Chemical graph theory and n-center electron delocalization indices: a study on polycyclic aromatic hydrocarbons

Relations between aromaticity indices derived from chemical graph theory and those based on 6-center electron delocalization are investigated for a series of polybenzenoid hydrocarbons. Aromatic stabilization obtained by means of the effective scaled electron delocalization is highly correlated to the resonance energy, RE, obtained both from SCF MO calculations and conjugated ring circuits model. Local aromaticity of benzene rings is discussed using two different criteria, in one of them aromaticity is just given by the cyclic pi-electron conjugation of the ring, whereas terms involving more than one ring are also considered in the other one. Indices derived from chemical graph theory and those obtained from the 6-center electron delocalization give rise to the same local aromaticity. Moreover, 6-center electron delocalization provides more quantitative information.     

Applying the conjugated circuits method to Clar structures of [n]phenylenes for determining resonance energies

We consider the aromaticity of biphenylene and structurally related linear or angular [n]phenylenes for which the direct application of the model of conjugated circuits does not offer valid expressions for resonance energy and aromaticity. We located the cause of this problem as being due to Kekulé valence structures in which neighboring benzenoid rings are connected by two CC double bonds. By restricting the selection of Kekulé valence structures to those that contribute to Clar structures of such systems, we were able to show that linear and angular [n]phenylenes have approximately similar resonance energies, with angular [n]phenylenes being slightly more stable due to second order contributions arising from disjoint conjugated circuits. Expressions for resonance energies of [n]phenylenes up to n = 8 are listed and recursion expressions for higher n values are outlined.     

The aromatic fluctuation index (FLU): a new aromaticity index based on electron delocalization

In this work, the aromatic fluctuation index (FLU) that describes the fluctuation of electronic charge between adjacent atoms in a given ring is introduced as a new aromaticity measure. This new electronic criterion of aromaticity is based on the fact that aromaticity is related to the cyclic delocalized circulation of pi electrons. It is defined not only considering the amount of electron sharing between contiguous atoms, which should be substantial in aromatic molecules, but also taking into account the similarity of electron sharing between adjacent atoms. For a series of rings in 15 planar polycyclic aromatic hydrocarbons, we have found that, in general, FLU is strongly correlated with other widely used indicators of local aromaticity, such as the harmonic-oscillator model of aromaticity, the nucleus independent chemical shift, and the para-delocalization index (PDI). In contrast to PDI, the FLU index can be applied to study the aromaticity of rings with any number of members and it can be used to analyze both the local and global aromatic character of rings and molecules.     

Aromaticity: an ab initio evaluation of the properly cyclic delocalization energy and the pi-delocalization energy distortivity of benzene

A complete active space self-consistent field (CASSCF) calculation of the pi system of a conjugated molecule enables one to define optimal valence pi and pi* molecular orbitals (MOs). One may define from them a set of atom-centered orthogonal pi orbitals, one per carbon atom, and the resulting upper multiplet is used to define the pi-electron delocalization energy. This quantity is confirmed to be slightly distortive, i.e., to prefer bond-alternated geometries. One may also define strongly localized bond MOs corresponding to a Kekule structure and then perturb the associated strongly localized single determinant under the effect of the delocalization between the bonds and of the electronic correlation. The third order of perturbation introduces the contribution of the cyclic circulation of the electrons around the benzene ring, i.e. the aromatic energy contribution. Its value is about 1.5 eV. It is antidistortive, but remains important under bond alternation. The cyclic correlation effects are of minor importance.     

