Ground-state properties of benzenoid hydrocarbons by simple bond orbital resonance theory approach

π-electron energies and bond orders of benzenoid hydrocarbons with up to five fused hexagons have been considered by the simple Bond Orbital Resonance Theory (BORT) approach. The corresponding ground states were determined according to four BORT models. In the first three models a diagonalisation of the Hückel-type Hamiltonian was performed in the bases of Kekulé, of Kekulé and mono-Claus and of Kekulé and Claus resonance structures, respectively. In the fourth model a simple BORT ansatz was used. According to this ansatz, the ground state is a linear combination of the positive Kekulé structures, all with equal coefficients. It was shown that π-electron energies and bond orders obtained by these models correlate much better with the PPP energies and bond orders than with the Hückel energies and bond orders. This indicates that a simple BORT approach is quite reliable in predicting the more sophisticated PPP results. Concerning the relative performance of the four BORT models, the best results were obtained with the BORT ansatz. The performance deteriorates with the expansion of the basis set. This is attributed to the fact that in these models the improvement of the basis set is not accompanied with the corresponding improvement of the Hamiltonian. Comparing the BORT-ansatz bond orders with the Pauling bond orders, it was shown that BORT-ansatz bond orders correlate much better with the PPP bond orders. This revised version was published online in July 2006 with corrections to the Cover Date.     

Heats of atomization of some conjugated molecules containing nitrogen or oxygen by a novel semiempirical method

Heats of atomization for a range of conjugated molecules containing nitrogen or oxygen are calculated by a semiempirical method that combines some features of both the MO and VB theories. The π ground state of each conjugated molecule is represented as a linear combination of Kekulé structures. Unlike in the VB theory, each Kekulé structure is a determinant containing bond orbitals. Here experimental heats of atomization are reproduced approximately as well as by the more sophisticated SCF –MO approach. The use of this method is, however, much simpler since it amounts to a single diagonalization of a matrix of the order equal to the number of Kekulé structures only.     

Ordering of Kekulé structures using nonadjacent numbers

Kekulé indices and conjugated circuits are computed for 36 Kekulé structures, together with two VB quantities associated with the corresponding factor graphs (previously called submolecules). These latter quantitites are nonadjacent numbers of Hosoya and the reciprocal of the connectivity indices of Randi?. It was found that the index of Hosoya successfully orders a set of Kekulé structures belonging to the same hydrocarbon in a parallel order as their Kekulé indices and branching indices. This substantiates the relation between VB and MO theories. A code is derived by summing contributions of nonadjacent numbers in all Kekulé stuctures of a hydrocarbon. The order of the resulting codes is found to be identical to the order of the molecular properties (resonance energies, π-energies, and eigenvalues) of the hydrocarbons.     

Novel graph-theoretical approach to estimating the relative importance of individual Kekulé valence structures. II. Benzenoid systems having four to seven fused benzene rings: “Pseudodegenerate” states

Kekulé structures of 10 nonlinear acenes comprising 83 graphs are studied through the use of connectivities [M. Randi?, J. Am. Chem. Soc. 97 , 6609 (1975)] of their corresponding submolecules [H. Joela, Theor. Chim. Acta 39 , 241 (1975)]. In certain rare cases states were identified to have identical branching indices but different Kekulé indices [A. Graovac, I. Gutman, M. Randi?, and N. Trinajsti?, J. Am. Chem. Soc. 95 , 6267 (1973)]. Such states are termed pseudodegenerate states. A method is described to forecast and another to remedy such situations. The method emphasizes the relation between VB (resonance) and MO theories using graph-theoretical concepts.     

An ab initio valence bond (VB) calculation of the π delocalization energy in borazine,B3N3H6

Valence bond (VB) calculations using a double‐zeta D95 basis set have been performed for borazine, B₃N₃H₆ and for benzene, C₆H₆ in order to determine the relative weights of individual standard Lewis structures. In the delocalized resonance scheme of borazine, the structure ( I ) with no double bonds and three lone pairs of electrons at the three nitrogen atoms is the major contributor with a structural weight of 0.17, followed by six equivalent Lewis structures with one double bond and two lone pairs at two nitrogen atoms ( II ) with weights of 0.08 each. In the case of benzene, the two Kekulé structures ( III ) contribute with structural weights of 0.15 each, followed by 12 equivalent ionic structures ( IV ) with weights of 0.03 each, followed by the three equivalent Dewar‐type structures ( V ) with structural weights of 0.02 each. The values of 54.1 and 45.8 kcal mol⁻¹ for the delocalization energies of borazine and benzene were estimated. Therefore, B₃N₃H₆ is calculated to have substantial aromatic character, similar to benzene, when we assume that the resonance energy can provide a criterion for aromaticity. © 2005 Wiley Periodicals, Inc. Heteroatom Chem 16:311–315, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20095     

