

S.N.

‡

NICS(0)†zz (NAI)

SPECIES

1

Benzene(D6h)

2

LMONICS(0)‡πzz (Ring) (NAI)

AIBIC (NAI)

-12.1 (0.000)

-36.9 (0.000) 4.842 (0.000)

Monofluorobenzene(C2v)

-7.6 (-0.372)

-36.6 (-0.008) 4.774 (-0.014)

3

1,2-difluorobenzene(C2v)

-9.2 (-0.240)

-37.1 (0.005) 4.750 (-0.019)

4

1,3-difluorobenzene(C2v)

-11.7 (-0.033)

-35.8 (-0.030) 4.715 (-0.026)

5

1,4-difluorobenzene(D2h)

-12.1 (0.000)

-36.9 (0.000) 4.722 (-0.025)

6

1,2,3-trifluorobenzene(C2v)

-12.0 (-0.008)

-36.9 (0.000) 4.740 (-0.021)

7

1,2,4-trifluorobenzene(Cs)

-12.9 (-0.066)

-36.7 (-0.005) 4.708 (-0.028)

8

1,3,5-trifluorobenzene(D3h)

-12.2 (0.008)

-34.6 (-0.062) 4.663 (-0.037)

9

1,2,3,4-tetrafluorobenzene(C2v)

-15.1 (0.248)

-37.4 (0.014) 4.746 (-0.020)

10

1,2,4,5-tetrafluorobenzene(D2h)

-13.7 (0.132)

-37.2 (0.008) 4.713 (-0.027)

11

1,2,3,5-tetrafluorobenzene(C2v)

-13.1 (0.083)

-36.1 (-0.022) 4.709 (-0.027)

12

Pentafluorobenzene(C2v)

-17.1 (0.413)

-37.1 (0.005) 4.769 (-0.015)

13

Hexafluorobenzene(D6h)

-15.3 (0.264)

-37.7 (0.022) 4.850 (0.002)

: Ref 35- PW91/IGLOIII; †: Ref 36- BP86/SVP.

NAI = Normalized Aromaticity Index(see text).


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Table 2 Aromaticity Index Based on Interaction Coordinates (AIBIC) for Six Membered Methyl Substituted Benzenes NICS(0)† (NAI) NICS(1)† (NAI) AIBIC (NAI)

S.N. SPECIES

†

1

Benzene(D6h)

-8.03 (0.000)

-10.20 (0.000) 4.842 (0.000)

2

Monomethylbenzene(Cs)

-8.01 (-0.002)

-10.07 (-0.013) 4.773 (-0.014)

3

1,2-dimethylbenzene(C2v)

-8.15 (0.015)

-10.16 (-0.004) 4.709 (-0.027)

4

1,3-dimethylbenzene(Cs)

-7.94 (-0.011)

-9.84 (-0.035) 4.707 (-0.028)

5

1,4-dimethylbenzene(Ci)

-8.01 (-0.002)

-9.89 (-0.030) 4.705 (-0.028)

6

1,2,3-trimethylbenzene(Cs)

-7.80 (-0.029)

-9.83 (-0.036) 4.657 (-0.038)

7

1,2,4-trimethylbenzene(C1)

-8.06 (0.004)

-9.91 (-0.028) 4.642 (-0.041)

8

1,3,5-trimethylbenzene(C3)

-9.78 (0.218)

-9.54 (-0.065) 4.638 (-0.042)

9

1,2,3,4-tetramethylbenzene(C2)

-7.82 (-0.026)

-9.78 (-0.041) 4.604 (-0.049)

10

1,2,3,5-tetramethylbenzene(C1)

-7.70 (-0.041)

-9.59 (-0.060) 4.592 (-0.052)

11

1,2,4,5-tetramethylbenzene(D2h)

-7.96 (-0.009)

-9.82 (-0.037) 4.582 (-0.054)

12

Pentamethylbenzene(C1)

-7.24 (-0.098)

-9.25 (-0.093) 4.553 (-0.060)

13

Hexamethylbenzene(D3d)

-7.32 (-0.088)

-9.37 (-0.081) 4.520 (-0.067)

: Ref 37- RB3LYP/6-311+G*(Table 8 of Ref 37).



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Table 3 Aromaticity Index Based on Interaction Coordinates (AIBIC) for Six Membered Heterocyclic Systems S.N. SPECIES 1 Benzene(D6h)

† ‡

NICS(0)† (NAI) -8.03 (0.000)

NICS(1)† (NAI) NICS(0)‡πzz (NAI) AIBIC (NAI) -10.20 (0.000) -36.12 (0.000) 4.842 (0.000)

2

Pyridine(C2v)

-6.82 (-0.151)

-10.17 (-0.003)

-35.94 (-0.005)

4.572 (-0.056)

3

Diazine12(C2v)

-5.33 (-0.336)

-10.53 (0.032)

-36.11 (0.000)

4.774 (-0.020)

4

Diazine13(C2v)

-5.51 (-0.314)

-9.99 (-0.021)

-35.15 (-0.027)

4.405 (-0.090)

