Quantification of Aromaticity of Heterocyclic Systems Using Interaction

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Quantification of Aromaticity of Heterocyclic Systems using Interaction Coordinates Soumyadeb Dey, Dhivya Manogaran, Sadasivam Manogaran, and Henry F. Schaefer J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b05041 • Publication Date (Web): 03 Aug 2018 Downloaded from http://pubs.acs.org on August 5, 2018

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The Journal of Physical Chemistry

Revised Manuscript (Manuscript ID: jp-2018-05041t.R1)

Quantification of Aromaticity of Heterocyclic Systems using Interaction Coordinates

Soumyadeb Dey†, Dhivya Manogaran†, Sadasivam Manogaran*,†,‡ and Henry F. Schaefer III*,‡

†

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

‡

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

‡

Author for correspondence, E-mail: [email protected], [email protected] †

Phone: +91 512 259 7700

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Recently, we proposed an aromaticity index based on interaction coordinates (AIBIC) (J. Phys. Chem. A 2016, 120, 2894-2901). This index works well for the aromatic hydrocarbons. However, in the case of heterocyclic systems, the AIBIC overestimates the aromaticity indicating many of them to be more aromatic than benzene which seems unlikely. Because of the differences in the electronegativity of the carbon and the other heteroatoms, the electron density is partially localized near the more electronegative atom(s) of the aromatic fragment. This localized electron density does not contribute to the aromaticity which is due to the delocalized electron density over the central ring. To account for this reduction in the delocalized electron density, a correction is introduced based on Pauling's electronegativity equation. When the corrected interaction coordinates are used in the computation of AIBIC, we get a new index ‒ aromaticity index based on interaction coordinates corrected (AIBICC). This new index, when computed for a variety of heterocyclic systems, yields results in line with the expectations, and its usefulness in quantifying aromaticity appears to be very promising.


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1. Introduction The concept of Aromaticity is more than 150 years old.1 Since aromaticity is not directly related to any one property of the molecule, it is not a directly observable physical quantity. It lacks an unambiguous definition and hence the attempts for the quantification of aromaticity are based on different measurable properties: resonance energy (RE),2 aromatic stabilization energy (ASE)3 based on energy, a harmonic oscillator model of aromaticity (HOMA) based on geometry,4,5 nucleus independent chemical shifts (NICS) based on magnetic criteria,6 and several others7–9 have been proposed as aromaticity indices for its quantification. Each one of these schemes has its own merits and limitations.7–11 Several reported aromaticity indices based on the energetic, geometric, and magnetic criteria of aromaticity are inconsistent with each other.7–12 Recently we proposed an aromaticity index (AI) based on interaction coordinates (AIBIC).11 Let us consider a simple example of pyridine. To calculate the AIBIC for pyridine (C5NH6), we consider only the aromatic cyclic fragment C5N. The projected force field of the C5N fragment is computed from the full pyridine molecular force field using its in-plane valence internal coordinates (6 bonds and 6 angles). The force field could equally well be represented by the force constant matrix or its inverse compliance matrix. The compliance matrix elements, compared to the force constants, are known to have several advantages ‒ they are well defined even when the coordinates in the internal basis set are redundant and are invariant to the other members of the basis set.13–16 Interaction coordinates (ICs) are defined15 as

, where i and k are the internal coordinates and

the compliance constants. In the IC,

and

are

measures how the coordinate i (bond or angle)

responds (length and angle changes) for constrained optimization when the coordinate k (bond or angle) is stretched by one unit. This also measures the electron density associated with the coordinate k.15



To obtain the AIBIC, we stretch each of the internal coordinates of the aromatic fragment successively and add only the respective immediate neighbor responses. Since the IC is a measure of electron density along the stretched coordinate k, the sum of the ICs, (the responses of the immediate neighbors when all internal coordinates are stretched, one after another respectively,) is a measure of the delocalized electron density associated with the aromatic ring (all internal coordinates) of the fictitious aromatic fragment and hence is an aromaticity index based on interaction coordinates (AIBIC). The AIBIC values thus obtained satisfactorily quantified the aromaticity in the hydrocarbons studied in our earlier work.11 However, it overestimated the aromaticity when the carbon ring includes one or more heteroatoms predicting several heterocyclic systems to be more aromatic than benzene. The present article locates the origin of this overestimation of AIBIC for heterocyclic systems and proposes a correction leading to a new index - aromaticity index based on interaction coordinates corrected (AIBICC). This new AIBICC values when computed for a variety of aromatic heterocyclic systems clearly brings out its usefulness and applicability for the quantification of aromaticity of heterocyclic systems.