A theoretical and structural investigation of thiocarbon anions

Density functional theory energies, geometries, and population analyses as well as nucleus-independent chemical shifts (NICS) have been used to investigate the structural and magnetic evidence for cyclic CnSn(2-) and CnSn (n = 3-6) electron delocalization. Localized molecular orbital contributions to NICS, computed by the individual gauge for localized orbitals method, dissect pi effects from the sigma single bonds and lone pair influences. CnSn(2-) (n = 3-5) structures in Dnh symmetry are minima. Their aromaticity decreases with increasing ring size. C3S3(2-) is both sigma and pi aromatic, while C4S4(2-) and C5S5(2-) are much less aromatic. NICS(0)pi, the C-C(pi) contribution to NICS(0) (i.e., at the ring center), decreases gradually with ring size. In contrast, cyclic C6S6(2-) prefers D2h symmetry due to the balance between aromaticity, strain energy, and the S-S bond energies and is as aromatic as benzene. The theoretical prediction that C6S6(6-) has D6h minima was confirmed by X-ray structure analysis. Comparisons between thiocarbons and oxocarbons based on dissected NICS analysis show that CnSn(2-) (n = 3-5) and C6S6(6-) are less aromatic in Dnh symmetry than their oxocarbon analogues.     

The origin of aromaticity: important role of the sigma framework in benzene.

The physical nature of aromaticity is addressed at a high ab initio level. It is conclusively shown that the extrinsic aromatic stabilization energy of benzene E(ease)B, estimated relative to its linear polyene counterpart(s), is very well-reproduced at the Hartree-Fock (HF) level. This is a consequence of the fact that the contributions arising from the zero-point vibrational energy (ZPVE) and electron correlation are rather small. More specifically, they yield together 2.0 kcalmol(-1) to the destabilization of benzene. A careful scrutiny of the HF energies by virial theorem shows further that the kinetic energies of the sigma and pi electrons E(T)HF(sigma) and E(T)HF(pi) are strictly additive in the gauge linear zig-zag polyenes, which also holds for their sum Et(T)HF This finding has the important corollary that E(ease)B is little dependent on the choice of the homodesmic reactions involving zig-zag polyenes. A detailed physical analysis of the sigma- and pi-electron contributions to extrinsic aromaticity requires explicit introduction of the potential energy terms Vne, Vee, and Vnn, which signify Coulomb interactions between the electrons and the nuclei. The Vee term involves repulsive interaction Vee(sigmapi) between the sigma and pi electrons, which cannot be unequivocally resolved into sigma and pi contributions. The same holds for the Vnn energy, which implicitly depends on the electron density distribution via the Born-Oppenheimer (BO) potential energy surface. Several possibilities for partitioning Vee(sigmapi) and Vnn terms into sigma and pi components are examined. It is argued that the stockholder principle is the most realistic, which strongly indicates that E(ease)B is a result of favorable sigma-framework interactions. In contrast, the pi-electron framework prefers the open-chain linear polyenes.     

Aromatic character of polycyclic π systems formed by fusion of two or more rings of the same size

The sequential line plot of topological resonance energy (TRE) against the number of π electrons (N(π)) for any polycyclic aromatic hydrocarbon (PAH) is very similar with the same number of extrema to that for benzene. Thus, global aromaticity of a PAH molecular ion strongly reflects that of a benzene molecular ion. Likewise, the N(π) dependence of TRE for any polycyclic π system formed by fusion of two or more rings of the same size reflects that for a monocyclic species of the same ring size. In general, TREs for such polycyclic π systems and their molecular ions can be interpreted consistently by reference to those for neutral and charged monocyclic species of the same ring size.     

QTAIM N-center delocalization indices as descriptors of aromaticity in mono and poly heterocycles

The implementation of the n-center electron delocalization indices, n-DIs, and n-order electron localization indices, n-LIs, within the framework of the quantum theory of atoms in molecules, QTAIM, is performed. n-DIs are shown to be very useful to study the local aromaticity in monocyclic and polycyclic compounds. Total and pi n-DIs from n=4 to 7 were computed for a series of typical 4, 5, 6, and 7-center aromatic and antiaromatic rings. For n>or=5 the pi n-DI accounts for the 95% of the total n-DI and can be employed alone to measure the aromaticity. A scaling factor on the n-DIs is required in order to compare the aromaticity of [5c-6e] and [6c-6e] rings, the same correction allows to estimate the relative aromatic stabilization of polycyclic compounds using the sum of its values for individual rings. This is called Effective Scaled Electron Delocalization, ESED. The comparison with other aromaticity indices reflects a good correlation between ESED and both resonance energies, and HOMA indices. The most important differences between scaled pi n-DIs and NICS(0) indices are found for compounds that contain rings with different number of centers or pi electrons.     

