Stability of Conjugated Carbon Nanocones

We use interlacing techniques to prove that carbon nanocones who have a Fries Kekulé structure have closed Hückel shells, and that this result can be extended to all conjugated cones where each edge belongs to a hexagonal face and the configuration of the non-hexagonal faces are consistent with a Fries Kekulé structure. Cones with Fries Kekulé structure or substructure are topical—not only from a valence bond theoretical point of view—since a previous ab initioanalysis favored cones where the pentagons at the tip are configured as in a Fries Kekulé structure. The question of interdependence will therefore be addressed.     

The number of Kekulé structures and the thermodynamic stability of conjugated systems

The dependence of Hückel π-electron energies, E_π, on the basic graph theoretical parameters N (the number of vertices), ν (the number of edges) and ASC (the algebraic structure count) is explored. The form with the ASC enters E_π is established and an equation for E_π is developed. It is shown how the early and apparent success of the (resonance) theory rested on the fortunate fact that all Kekulé structures for benzenoid hydrocarbons and acyclic polyenes have the same parity. The significance of ASC in determining chemical stability and reactivity is dicussed briefly.     

Excited stateπ-electron polarizabilities for some condensed aromatic molecules

Excited state π-electron polarizabilities are calculated with Hückel molecular orbitals where the β parameter is calibrated to electrochromic effect data for some condensed aromatic systems. The excited state parameter is found to beβ_c=3.6 eV as compared to the ground state value of β_g=7.5 eV. Our results are about the same as calculations with PPP orbitals and agreement with experimental data is generally good.     

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.     

Bond length alternation in cyclic polyenes. VII. Valence bond theory approach

The problem of bond length alternation in linear extended ϕ-electron systems with conjugated double bonds is examined using the valence bond theory applied to a simple model of cyclic polyenes C_NH_N with N = 4v and N = 4v + 2 sites as described by the Pariser-Parr-Pople Hamiltonian. Overlap enhanced atomic orbitals are employed in order to achieve the optimal treatment with only two Kekulé structures. The predicted bond length alternation and its magnitude are in good agreement with earlier molecular orbital based calculations and with experiment. Special attention is given to the discussion of the origin of bond length alternation in long polyenic chains and to the role of the resonance energy leading to stabilization of undistorted, symmetric structures for small aromatic (N = 4v + 2) cycles. © 1996 John Wiley & Sons, Inc.     

Heterocyclic nitro compounds

The MO LCAO method with the Hückel approximation was used to calculate the -electron densities, the bond orders, and the energies of the -electron interaction of a number of 1,2,4-triazole derivatives. The results obtained agree satisfactorily with the chemical and physicochemical properties of the triazoles.See [1] for communication IX.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 409–413, March, 1971.     

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.     

Variable electronegativity SCF-MO calculations on the electronic structure and spectra of some substituted benzenes I. Monosubstitutions

π-electron SCF-MO theory in its variable electronegativity formalism has been applied to some monosubstituted benzenes. Calculated charge densities and bond orders for the ground and the first excited electronic states are correlated with chemical reactivity and the changes in molecular geometry on electronic excitation. The calculated results for spectra are compared with those obtained using the PPP method and also with the available experimental data.     

Semiempirical MO study on the abnormal bond orders of large networks of highly branched polyenes

The π-electronic structures of the ground state of linear and highly branched polyenes with up to 80 π-electrons are calculated with particular reference to the alternation of the bond orders. The MO methods adopted are HMO, PPP , variable-β, γ, and its improved version. The effect of the electron correlation through singly and doubly excited configurations is estimated with a second-order perturbation calculation. The calculated bond orders systematically vary with the degree of approximation used. Most of the bond order values can be grouped into either a single or double bond region. In certain series of highly branched polyenes the bond orders of double and single bonds at the root of branching, respectively, get smaller and larger as the size of the molecule increases and sometimes their difference gets diminishingly small. The origin of these abnormal bond orders is discussed in terms of the π-electron flow networks.     

Pancake Bond Orders of a Series of π‐Stacked Triangulene Radicals

Conjugated radicals are capable of forming π‐stacking “pancake‐bonded” dimers. Members of the family of triangulene hydrocarbons, non‐Kekulé neutral multiradicals, can utilize more than one singly occupied molecular orbital (SOMO) to form multiple pancake‐bonded dimers with formal bond orders of up to five. The resulting dimer binding energies can be quite high and the intermolecular contacts rather small compared to the respective van der Waals values. The preferred configurations are driven by the large stabilization energy of overlapping SOMOs.     