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2. Methodology It should be noted that when one of the hydrogen atoms in benzene is substituted by either an electron donating group or an electron withdrawing group, the aromaticity decreases from that of benzene because of the partial localization of the electron density.17,18 It is not clear whether any compound with higher aromaticity index than benzene could exist. Until one is found benzene will have the highest aromaticity index. The inference made here is that all the needed criteria to exhibit aromaticity, which are not fully deciphered yet, are met by benzene in its delocalized, highly symmetric electron density distribution and hence, it has the highest value of the AI. Any deviation of electron density distribution from such an ideal situation affects the aromatic behaviour, decreasing the aromaticity.

2.1 Pauling's Electronegativity Equation Linus Pauling's simple, intuitive equation relating the bond dissociation enthalpy of a bond between atoms A and B having electronegativities

and

is given by.2,19 (1)

Rearranging this equation we get, (2) In Pauling’s picture, the inherent (covalent) bonding ability of atoms A and B are given by D(AA) and D(BB) and the relative tendency to distort the equal sharing of electrons between atoms A and B is given by

, the electronegativity difference squared. This is

equivalent to saying that the dissociation enthalpy of a bond made up of atoms A and B is proportional to the product of their electronegativities. (3) When A and B are same we find, and


(4)


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When these expressions are substituted in Pauling equation (1) the result is:

(5) This

agrees

with

the

Pauling

equation,

validating

the

assumption

and is expected to give reasonable results since Pauling equation has been shown to describe bond dissociation enthalpies quite accurately.19 Hence, D(AB) is proportional to

and this relationship measures the relative

tendency to distort the equal sharing of the electrons between the atoms A and B. If it is a heteronuclear CX bond, this term becomes

. In benzene, the electron density along

the CC bond is perfectly delocalized and is highly symmetric. This symmetry gets distorted by unequal sharing of the electrons between the bonded atoms in CX depending upon the electronegativity of X

or

,

, reducing the aromaticity of the ring

containing CX bond(s). That is, whenever the bonds contain atoms different from C, the unequal electron distribution between the atoms reduces the aromaticity. The Pauling equation given above can be applied only to the normal covalent bonds. For the so called ‘transargononic bonds’ and weak bonds containing noble gas elements, a modified equation has to be used.20

2.2 Partial Localization of Electrons near the Heteroatoms The interaction coordinate (IC) used in the AIBIC calculation measures the local electron density along the bond (or internal coordinate) which may contain atoms of different electronegativities. Because of the differences in the electronegativities of the bonded atoms, the electron densities near the more electronegative atoms are partially localized, reducing the amount of delocalized electron density which in turn reduces the aromaticity. The IC measures both the partially localized electron density near the more electronegative atom, and


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the delocalized electron density contributing to the aromaticity. If we can calculate the fraction of the delocalized electron density leading to aromaticity, excluding the partially localized contribution from the total electron density measured by the ICs, we can correct the unrealistically overestimated AIBIC values.

2.3 Correction to Partial Localization of Electrons Near the Heteroatom We used water example in our earlier paper.11 Since this example helps to understand the meaning of the compliance constants and the ICs, it is briefly mentioned here again. Let us consider the water molecule at equilibrium with the internal coordinate values

,

, and

and energy

,

, and .

. At equilibrium there are no forces on the internal coordinates

Now let us stretch

by 0.01Å, which gives a non-equilibrium structure and hence nonzero

forces appear on all the internal coordinates. Keeping

fixed at

, we do a

partial optimization to remove the forces in all other coordinates viz., partial optimization, let the change in energy be

, and . After the

and the change in

be

relative to the equilibrium structure. Then the compliance constants are given by .15 The IC is

and defined by

with

When

is 1, we get the IC as

measured as

for constraining

. Hence, the IC

.