The electronic structure of inorganic benzenes: valence bond and ring-current descriptions

Valence bond (VB) theory and ring-current maps have been used to study the electronic structure of inorganic benzene analogues X(6)H(6) (X = C (1), Si (2)), X(6) (X = N (3), P (4)), X(3)Y(3)H(6) (X,Y = B,N (5), B,P (6), Al,N (7), Al,P (8)), and B(3)Y(3)H(3) (Y = O (9), S (10)). It is shown that the homonuclear compounds possess benzene-like character, with resonance between two Kekulé-like structures and induced diatropic ring currents. Heteronuclear compounds typically show localization of the lone pairs on the electronegative atoms; Kekulé-like structures do not contribute. Of the heteronuclear compounds, only B(3)P(3)H(6) (6) has some benzene-like features with a significant contribution of two Kekulé-like structures to its VB wave function, an appreciable resonance energy, and a discernible diatropic ring current in planar geometry. However, relaxation of 6 to the optimal nonplanar chair conformation is accompanied by the onset of localization of the ring current.     

Novel graph-theoretical approach to estimating the relative importance of individual Kekulé valence structures. I. Simple catacondensed systems

A novel graph-theoretical approach for ordering Kekulé valence structures of benzenoid hydrocarbons is presented. The approach involves the transformation of the Kekulé structures into the subspaces of their individual double bonds. The submolecules generated in this way [H. Joela, Theor. Chim. Acta 39 , 241 (1975)] are ordered according to suitable connectivity indices. The resulting orders parallel those predicted from the so called Kekulé indices [A. Graocvac, I. Gutman, M. Randi?, and N. Trinajst?, J. Am. Chem. Soc. 95 , 6267 (1973)]. A relation is thus illustrated between VB and MO theories. The method is new and allows the prediction of the relative stabilities of structures from purely combinatorial vent without resort to computer.     

Innate degree of freedom of a graph

For a Kekulé structure we consider the smallest number of placements of double bonds such that the full Kekulé structure on the given parent graph is fully determined. These numbers for each Kekulé structure of the parent graph sum to a novel structural invariant F, called the degree of freedom of the graph. Some qualitative characteristics are identified, and it is noted that apparently it behaves differently from a couple of other invariants related to Kekulé structures.     

Coding and ordering Kekulé structures

The concept of numerical Kekulé structures is used for coding and ordering geometrical (standard) Kekulé structures of several classes of polycyclic conjugated molecules: catacondensed, pericondensed, and fully arenoid benzenoid hydrocarbons, thioarenoids, and [N]phenylenes. It is pointed out that the numerical Kekulé structures can be obtained for any class of polycyclic conjugated systems that possesses standard Kekulé structures. The reconstruction of standard Kekulé structures from the numerical ones is straightforward for catacondensed systems, but this is not so for pericondensed benzenoid hydrocarbons. In this latter case, one needs to use two codes to recover the geometrical Kekulé structures: the Wiswesser code for the benzenoid and the numerical code for its Kekulé structure. There is an additional problem with pericondensed benzenoid hydrocarbons; there appear numerical Kekulé structures that correspond to two (or more) geometrical Kekulé structures. However, this problem can also be resolved.     

Resonance energies of large conjugated hydrocarbons by a statistical method

We developed a theoretical method for studying the aromatic stability of large molecules, molecules having a dozen and more fused benzene rings. Such molecules have so far often been outside the domain of theoretical studies. Combining the statistical approach and a particular graph theoretical analysis, it is possible to derive the expressions for molecular resonance energy for molecules of any size. The basis of the method is enumeration of conjugated circuits in random Kekulé valence structures. The method has been applied to evaluation of the resonance energies of conjugated hydrocarbons having about a dozen fused benzene rings. The approach consists of (1) construction of random Kekulé valence structures, (2) enumeration of conjugated circuits within the generated random valence structures, and (3) application of standard statistical analysis to a sufficiently large sample of structures. The construction of random valence forms is nontrivial, and some problems in generating random structures are discussed. The random Kekulé valence structures allow one not only to obtain the expression for molecular resonance energies (RE ) and numerical estimates for RE , but also they provide the basis for discussion of local molecular features, such as ring characterization and Pauling bond orders.     