5

Diazine14(D2h)

-5.30 (-0.340)

-10.24 (0.004)

-34.75 (-0.038)

4.158 (-0.141)

6

Triazine123(C2v)

-4.32 (-0.462)

-10.80 (0.059)

-36.34 (0.006)

5.338 (0.102)

7

Triazine124(Cs)

-3.77 (-0.531)

-10.36 (0.016)

-35.88 (-0.007)

4.527 (-0.065)

8

Triazine135(D3h)

-3.55 (-0.558)

-33.77 (-0.065)

4.319 (-0.108)

9 10

Tetrazine1234(C2v) Tetrazine1235(Cs)

-2.67 (-0.667) -2.37 (-0.705)

-10.78 (0.057) -10.36 (0.016)

-36.36 (0.007) -35.50 (-0.017)

5.985 (0.236) 5.291 (0.093)

11

Tetrazine1245(D2h)

-1.80 (-0.776)

-10.58 (0.037)

-36.66 (0.015)

5.015 (0.036)

: Ref 37- RB3LYP/6-311+G**(Table 35 of Ref 37); : Ref 39- PW91/IGLOIII//B3LYP/6-311+G**.



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Table 4 Aromaticity Index Based on Interaction Coordinates (AIBIC) for Five Membered Heterocyclic Systems S.N. SPECIES 1

Benzene(D6h)

2

NICS(0)† (NAI)

NICS(1)† (NAI) NICS(0)‡πzz (NAI) AIBIC (NAI)

-8.03 (0.000)

-10.20 (0.000)

Thiophene(C2v)

-12.87 (0.603)

-10.24 (0.004)

4.572 (-0.056)

3

Pyrrole(C2v)

-13.62 (0.696)

-10.09 (-0.011)

4.435 (-0.084)

4

Furan(C2v)

-11.88 (0.479)

-9.38 (-0.080)

4.262 (-0.120)

5

Pyrazole(Cs)

-13.61 (0.695)

-11.30 (0.108)

-34.1 (-0.056)

4.258 (-0.121)

6

Imidazole(Cs)

-13.10 (0.631)

-10.55 (0.034)

-32.9 (-0.089)

4.269 (-0.118)

7

Triazole123-1H(Cs)

-13.97 (0.740)

-12.73 (0.248)

-35.2 (-0.025)

4.576 (-0.055)

8

Triazole123-2H(C2v)

-13.64 (0.699)

-11.28 (0.106)

-35.5 (-0.017)

4.163 (-0.140)

9

Triazole124-1H(Cs)

-13.09 (0.630)

-11.57 (0.134)

4.103 (-0.153)

10

Triazole124-4H(C2v)

-13.95 (0.737)

-12.76 (0.251)

4.394 (-0.093)

11

Tetrazole-1H(Cs)

-14.33 (0.785)

-13.49 (0.323)

-33.9 (-0.061)

4.826 (-0.003)

12

Tetrazole-2H(Cs)

-14.46 (0.801)

-13.89 (0.362)

-36.0 (-0.003)

4.434 (-0.084)

13

Pentazole(C2v)

-16.72 (1.082)

-15.76 (0.543)

14

Oxazole(Cs)

-11.43 (0.423)

-9.72 (-0.047)

-28.0 (-0.225)

4.178 (-0.137)

15

Isoxazole(Cs)

-12.23 (0.523)

-10.51 (0.030)

-28.1 (-0.222)

4.368 (-0.098)

16

Oxadiazole124(Cs)

-11.85 (0.476)

-10.64 (0.043)

-26.7 (-0.261)

4.253 (-0.122)

17

Oxadiazole134(C2v)

-13.40 (0.669)

-12.29 (0.205)

18

Oxadiazole125(C2v)

-11.11 (0.384)

-10.29 (0.009)

†

-36.12 (0.000)

4.842 (0.000)

5.332 (0.101)

4.323 (-0.107) -28.7 (-0.205)

4.627 (-0.044)

: Ref 37- RB3LYP/6-311+G**(Table 18, 22 and 24 of Ref 37 ); ‡ : Ref 41- PW91/IGLO-III//B3LYP/6-311+G**(Table S2 in Supplementary Information of Ref 41). NAI = Normalized Aromaticity Index(see text).


24

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Table 5 Aromaticity Index Based on Interaction Coordinates (AIBIC) for Six Membered Fluorine Substituted Borazines (1,3,5-Nitrogen and 2,4,6-Boron) NICS(0)†πzz (NAI) AIBIC (NAI)

S.N. SPECIES

†

1

Benzene(D6h)

-35.77 (0.000)

4.842 (0.000)

2

Borazine(D3h)

-7.87 (-0.780)

4.769 (-0.015)

3

1-fluoroborazine(C2v)

-9.01 (-0.748)

4.629 (-0.044)

4

2-fluoroborazine(C2v)

-6.90 (-0.807)

4.810 (-0.07)

5

2,4-difluoroborazine(C2v)

-6.21 (-0.826)

4.866 (-0.005)

6

2,4,6-trifluoroborazine(D3h)