is the response of

by unit displacement followed by constrained

optimization for minimum energy. The important thing to note here is that if we have more electron density in the covalent bond (stronger

bond), we have to spend more energy to stretch it by 0.01Å compared to a

bond with less electron density (weaker more nonzero force(s) in the stretching of

to

bond). As a result, the stronger bond

(and ) compared to a weaker

. The force introduced in

is measured by the response of


introduces by

which appears as the


IC

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, the bond either elongates or shortens] and is also a quantitative measure of

electron density in the stretched bond

. (This argument is valid even for an ionic bond

where the electron density in the bond is replaced by the electrostatic attractive force between the bonded atoms in

.11)

In a diatomic molecule at equilibrium, we have a minimum restoring force on the bond (ground vibrational state) which goes to zero on dissociation. The difference between the ground vibrational state and the dissociation limit is given by the dissociation enthalpy, and the force changes from nonzero equilibrium value to zero. If we consider the water example with

stretched by a unit displacement, we have nonzero forces on

zero (by partial optimization) we get the response of IC. The difference in energy density in

which is measured by the

is a measure of the bond strength or the electron

and is proportional to the IC for stretched

analogies we can correlate

as

. By making this force

as shown earlier. If we take the two

of water with the dissociation enthalpy D(AB), since the

force goes from nonzero value to zero in both cases. The same inference could be obtained by considering the strength of hydrogen bonds (HBs). Recently, we showed that the response of the neighboring covalent bond for the stretching of the HB by unit displacement followed by constrained optimization (given by the IC of the HB) is a quantitative measure of its strength.21 Hence the IC of the stretched hydrogen bond could easily be seen to quantify its bond strength. Thus we get a bond strength is proportional to the IC. Using the results derived from the Pauling equation and assuming that the bond dissociation enthalpy is the same as the bond strength at small displacements, the IC of a stretched bond is proportional to the product of the electronegativities of the atoms involved in the bond. If we extend the idea to the bond angle, the IC of a stretched angle is proportional to the product of the electronegativities of the atoms forming the angle. Since aromaticity is evaluated usually


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relative to benzene, the CC bond and CCC angle of the same could be used as the reference for evaluating the fraction of the local electron density measured by the ICs contributing to the delocalized part leading to aromaticity, which has to be less than one. Hence, the fraction of the IC contributing to the aromaticity for the bond CX is and its reciprocal when

when

, both being less than unity. For the ICs of

angles, we will have the product of the three electronegativities of the atoms forming the respective angles. For example for the CXC angle this fraction is given by or its inverse if

if

, both being less than

unity. When all the atoms involved are carbons, the correcting fraction turns out to be one as expected for both bonds and angles. Thus the IC corrected for the electronegativity difference between the atoms making the bonds and angles of the aromatic fragment is given by: IC corrected = ICC for bond AX: if if IC corrected = ICC for angle AXY: if if When the corrected ICs are used to calculate the AIBIC, we get a new index, AIBIC-Corrected (AIBICC); the AIBICC values when computed for different heterocyclic rings are more in line with the expectations and appear to be very promising for the elusive quantification of aromaticity for heterocyclic compounds.



3. COMPUTATIONAL DETAILS All the Cartesian force constants were computed at the optimized geometries of the systems using the Gaussian09 package.22 The hybrid B3LYP functional23–26 was used with cc-pVTZ basis sets27,28 for geometry optimizations and vibrational frequency calculations. All frequencies are positive, indicating the minima of the potential energy surface for all the molecules studied. The force and the compliance constants describing the projected force field in the internal coordinates, values of the ICs, and the new corrected AIBICC were evaluated using computer programs developed in IIT-Kanpur. The electronegativity values for the atoms used in the calculations are 2.051, 2.544, 3.066, 3.610, 2.589 for boron, carbon, nitrogen, oxygen and sulfur respectively.29