Infrared spectra of thiopyrylium and pyrylium cations

Normal coordinate analysis has been carried out for the in-plane and out-of-plane vibrations of thiopyrylium (1) and pyrylium (2) cations which are isoelectronic with benzene, in order to investigate the structural characteristics (the contribution of the carbonium ion structures and the Kekulé structures to their resonance hybrid). Several sets of parameters for the double bond stretching constants have been chosen considering the delocalization of the positive charge. As a result, much more delocalization of the positive charge in 1 than in 2 has been found.     

Nanotubes: number of Kekulé structures and aromaticity

Carbon nanotubes (CNTs) are composed of cylindrical graphite sheets consisting of sp(2) carbons. Due to their structure CNTs are considered to be aromatic systems. In this work the number of Kekulé structures (K) in "armchair" CNTs was estimated by using the transfer matrix technique. All Kekulé structures of the cyclic variants of naphthalene and benzo[c]phenanthrene have been generated and the basic patterns have been obtained. From this information the elements of the transfer matrix were derived. The results obtained indicate that K (and the resonance energy) is greater if tubulenes are extended in the vertical than in the horizontal direction. Tubulenes are therefore more stabile than cyclic strips. An illustration, obtained by using scanning probe microscope, has been attached to affirm the existence of thin CNTs.     

A combinatorial/geometric analysis of parallelogram-like benzenoids

We recently reported an algorithm to count Kekulé (resonance) structures for convex cyclofusenes using a combinatorial/geometric approach. Previously, we presented an algorithm for counting resonance structures for parallelogram-like benzenoids with holes by counting descending paths using rectangular meshes with holes. In this article, we employ a similar combinatorial/geometric approach to determine algorithms that will facilitate counting of the resonance structures in parallelogram-like benzenoids with no holes.     

The valence bond description of xylylenes

The ground states or ortho-, meta- and para-xylylenes and low lying excited states of meta-xylylenes are investigated by the valence-bond approach. Weights of structural formulas are calculated. A criterion for biradical character is defined as the sum of the weights of biradical structures. It is found that meta-xylylene is best described as a benzene ring relatively unperturbed by the two adjacent méthylène radicals, and that ortho- and para-xylylene are unequal mixtures of localized Kékulé structures and aromatic biradical structures. Surprisingly, low lying excited states of meta-xylylene deviate from the zwitterionic picture expected for singlet excited states of biradicals.     

Computing the Kekulé structure count for alternant hydrocarbons

A fast computer algorithm brings computation of the permanents of sparse matrices, specifically, molecular adjacency matrices. Examples and results are presented, along with a discussion of the relationship of the permanent to the Kekulé structure count. A simple method is presented for determining the Kekulé structure count of alternant hydrocarbons. For these hydrocarbons, the square of the Kekulé structure count is equal to the permanent of the adjacency matrix. In addition, for alternant structures the adjacency matrix for N atoms can be written in such a way that only an N/2 × N/2 matrix need be evaluated. The Kekulé structure count correlates with topological indices. The inclusion of the number of cycles improves the fit. When comparing with previous results, the variance decreases 74%. The calculated standard heat of formation correlates with the logarithm of the Kekulé structure count. This heat increments 349 kJ/mol each time the Kekulé structure count increases by one order of magnitude. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Algebraic Kekulé formulas for benzenoid hydrocarbons

By assigning two pi-electrons of CC double bonds in a Kekulé valence structure to a benzene ring if not shared by adjacent rings and one pi-electron if CC double bond is shared by two rings we arrived at numerical valence formulas for benzenoid hydrocarbons. We refer to numerical Kekulé formulas as algebraic Kekulé valence formulas to contrast them to the traditional geometrical Kekulé valences formulas. The average over all numerical Kekulé valence structures results in a single numerical structure when a benzenoid hydrocarbon molecule is considered. By ignoring numerical values the novel quantitative formula transforms into a qualitative one which can replace incorrectly used notation of pi-electron sextets to indicate aromatic benzenoids by placing inscribed circles in adjacent rings-which contradicts Clar's characterization of benzenoid hydrocarbons.     

价键理论新进展

概要介绍了现代价键理论的几个主要方法,并讨论了它们各自的特点及其发展现状,并重点介绍了键表方法的基本理论、计算程序及一些应用。