Explaining the derivation and functioning of the exact infinite-order two-component Dirac theory in terms of the Hückel model

The transition from the four-component Dirac theory to the exact two-component formalism is considered by using a simple algebraic model of the Dirac hamiltonian. This model is found to correspond to the four-center Hückel matrix and permits to replace the complex operator algebra by very easy matrix operations. This mapping of operators onto number matrices shows how the exact two-component relativistic hamiltonians are derived. It also explains certain conceptual aspects of the relation between four-component and two-component hamiltonians and their eigenfunctions. The generalized Hückel model of a four-center heteroatomic π-electron system can be used to analytically analyze the essential features of a variety of different exact and approximate two-component methods of relativistic quantum chemistry. This article is dedicated to Professor Tadeusz Marek Krygowski on the occasion of his 70th birthday.     

π-Electron currents in fixed π-sextet aromatic benzenoids

In view of different patterns of π-electron density currents in benzenoid aromatic compounds it is of interest to investigate the pattern of ring currents in various classes of compounds. Recently such a study using a graph theoretical approach to calculating CC bond currents was reported for fully benzenoid hydrocarbons, that is, benzenoid hydrocarbons which have either π-sextets rings or “empty” rings in the terminology of Clar. In this contribution we consider π-electron currents in benzenoid hydrocarbons which have π-electron sextets and C=C bonds fully fixed. Our approach assumes that currents arise from contributions of individual conjugated circuits within the set of Kekulé valence structures of these molecules.     

Predictions of molecular geometries and electronic spectra of complex unsaturated molecules from MC-LCAO-MO method with particular reference to triplet-triplet transitions of naphthalene

An MC-LCAO-MO approach which has been proposed for open-shell systems of unsaturated hydrocarbons having degenerate MO's is applied to naphthalene, calculating its molecular geometry and electronic spectrum. The results are compared with those obtained by the usual semi-empirical SCF-CI method and with experiment. As for benzene, anthracene, phenanthrene and triphenylene, the bond lengths and the -electron energies in their ground states are calculated in the same manner. Most of the calculated bond lengths are in fairly good agreement with experiment. The total -electron energies of the ground states obtained by the MC-LCAO-MO and SCF-CI methods agree within about 0.01 eV when CI is included and within about 0.1 eV when CI is not invoked. It is found that the electronic spectrum of naphthalene obtained by the present method is in good agreement with that derived from the SCF-CI method and also explains most part of experiments. A detailed discussion is given on the calculated triplet-triplet absorption spectrum and its intensity distribution of naphthalene.     

Properties of the low-lying electronic states of phenanthrene: Exact PPP results

We report properties of the exact low-lying states of phenanthrene, its anion and dianion within the Pariser-Parr-Pople (PPP ) model. The experimentally known singlet states of the neutral molecule are well reproduced by the model. The intensities for one and two photon absorption to various singlet states are also in good agreement with experiment. From the bond orders of these states, we predict the equilibrium geometries. The relaxation energies of these states, computed from charge-charge correlations and bond orders, are presented. We also present results of ring current calculations in the singlet ground state of phenanthrene. We have also reported energies, spin densities, bond orders, and relaxation energies of several triplet states and compared them with experiments as well as with other calculations, where available. The fine structure constants D and E, computed in the lowest triplet state, compare well with those obtained from experiments. These properties are also presented for the anions and the dianions. The PPP model in these cases predicts a low-energy (<1 eV) dipole excitation. © 1996 John Wiley & Sons, Inc.     

Molecular and electronic structures of bipolaron in poly-para-phenylene in terms of molecular orbital symmetry

The molecular structures of the model systems of the polaron and the bipolaron in poly-para-phenylene (PPP) were calculated by an ab initio molecular orbital (MO) method with fairly sophisticated approximations. The calculated models are monocations, dications, monoanions and dianions of biphenyl, para-terphenyl, para-quaterphenyl, para-quinquephenyl and para-hexaphenyl. The calculations show that the longer the PPP oligomer is, the stronger is the tendency to take on a non-planar twisting structure. This was accounted for by the combination of repulsions between proximate ortho-hydrogen atoms with resonance interactions between benzene π MOs. The magnitude of the resonance interactions was assessed by using the symmetry of benzene π MOs as well as an analytical Hückel solution of the π MO for polyene. In addition, negatively charged polarons and bipolarons were found to have a stronger tendency to take on a planar structure than positively charged ones. This result was also explained by comparing the benzene π HOMO with the benzene π LUMO. Received: 30 June 1998 / Accepted: 9 September 1998 / Published online: 23 February 1999     

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.     

Vibrational studies of biquinonyl

Using theoretical calculations, the IR and Raman spectra of biquinonyl, 2,2'-Bi-(2,5-cyclohexadiene-1,4-dione), were interpreted. The force field of this molecule was analysed and the changes caused by joining two p-benzoquinone groups were discussed and compared with the calculated π-electron bond orders (PPP).     

Electronic states of an infinite polyene under local perturbations

A perturbation theory method is developed in the tight-binding LCAO MO treatment of a one-dimensional polymer under local perturbation with the aid of the Wannier function. As the first step, electronic states of an infinite polyene under a few of significant cases of perturbation are formulated in the scheme of the Hückel MO approach, giving the changes in total energies, electron densities, and bond orders of the perturbed systems.