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4. Results and Discussion The aromaticity indices available in the literature for heterocyclic systems appear to depend largely on the properties used to define aromaticity. This is true for AIBICC also. Since it is calculated from the projected force field of the aromatic fragment, the ‘correctness’ of the index depends on the ‘reliability’ of the force field from which it is calculated. This has to be kept in mind although AIBICC could be evaluated by using any reasonable force field, including empirical force fields used in large bio-molecular structure and property calculations. For example, AIBICC could be calculated for different aromatic rings in a protein when its force field is available. The aromatic carbon rings contain the CH groups arranged cyclically. The substitution of one or more of the CH group(s) by the heteroatom(s) [B(H), N, O, or S] in the carbon ring results in the aromatic heterocyclic systems. The heteroatom incorporation into the ring necessarily introduces structural changes in the aromatic ring. The heteroatom(s) in the ring causes an uneven electron distribution of the electron density which was earlier evenly delocalized over all the carbon atoms in the ring (as in benzene) making it perfect for the most aromatic is now concentrated and partially localized in the vicinity of the more electronegative heteroatom(s). This makes the electron density distribution in the heterocyclic ring less symmetric or less perfect, and their aromaticity will be less than that of benzene. Hence, the electronegativities of the heteroatoms control the fraction of the electron density that is localized and the fraction that is delocalized contributing to the aromaticity. The AIBICC index can be interpreted as a measure of the electron density and its symmetry involved in the cyclic delocalization throughout the ring. A decrease in the AIBICC value indicates decrease in the delocalized electron density as well as its symmetry; this could be caused by the loss of the symmetry of the π-system and/or decrease in the delocalized electron density and/or increase in the localized

electron

density

(vide

infra)

because

of


substitution(s),

presence

of


heteroatom(s) (X) etc. The AIBICC value of a heteroaromatic system depends on three major factors: (i) the electronegativity value of X; (ii) the number of Xs present in the ring fragment; and (iii) the relative positions of the Xs. As the electronegativity of X changes, concentration and localization of the electron density changes in the vicinity of X altering the contribution of the delocalized electron density and hence the aromaticity. We have performed the AIBICC calculations for most of the molecules that were investigated in our earlier work11 and of course the new systems of interest here. However, the correction is needed only for heteroatomic systems. The observed trends in the AIBICC values broadly satisfy the general expectations for the quantification of aromaticity. For example, the relative ordering of thiophene, pyrrole, furan, and the positional isomers as the three triazines, as well as the variations within given related systems like azines.8

4.1. Azabenzenes When we replace the CH groups in Benzene(1) by nitrogen atoms successively, we get Pyridine(2), three Diazines (12;13;14) (3-5), three Triazines (123;124;135) (6-8), three Tetrazines (1234;1235;1245) (9-11), and one Pentazine(12); a total of eleven azabenzenes (see Table 1). The results of different methods used for the quantification of aromaticity of these azines are inconsistent with each other.30 The experimental geometries and the vibrational frequencies for some azabenzenes are collected in reference 31. As the number of nitrogen atoms increase, because of nitrogen's higher mass and partial localization of electrons near it, the rings become more rigid and less aromatic. This decrease in aromaticity is in agreement with the increase in inplane modes and decrease in the out of plane modes of the vibrational frequencies of the azines.31 The AIBICC values in general agree with this conclusion.


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AIBICC predicts the contiguous nitrogen containing azines to be more aromatic than the corresponding non-contiguous nitrogen containing ones. Also as the number of heteroatoms increase, due to more localization of electron density near the more electronegative nitrogen, the aromaticity decreases. If the heteroatoms in the ring are adjacent to each other, there is more uniform delocalization in the rest of the ring compared to when the heteroatoms are apart. In that case the whole ring can be imagined to be constructed from many smaller regions with different uniform electron densities, thus reducing the symmetry of the delocalized electron density and hence the aromaticity. This is in accordance with the earlier reports.32 AIBICC values predict the following aromaticity order for azines containing contiguous nitrogen atoms: benzene(1) > pyridine(2) > 1,2-diazine(3) > 1,2,3-triazine(6) > 1,2,3,4-tetrazine(9); for diazines:1,2-diazine(3) > 1,3-diazine(4) > 1,4-diazine(5); for triazines: 1,2,3-triazine(6) > 1,2,4-triazine(7) > 1,3,5-triazine(8). For the tetrazines we find aromaticities 1,2,3,4-tetrazine(9) > 1,2,3,5-tetrazine(10) > 1,2,4,5-tetrazine(11). Pentazine has a value closer to Pyridine because the symmetry is similar (one atom in the ring is different), with the more electronegative nitrogens contributing somewhat less to the aromaticity due to the higher fraction of localized electrons. Table 1. NICS(0)πzz, AIBIC and AIBICC Values for Benzene and Azabenzenes Entry System NICS(0)πzza AIBICb AIBICC 1 Benzene ‒36.12 4.842 4.842 2 Pyridine ‒35.94 4.572 4.087 3 1,2-diazine ‒36.11 4.774 3.759 4 1,3-diazine ‒35.15 4.405 3.469 5 1,4-diazine ‒34.75 4.158 3.199 6 1,2,3-triazine ‒36.34 5.338 3.637 7 1,2,4-triazine ‒35.88 4.527 3.058 8 1,3,5-triazine ‒33.77 4.319 2.959 9 1,2,3,4-tetrazine ‒36.36 5.985 3.492 10 1,2,3,5-tetrazine ‒35.50 5.296 3.121 11 1,2,4,5-tetrazine ‒36.66 5.015 2.964 12 Pentazine ‒36.70 7.480 3.868 a NICS(0)πzz (ppm) [at PW91/IGLOIII//B3LYP/6-311+G**] values were taken from ref. 30, b AIBIC values were taken from ref. 11.