The leap-frog effect of ring currents in benzene

Symmetry arguments show that the ring-current model proposed by Pauling, Lonsdale, and London to explain the enhanced diamagnetism of benzene is flawed by an intrinsic drawback. The minimal basis set of six atomic 2p orbitals taken into account to develop such a model is inherently insufficient to predict a paramagnetic contribution to the perpendicular component of magnetic susceptibility in planar ring systems such as benzene. Analogous considerations can be made for the hypothetical H(6) cyclic molecule. A model allowing for extended basis sets is necessary to rationalize the magnetism of aromatics. According to high-quality coupled Hartree-Fock calculations, the trajectories of the current density vector field induced by a magnetic field perpendicular to the skeletal plane of benzene in the pi electrons are noticeably different from those typical of a Larmor diamagnetic circulation, in that (i) significant deformation of the orbits from circular to hexagonal symmetry occurs, which is responsible for a paramagnetic contribution of pi electrons to the out-of-plane component of susceptibility, and (ii) a sizable component of the pi current density vector parallel to the inducing field is predicted. This causes a waving motion of pi electrons; streamlines are characterized by a "leap-frog effect".     

Molecules-in-molecule estimation of the extent of localization of Kekuléan substructures in polycyclic aromatic hydrocarbons

This article first revises graph-theoretical (local aromaticity and overall molecular) indices, introduced by M. Randi? in 1975, for benzenoid hydrocarbons and somewhat improves them for computer enumeration. This goes beyond total Kekulé structure enumeration, yielding an index calculation useful for the quantitative estimation of localization of different Kekuléan substructures (including ethylene-, benzene-, annulene-, and radialene-units). This may be viewed as a "molecules-in molecule" approach to polycyclic aromatic hydrocarbons within the context of graph theoretical partitioning.     

NIR vibrational overtone spectra of N-methylaniline, N,N-dimethylaniline and N,N-diethylaniline--a conformational structural analysis using local mode model

In aniline, the lone pair electrons on the nitrogen atom in the amino group interact with the pi electrons of the ring and the mechanical frequency of the ring CH oscillator shows a red shift from that of benzene. This happens because of the parallel orientation of the pi electrons in the two molecules. This effect is observed in N-methylaniline also. But in N,N-dimethylaniline, the addition of two alkyl group to the amino group changes the parallel orientation of pi electrons of the nitrogen. This changes the electron donating nature of the amino substituent and as a result, a blue shift is observed in the mechanical frequency of the ring CH oscillator from that of benzene. The same effect is observed in the ring CH oscillator frequency of N,N-diethylaniline also.     

Non-fused polyaromatic hydrocarbons: interactions of aromatic and antiaromatic rings through a CC bond

The interaction of the moieties of benzene, cyclobutadiene, cyclopentadinyl anion, and the cyclopentadianide cation upon each other and upon a CC bond connecting pairs of these rings is investigated computationally. The resulting non-fused bicycles include biphenyl, phenylcyclobutadiene, phenylcyclopentadienylium, phenylcyclopentadienide, pentafulvalene, cyclobutadienyl–cyclopentadienylium, cyclobutadienyl–cyclopentadienide, and bicyclobutadiene. The relative stability and aromaticity are assessed from hydrogenation energies, aromatic stabilization energies, ring separation energies, nucleus-independent chemical-shift, harmonic oscillator model of aromaticity, and natural bond orbital analysis. Calculations are performed with density functional theory (B3LYP) and Møller–Plesset perturbation theory of second order (MP2). Enthalpy quantities are also determined by G3. When both rings are aromatic in character, the bridging bond is mostly σ in character. When one or both of the rings is antiaromatic, the bridging bond has significant π character. Systems with contrasting aromaticities have CC bridging bonds of lengths between CC single bond lengths and CC double bond lengths and where the systems were charged, the charge is evenly distributed between the rings.     