-5.77 (-0.839)

4.934 (-0.019)

7


-7.97 (-0.777)

4.683 (-0.033)

8


-10.14 (-0.717)

4.497 (-0.071)

9

1,3,5-trifluoroborazine(D3h)

-11.21 (-0.687)

4.331 (-0.106)

10

1,2-difluoroborazine(Cs)

-7.99 (-0.777)

4.703 (-0.029)

11

1,2,6-trifluoroborazine(C2v)

-7.21 (-0.798)

4.799 (-0.009)

12

1,2,5-trifluoroborazine(Cs)

-9.06 (-0.747)

4.583 (-0.053)

13

1,2,4-trifluoroborazine(Cs)

-7.20 (-0.799)

4.772 (-0.014)

14

1,2,4,6-tetrafluoroborazine(C2v)

-6.67 (-0.814)

4.881 (-0.008)

15


-8.21 (-0.770)

4.684 (-0.033)

16

1,2,3-trifluoroborazine(C2v)

-9.05 (-0.747)

4.606 (-0.049)

17


-10.10 (-0.718)

4.503 (-0.070)

18

1,2,3,4-tetrafluoroborazine(Cs)

-8.20 (-0.771)

4.722 (-0.025)

19

1,2,3,4,5-pentafluoroborazine(C2v)

-9.19 (-0.743)

4.652 (-0.039)

20

1,2,3,4,6-pentafluoroborazine(C2v)

-7.58 (-0.788)

4.841 (0.000)

21

Hexafluoroborazine(D3h)

-8.48 (-0.763)

4.827 (-0.003)

: Ref 45- B3LYP/6-311+G**.



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Table 6 Aromaticity Index Based on Interaction Coordinates (AIBIC) for Some Mono and Polycyclic Aromatic Systems S.N.

SPEICIES

NICS(1)†zz (NAI)

AIBIC (NAI)

-32.5 (0.000)

4.842 (0.000)

A 1

Benzene(D6h)

2

2+

C8H8 (D8h)

5.334 (0.102)

2

C8H82-(D8h)

5.273 (0.089)

3

+

C7H7 (D7h)

4.860 (0.004)

4

-

4.332 (-0.105)

C5H5 (D5h)

B 1

Naphthalene(D2h)

-30.6 (-0.058) Inner ring

Outer ring

Inner ring

Outer ring

2

Anthracene(D2h)

-38.4 (0.182)

-24.8 (-0.237)

4.621 (-0.046)

4.672 (-0.035)

3

Phenanthrene(C2v)

-20.0 (-0.385)

-31.5 (-0.031)

4.518 (-0.067)

4.780 (-0.013)

C-Ring

†

4.743 (-0.020)

4

Quinoline(Cs)

5

Isoquinoline(Cs)

-30.7 (-0.055)

N-Ring -29.5 (-0.092)

C-Ring 4.723 (-0.025)

4.437 (-0.084)

4.717 (-0.026)

4.275 (-0.117)

: Ref 46- HF/6-31G*.



26

N-Ring

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Table 7 Aromaticity Index Based on Interaction Coordinates (AIBIC) for Larger Equilibrium Structures Containing Distorted Benzene and Naphthalene Aromatic Fragments S.N.

SPEICIES

AIBIC (NAI)

(B3LYP/cc-pVTZ) 1A

Benzene( D6h)

4.842 (0.000)

1B

Naphthalene(D2h)

4.743 (-0.020)

1C

Distorted naphthalene in a larger

Inner ring

Outer ring

4.331 (-0.105)

4.798 (-0.009)

†

equilibrium system (C2V)

(B3LYP/6-31G*) 2A

Benzene(D6h)

4.756 (0.000)

2B

Distorted benzene in a larger

4.492 (-0.056)

‡

equilibrium system (C2) †

: Figure 1 ; ‡: Figure 2


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6.

Supplementary Information

The AI based on RFCs are given for furan, pyrrole and thiophene in Table S1. The computed AIBIC values for benzene, naphthalene, anthracene and phenanthrene are reported in Tables S2-S5. The calculation of AIBIC values for the linear conjugated all trans butadiene, hexatriene and octatetraene are shown in Tables S6-S8. The calculation of AIBIC values for distorted benzene and naphthalene in larger equilibrium structures are given in Tables S9-S10.

Acknowledgments The authors acknowledge the Department of Science and Technology, Government of India, New Delhi for supporting the Computational Facilities in the Computer Center and also in the Department of Chemistry, Indian Institute of Technology, Kanpur-208 016, India. SKP thanks, UGC, Government of India, for a Research Fellowship. DM thanks IITK for supporting post-doctoral research. The authors thank Dr. DLVK Prasad for helpful discussions. HFS was supported by the U. S. Department of Energy, Office of Basic Energy Sciences, Grant DE-FG0297ER14748. SM acknowledges a Fulbright-Nehru Award while serving as a Visiting Professor at the University of Georgia.


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Figure 1

P-fused double helicene

Figure 2

Distorted Naphthalene Made by Annelation with Bicyclo[2.1.1]hexene Units


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