4.2. Five-membered Heterocycles Containing S, N, and O as Heteroatom(s) With the five membered heterocyclic rings thiophene, pyrrole, and furan, aza-substituted for CH, one gets thia-azoles, azoles, and oxa-azoles respectively. The chemistry of azoles is important because they form subunits of several bio-systems and are studied experimentally and theoretically.8,33,34 The aromaticities of 5-membered heterocyclic systems have been extensively studied and the reported aromaticity orders have considerable variation.8,9,33–37 As in the case of 6-membered azines, we can expect that the contiguous nitrogen atom systems are likely to be more aromatic than systems having non-contiguous nitrogen atoms. As a result, pyrazole is more aromatic than imidazole as indicated by the AIBICC. Given that imidazole is more stable than pyrazole,36 this may appear to be inconsistent, but this is not so. The molecular stability is related to distribution of total electron density in the molecule, while the aromaticity is related to only that part of electron density which is delocalized, and this excludes the localized portion of electron density. This aromaticity order is in agreement with earlier reports.33,36 Isothiazole and thiazole have AI very close and AIBICC of isoxazole is greater than oxazole as shown in Table 2. The aromaticity order for all azoles given in Table 2 broadly follow the order: thia-azoles > azoles > oxa-azoles, in consensus with the widely accepted aromaticity order: thiophene > pyrrole > furan.37,38 The AIBICC values of five membered heterocycles given in Table 2 appear to be consistent with the expected order and lend confidence in the AIBICC methodology.


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Table 2. NICS(1), AIBIC and AIBICC Values of Some Selected Five-membered Heterocycles Containing S, N, and O as Heteroatom(s) Entry System NICS(1)a AIBIC AIBICC S1 Thiophene ‒10.24 4.573b 4.497 b S2 Isothiazole ‒11.15 4.377 3.696 S3 Thiazole ‒11.07 4.292 b 3.705 b S4 1,2,3-thiadiazole ‒12.66 5.525 3.871 S5 1,2,4-thiadiazole ‒11.92 4.141 b 2.968 b S6 1,2,5-thiadiazole ‒12.20 4.253 2.998 S7 1,3,4-thiadiazole ‒12.35 4.294 b 3.210 b N1 Pyrrole ‒10.09 4.435 3.798 N2 Pyrazole ‒11.30 4.258b 3.171 b N3 Imidazole ‒10.55 4.269 3.084 N4 1H-1,2,3-triazole ‒12.73 4.576b 2.843 N5 2H-1,2,3-triazole ‒11.28 4.163b 2.620 b N6 1H-1,2,4-triazole ‒11.57 4.103 2.502 N7 4H-1,2,4-triazole ‒12.76 4.394b 2.668 b N8 1H-tetrazole ‒13.49 4.826 2.485 N9 2H-tetrazole ‒13.89 4.434b 2.293 b N10 Pentazole ‒15.76 5.332 2.325 O1 Furan ‒9.38 4.262b 3.254 b O2 Isoxazole ‒10.51 4.368 2.802 O3 Oxazole ‒9.72 4.178b 2.626 b O4 1,2,3-oxadiazole ‒11.62 6.702 3.215 O5 1,2,4-oxadiazole ‒10.64 4.253b 2.203 O6 1,2,5-oxadiazole ‒10.29 4.627b 2.435 b O7 1,3,4-oxadiazole ‒12.29 4.323 2.261 a b NICS(1) (ppm) [RB3LYP/6-311+G**] values were taken from ref. 35, AIBIC values were taken from ref. 11.