运用密度泛函活性理论的信息论方法研究苯并富烯衍生物的芳香性

文献中已有越来越多的芳香性体系被发现,同时也有越来越多的芳香性指标被提出来,但是如何解释芳香化合物稳定性的起源以及理解芳香性的本质仍然是当今理论化学中一个悬而未决的难题。运用我们新近提出的密度泛函活性理论信息论方法,不久前我们曾对一系列富烯衍生物进行了系统研究并得到了一个全新的认识。本文进一步探讨苯并富烯衍生物的芳香性行为,目的在于考察一个或多个苯环与富烯连接之后其芳香性发生变化的情况。运用香农熵,费舍尔信息,Ghosh-Berkowitz-Parr熵,Onicescu信息能,信息增益,以及相对Rényi熵六个信息量,和四种芳香指标,ASE,HOMA,FLU和NICS,我们系统地研究了信息量和芳香性指标在单、双、三苯并富烯衍生物中的相关性。我们发现,不管是否有苯环与富烯相连,芳香指标和信息量的交叉相关性都是一样的。这表明,虽然苯环本身具有芳香性,但苯环与富烯相连并不能改变富烯的芳香性与反芳香性本质。苯并富烯衍生物与富烯衍生物的芳香性和反芳香性一致。苯并富烯衍生物的芳香性和反芳香性完全取决于富烯本身的芳香性和反芳香性。这些结果为认识和理解复杂体系芳香性和反芳香性起源和本质将提供有益的启示。     

Aromaticity and relative stabilities of azines

The most refined nucleus-independent chemical shift index (NICS(0)(πzz)) and the extra cyclic resonance energies (ECREs), based on the block localized wave function (BLW) method, show that the aromaticity of all azines is like that of benzene. The same is true for aza-naphthalenes relative to naphthalene. The lower relative energies of isomers with vicinal N's are due to the weakness of NN bonds rather than to reduced aromaticity.     

Influence of bond fixation in benzo-annulated N-salicylideneanilines and their ortho-C(=O)X derivatives (X = CH3, NH2, OCH3) on tautomeric equilibria in solution

1H, 13C, and 15N NMR spectra show that an ortho-C(=O)X group present in the molecules of N-salicylideneanthranilamide (X = NH2), methyl N-salicylideneanthranilate (X = OCH3), N-salicylidene-o-aminoacetophenone (X = CH3), and their benzo analogues have only a minor effect on the tautomeric OH/NH-equilibrium in solution. Only two of three possible tautomers were detected. Lability of the absent form was proved by theoretical calculations. Calculated energies show that the enolimino form (OH) is less stable than the enaminone (NH) form only for dibenzo-annulated N-salicylideneanilines. The population of each species in the tautomeric mixture was found to be inversely proportional to its energy. Application of the geometry-based aromaticity index HOMA shows that the effectiveness of the pi-electron delocalization in different rings in the molecule depends mostly on the position of benzo-annulation. Both the NH...O and N...HO hydrogen bonds present in the NH and OH tautomers, respectively, increase the aromaticity of the quasirings H-O-C=C-C=N and O=C-C=C-N-H and decrease the aromatic character of the fused benzene ring. These results seem to be reliable when N-salicylideneanilines studied are compared with naphthalene and their benzo-annulated derivatives, i.e., phenanthrene, anthracene, and triphenylene. An analysis of the effectiveness of pi-electron delocalization confirms that in all cases studied, the OH form is more stable. Although the HOMA values and calculated energies are not a criterion that allows determination of the dominating tautomer, both of these parameters correctly show the effect of changes in the molecular topology on tautomeric preferences.     