4.3. Borazine, Azaborines and Fluorine Substituted Borazines The replacement of a CC unit in benzene by the isoelectronic BN unit has received much attention recently.7,39,40 The effects of this replacement on the properties, especially the aromaticity of the BN-substituted systems, are not fully understood yet. A study of aromaticity in simple aromatic azaborines and borazine can help in understanding their structure and properties. Hence, we studied the aromaticity of 1,2-dihydro-1,2-azaborine(3), 1,3-dihydro-1,3-azaborine(4), 1,4-dihydro-1,4-azaborine(5) and borazine systems

by

computing their AIBICC values. The AIBICC values for the systems in the same listed order are 4.11, 3.61, 3.42 and 4.26 as given in Table 3 compared to the benzene value 4.84. Thus



the AIBICC method predicts borazine to be less aromatic than benzene. In five or six membered heterocycles when two nitrogen atoms are adjacent, these systems are more aromatic than the equivalent rings, where the two nitrogen atoms are not adjacent. Similarly, in structure 3 the boron and nitrogen are adjacent atoms, and hence it is reasonable to expect 3 to be more aromatic than 4 and 5. AIBICC predicts 3 is more aromatic than 4 or 5 as shown in Table 3. Borazine contains symmetrically placed boron and nitrogen atoms with 6 π-electrons and all B-N bond lengths equal. It contains two types of angles, a larger BNB (~123 degrees) and a smaller NBN (~117 degrees) giving the free molecule D3h symmetry. Since the symmetry is less than D6h we expect it to be less aromatic than benzene. The question of whether borazine is aromatic is debated in the literature and many agree that it is aromatic but less aromatic than benzene.41–44 The electron deficient boron atoms have empty p-orbitals and the electronegative nitrogen atoms have lone pair electrons in the p-orbitals. The nitrogen atoms donate the lone pair electrons to the boron atom p-orbitals leading to six π-electrons and hence to the aromaticity. Fluorine is the most electronegative atom in the periodic table, and when substituted for hydrogens on boron, the boron can withdraw more electrons from the nitrogen, thus increasing the aromaticity. When the fluorines are substituted for the hydrogens attached to nitrogen, because of the electronegativity of fluorine, nitrogen donates less and the compound becomes less aromatic than borazine. Thus while borazine has the AIBICC value 4.26, B-trifluoroborazine(17) has the highest aromaticity (4.39) and N-trifluoroborazine(16) has the lowest (3.91). The balance between the two opposing effects decides the AIBICC values of the mixed fluorine substituted borazines. Our AIBICC results are largely in agreement with the literature values.41 Thus the following order is observed: B-trifluoroborazine(17) > B-difluoroborazine(11) > B-monofluoroborazine(7) > borazine(2) > N-fluoroborazine(6) > N-difluoroborazine(9) > N-trifluoroborazine(16). Other mixed


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substituted borazines have AI values in between those of B-trifluoroborazine(17) and N-trifluoroborazine(16), depending on the number and position of the substitution. The consistency of the AIBICC values with the expected aromaticity order validates their reliability.

Table 3. NICS(0)πzz, AIBIC and AIBICC Values for Borazine, Azaborines and Fluorine Substituted Borazines Entry System* NICS(0)πzza AIBICc AIBICC 1 Benzene ‒35.77 4.842 4.842 2 Borazine ‒7.87 4.769 4.261 b 3 1,2-dihydro-1,2-azaborine ‒25.42 4.733 4.114 4 1,3-dihydro-1,3-azaborine ‒31.15b 4.693 3.612 5 1,4-dihydro-1,4-azaborine ‒33.51b 4.588 3.416 6 1-fluoroborazine ‒9.01 4.629 4.135 7 2-fluoroborazine ‒6.90 4.810 4.292 8 1,2-difluoroborazine ‒7.99 4.703 4.197 9 1,3-difluoroborazine ‒10.14 4.497 4.016 10 1,4-difluoroborazine ‒7.97 4.683 4.177 11 2,4-difluoroborazine ‒6.21 4.866 4.336 12 1,2,3-trifluoroborazine ‒9.05 4.606 4.111 13 1,2,4-trifluoroborazine ‒7.20 4.772 4.252 14 1,2,5-trifluoroborazine ‒9.06 4.583 4.088 15 1,2,6-trifluoroborazine ‒7.21 4.799 4.278 d 16 1,3,5-trifluoroborazine ‒11.21 4.376 3.906 17 2,4,6-trifluoroborazine ‒5.77 4.934 4.391 18 1,2,3,4-tetrafluoroborazine ‒8.20 4.722 4.211 19 1,2,3,5-tetrafluoroborazine ‒10.10 4.503 4.017 20 1,2,4,5-tetrafluoroborazine ‒8.21 4.684 4.174 21 1,2,4,6-tetrafluoroborazine ‒6.67 4.881 4.345 22 1,2,3,4,5-pentafluoroborazine ‒9.19 4.652 4.149 23 1,2,3,4,6-pentafluoroborazine ‒7.58 4.841 4.312 24 Hexafluoroborazine ‒8.48 4.827 4.302 * In the nomenclature of the Fluoroborazine Systems (entry no. 6-24) the numbers 1, 3, 5 denote N and the numbers 2, 4, 6 denote B. aNICS(0)πzz (ppm) [B3LYP/6-311+G**] values were taken from ref. 44. bNICS(0)πzz (ppm) [B3LYP/6-311+G**] values were taken from ref. 39. cAIBIC values were taken from ref.8. d The AIBIC value (4.331) in the previous paper ref. 11 is corrected.



4.4. Some Selected Substituted Pyrazole and Imidazole Systems In the aromatic carbon ring, successive substitutions of heteroatom(s) X [X = B(H), N, O, S] for the CH group(s), leads to rich heterocyclic chemistry because of the structural changes effected by the ring atom substitution(s). Instead if we substitute the hydrogen attached to a carbon atom, the ring structure remains almost intact while modifying the electronic features due to the electron donating or electron withdrawing substituents. It will be of interest to see how the aromaticity of the ring is modified by these substituents. For this purpose, we investigated some substituted pyrazoles and imidazoles and the final AIBICC results are given in Table 4 and Table 5. As explained earlier, introducing a second nitrogen atom in the pyrrole ring reduces the aromaticity in pyrazole and imidazole, the former being slightly more aromatic. The reason for this decrease is the partial localization of the electron density near the newly introduced nitrogen, reducing the delocalized part contributing to the aromaticity. The modification by substitution may enhance or reduce the aromaticity by changing the fraction of localized versus delocalized electron densities. This is what we observe in Tables 4 and 5. The cyano group (CN) makes both pyrazole and imidazole more aromatic while the others (NH2, OH, Cl, SH, NO2, SO2F, SO2CF3, and N(SO2CF3)2) make them slightly less aromatic. A systematic study of the substituent effects is likely to give useful information on the factors contributing to the changes in aromaticity.


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Table 4. NICS(1)πzz, AIBIC and AIBICC Values of Some Selected Substituted Pyrazole Systems Entry

NICS(1)zza

AIBIC

AIBICC

X= 1 NH2 ‒29.83 4.180 3.115 2 OH ‒29.64 4.105 3.082 3 Cl ‒29.95 4.152 3.098 4 SH ‒29.77 4.199 3.118 5 H ‒32.79 4.258 3.171 6 NO2 ‒25.24 4.059 3.049 7 CN ‒28.21 4.325 3.195 8 SO2F ‒27.95 4.165 3.099 9 SO2CF3 ‒28.47 4.163 3.098 10 N(SO2CF3)2 ‒27.65 4.208 3.135 Entry no. 1-4 are π-donating substituents and entry no. 6-10 are π-accepting substituents. a NICS(0)zz (ppm) [B3LYP/6-311+G**] values were taken from ref. 36.