An energetic measure of aromaticity and antiaromaticity based on the Pauling-Wheland resonance energies

Various criteria based on geometric, energetic, magnetic, and electronic properties are employed to delineate aromatic and antiaromatic systems. The recently proposed block-localized wave function (BLW) method evaluates the original Pauling-Wheland adiabatic resonance energy (ARE), defined as the energy difference between the real conjugated system and the corresponding virtual most stable resonance structure. The BLW-derived ARE of benzene is 57.5 kcal mol(-1) with the 6-311+G** basis set. Kistiakowsky's historical experimental evaluation of the stabilization energy of benzene (36 kcal mol(-1)), based on heats of hydrogenation, seriously underestimates this quantity due to the neglect of the partially counterbalancing hyperconjugative stabilization of cyclohexene, employed as the reference olefin (three times) in Kistiakowsky's evaluation. Based instead on the bond-separation-energy reaction involving ethene, which has no hyperconjugation, as well as methane and ethane, the experimental resonance energy of benzene is found to be 65.0 kcal mol(-1). We derived the "extra cyclic resonance energy" (ECRE) to characterize and measure the extra stabilization (aromaticity) of conjugated rings. ECRE is the difference between the AREs of a fully cyclically conjugated compound and an appropriate model with corresponding, but interrupted (acyclic) conjugation. Based on 1,3,5-hexatriene, which also has three double bonds, the ECRE of benzene is 36.7 kcal mol(-1), whereas based on 1,3,5,7-octatetraene, which has three diene conjugations, the ECRE of benzene is 25.7 kcal mol(-1). Computations on a series of aromatic, nonaromatic, and antiaromatic five-membered rings validate the BLW-computed resonance energies (ARE). ECRE data on the five-membered rings (derived from comparisons with acyclic models) correlate well with nucleus-independent chemical shift (NICS) and other quantitative aromaticity criteria. The ARE of cyclobutadiene is almost the same as butadiene but is 10.5 kcal mol(-1) less than 1,3,5-hexatriene, which also has two diene conjugations. The instability and high reactivity of cyclobutadiene thus mainly result from the sigma-frame strain and the pi-pi Pauli repulsion.     

Aromaticity: molecular-orbital picture of an intuitive concept

Geometry is one of the primary and most direct indicators of aromaticity and antiaromaticity: a regular structure with delocalized double bonds (e.g., benzene) is symptomatic of aromaticity, whereas a distorted geometry with localized double bonds (e.g., 1,3-cyclobutadiene) is characteristic of antiaromaticity. Here, we present a molecular-orbital (MO) model of aromaticity that explains, in terms of simple orbital-overlap arguments, why this is so. Our MO model is based on accurate Kohn-Sham DFT analyses of the bonding in benzene, 1,3-cyclobutadiene, cyclohexane, and cyclobutane, and how the bonding mechanism is affected if these molecules undergo geometrical deformations between regular, delocalized ring structures, and distorted ones with localized double bonds. We show that the propensity of the pi electrons is always, that is, in both the aromatic and antiaromatic molecules, to localize the double bonds, against the delocalizing force of the sigma electrons. More importantly, we show that the pi electrons nevertheless decide about the localization or delocalization of the double bonds. A key component of our model for uncovering and resolving this seemingly contradictory situation is to analyze the bonding in the various model systems in terms of two interpenetrating fragments that preserve, in good approximation, their geometry along the localization/delocalization modes.     

Effect on ring current of the Kekulé vibration in aromatic and antiaromatic rings

Derivative current-density maps are used to follow the changes in ring-current (and hence, on the magnetic criterion, the changes in aromaticity) with the Kekulé vibrations of the prototypical aromatic, antiaromatic, and nonaromatic systems of benzene, cyclooctatetraene (COT), and borazine. Maps are computed at the ipsocentric CHF/6-31G**//RHF/6-31G** level. The first-derivative map for benzene shows a growing-in of localized bond currents, and the second-derivative map shows a pure, paratropic "antiring-current", leading to the conclusion that vibrational motion along the Kekulé mode will reduce the net aromaticity of benzene, on average. For planar-constrained D(4h) COT, the Kekulé mode (positive for reduction of bond-length alternation) increases paratropicity at both first and second order, indicating an average increase in antiaromaticity with zero-point motion along this mode. On the ring-current criterion, breathing expansions of benzene and D(4h) COT reduce aromaticity and increase antiaromaticity, respectively.