Table 5. NICS(1)πzz, AIBIC and AIBICC Values of Some Selected Substituted Imidazole Systems Entry

NICS(1)zza

AIBIC

AIBICC

X= 1 NH2 ‒28.45 4.142 3.002 2 OH ‒29.03 4.106 2.980 3 Cl ‒28.87 4.048 2.941 4 SH ‒28.72 4.121 2.988 5 H ‒31.68 4.269 3.084 6 NO2 ‒22.24 4.077 2.960 7 CN ‒26.87 4.368 3.152 8 SO2F ‒25.86 4.172 3.021 9 SO2CF3 ‒26.63 4.166 3.017 10 N(SO2CF3)2 ‒25.97 4.175 3.028 Entry no. 1-4 are π-donating substituents and entry no. 6-10 are π-accepting substituents. a NICS(0)zz (ppm) [B3LYP/6-311+G**] values were taken from ref. 36.



4.4.6. Neutral and Charged Imidazole and Pyrazole Systems When a given set of structures is very similar and the differences in their AIs are small, it becomes difficult to assess the relative aromaticity order. For example, the NICS(1) values calculated using the GIAO/B3LYP/6-311++G** level of theory predict values for imidazole(I0), imidazolium cation(I+), and imidazolate anion(I‒) are -10.57, -10.13 and 10.97 ppm, respectively, while that of benzene is ‒10.23 ppm.45 Since the numbers are very close, it is of interest to see the AIBICC predictions. We computed the AIBICC values for all the three systems and the results are reported in Table 6. Assuming the B3LYP/cc-pVTZ force field is sufficient to represent the relative orders of these systems, the aromaticity order predicted by AIBICC is cation(I+) > neutral(I0) > anion(I‒), as noted in Table 6. To check for consistency, we computed the AIBICC values for pyrazole(P0) and the corresponding ions (pyrazolium(P+) and pyrazolate(P‒)) as well. The AIBICC values are consistent, predicting cations(P+) to be more aromatic and anions(P‒) to be less aromatic compared to the neutral ones(P0). The positive charge reduces the fraction of localized electron density, in turn increasing the fraction that is delocalized and thus increasing the aromaticity. The negative charge in the anion does the reverse, localising more electron density and thus decreasing the aromaticity.

Table 6. NICS(1), AIBIC and AIBICC Values of Neutral and Charged Imidazole and Pyrazole Systems Entry System NICS(1) AIBIC AIBICC a I0 Imidazole ‒10.57 4.269 3.084 I+ Imidazolium ion ‒10.13a 4.572 3.282 I‒ Imidazolate ion ‒10.97a 3.990 2.890 b P0 Pyrazole ‒12.4 4.258 3.171 P+ Pyrazolium Ion ‒13.3b 4.513 3.355 b P‒ Pyrazolate Ion ‒11.6 4.239 3.113 a b NICS(1) (ppm) [B3LYP/6-311++G**] values were taken from ref. 45. NICS(1) (ppm) [B3LYP/6-31G*] values were taken from ref. 46.


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5. Conclusions The electron density of a heterocyclic aromatic fragment is partially localized near the more electronegative atom(s) of the ring. This reduces the delocalization, and hence the heterocylic systems are expected to be less aromatic than the analogous carbocyclic systems. This reduction in the delocalized electron density is not included in AIBIC, our previously proposed aromaticity index. Therefore, a correction based on Pauling's electronegativity equation has been introduced to the AIBIC methodology and a new index – AIBICC (AIBIC Corrected) is defined in the present work. The performance of the new index (AIBICC) has been tested extensively on several five and six membered heteroaromatic systems. The aromaticity trends thus observed are generally in line with the expectations based on chemical intuition, indicating that the adopted methodology is very promising for the quantification of aromaticity.



6. Acknowledgements The authors acknowledge the SERB project EMR/2016/001090 from Department of Science and Technology (DST), Government of India, New Delhi, for supporting this project in part and the Computational Facilities in the Computer Centre, Indian Institute of Technology Kanpur, Kanpur 208 016, India. S.D. thanks UGC and DST, Government of India, for Research Fellowships. D.M. thanks IITK for supporting postdoctoral research and Professor S. Yashonath for encouragement. The authors thank Mr. S. K. Pandey for helpful discussions. H.F.S. was supported by the U.S. National Science Foundation, Grant CHE – 1661604.


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7. Supporting Information The Cartesian coordinates and the total energies of the optimized minimum energy structures of all the systems reported in the present work are given in the Supporting Information (Tables S1-S6).



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Quantification of Aromaticity of Heterocyclic Systems Using Interaction

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