Generation of Kekulé valence structures and the corresponding valence bond wave function

A new scheme, called "list of nonredundant bonds", is presented to record the number of bonds and their positions for the atoms involved in Kekulé valence structures of (poly)cyclic conjugated systems. Based on this scheme, a recursive algorithm for generating Kekulé valence structures has been developed and implemented. The method is general and applicable for all kinds of (poly)cyclic conjugated systems including fullerenes. The application of the algorithm in generating Valence Bond (VB) wave functions, in terms of Kekulé valence structures, is discussed and illustrated in actual VB calculations. Two types of VBSCF calculations, one involving Kekulé valence structures only and the second one involving all covalent VB structures, were performed for benzene, pentalene, benzocyclobutadiene, and naphthalene. Both strictly local and delocalised p-orbitals were used in these calculations. Our results show that, when the orbitals are restricted to their own atoms, other VB structures (Dewar structures) also have a significant contribution in the VB wave function. When removing this restriction, the other VB structures (Dewar and also the ionic structures) are accommodated in the Kekulé valence structures, automatically. Therefore, at VBSCF delocal level, the ground states of these systems can be described almost quantitatively by considering Kekulé valence structures only at a considerable saving of time.     

An ab initio valence bond study on cyclopenta-fused naphthalenes and fluoranthenes

To probe the effect of external cyclopenta-fusion on a naphthalene core, ab initio valence bond (VB) calculations have been performed, using strictly atomic benzene p-orbitals and p-orbitals that are allowed to delocalize, on naphthalene (1), acenaphthylene (2), pyracylene (3), cyclopenta[b,c]acenaphthylene (4), fluoranthene (5), and cyclopenta[c,d]fluoranthene (6). For the related compounds 1-4 and 5,6 the total resonance energies (according to Pauling's definition) are similar. Partitioning of the total resonance energy in contributions from the possible 4n + 2 and 4n pi-electron conjugated circuits shows that only the 6pi-electron conjugated circuits (benzene-like) contribute to the resonance energy. The results show that cyclopenta-fusion does not extend the pi system in the ground state; the five-membered rings act as peri-substituents. As a consequence, the differences in (total) resonance energy do not coincide with the differences in thermodynamic stability. Notwithstanding, the relative energies of the Kekule structures can be estimated using Randic's conjugated circuits model.     

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。     

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.     

Hückel and Möbius Aromaticity in Charged Sigma Complexes

In sigma complexes, intermediates in nucleophilic and electrophilic aromatic substitution and other reactions, delocalization in the aromatic ring is formally disrupted. Unexpectedly, computational evidence is presented that favorable processes contain aromatic sigma complexes. Tetracoordinated carbon therein surprisingly employs orbitals that are more similar to sp² than to sp³ hybrids in sigma bonds with adjacent ring atoms. Both leaving groups and nucleo- or electrophiles may donate electrons to the π-system depending on the availability of p-type orbitals to fulfill Hückel (4N+ 2) or Möbius (4N) rules of aromaticity in analogy to conjugated transition-metal metallacycles.     

Mass spectra of the negative ions of some steroids

It has been shown that the main directions of the fragmentation of the molecular negative ions are connected with the formation of systems of conjugated bonds and the delocalization of the negative charge over a π-system of electrons. The mass spectrometry of the negative ions formed by the dissociative capture of electrons (DCE) is promising for the study of the molecules of steroid compounds.     

Block-localized wavefunction (BLW) method at the density functional theory (DFT) level

The block-localized wavefunction (BLW) approach is an ab initio valence bond (VB) method incorporating the efficiency of molecular orbital (MO) theory. It can generate the wavefunction for a resonance structure or diabatic state self-consistently by partitioning the overall electrons and primitive orbitals into several subgroups and expanding each block-localized molecular orbital in only one subspace. Although block-localized molecular orbitals in the same subspace are constrained to be orthogonal (a feature of MO theory), orbitals between different subspaces are generally nonorthogonal (a feature of VB theory). The BLW method is particularly useful in the quantification of the electron delocalization (resonance) effect within a molecule and the charge-transfer effect between molecules. In this paper, we extend the BLW method to the density functional theory (DFT) level and implement the BLW-DFT method to the quantum mechanical software GAMESS. Test applications to the pi conjugation in the planar allyl radical and ions with the basis sets of 6-31G(d), 6-31+G(d), 6-311+G(d,p), and cc-pVTZ show that the basis set dependency is insignificant. In addition, the BLW-DFT method can also be used to elucidate the nature of intermolecular interactions. Examples of pi-cation interactions and solute-solvent interactions will be presented and discussed. By expressing each diabatic state with one BLW, the BLW method can be further used to study chemical reactions and electron-transfer processes whose potential energy surfaces are typically described by two or more diabatic states.     

价键方法中的非活性轨道优化新算法

本文通过引进一组正交的辅助非活性轨道和与它正交的辅助活性轨道,将价键理论方法中的冻核近似推广到轨道非正交的情形,得到了体系能量及其对非活性轨道的梯度解析表达式,简化了价键自洽场方法中非正交轨道能量梯度的计算．该方法的标度为（Na＋1）m^4,其中Na和m分别是活性轨道和基函数的个数．分析表明,与现有的其他算法相比较,该方法具有更低的计算标度,因而计算效率更高．     

Rational design of high-spin biradicaloids in the isobenzofulvene and isobenzoheptafulvene series

The relative energies of singlet biradicaloid and of triplet and singlet biradical electronic states for a series of benzannelated isobenzofulvenes and isobenzoheptafulvenes were calculated at the (u-)B3LYP/6-31G(d), full π-space CASSCF-CASPT2 (≤14 π-e(-)s), and full π-space RASSCF-RASPT2 (≤24 π-e(-)s) levels of theory. Both absolute and relative CASPT2 energies were reproduced quite well by the RASPT2 approach, which can be extended to much larger active spaces. RASPT2 (and DFT) calculations find that increasing benzannelation leads to triplet ground states in both hydrocarbon series, in violation of the classical principle of maximum bonding. This confirmed the expectations that the combined effects of resonance energy and aromaticity could compensate for the extra formal π-bond of the biradicaloid singlet, and that the strong exchange coupling inherent to the embedded trimethylenemethane (TMM) would manifest itself in the biradicaloids. The relative energy of the biradicaloid singlet rises rapidly upon benzannelation, as π-bonding between the high-energy delocalized GVB orbitals decreases. The underlying π-orbital topology is revealed when this weak π-bonding is artificially eliminated by a 1:1 mixing of the nondegenerate HOMO and LUMO to produce an overcorrelated valence bond (OCVB) orbital pair. For members of both biradicaloid series, the OCVB pairs are nondisjoint, revealing a limiting triplet preference with increasing benzannelation. Within the two-electron, two-orbital approximation, the effects of π-bonding in the singlet biradicaloids and orbital localization away from the acene π-system in the triplet biradicals can be analyzed as perturbations of the singlet OCVB biradicals. The application of a VB-based spin coupling scheme is discussed, in which the unpaired electrons of these species can be considered both ferromagnetically and antiferromagnetically coupled, with the strength of the latter strongly dependent on the acene subunit.     

Resonance energy of very large benzenoid hydrocarbons

The resonance energy of conjugated benzenoid systems is expressed as contributions arising from independent conjugated circuits. The scheme has been applied to numerous very large conjugated systems. In many cases, it was possible to find regularities in the increments for the resonance energy within a family of benzenoid systems as the number of benzene rings is increased.     

Graphical representation of a new algorithm for nonorthogonalab initio valence bond calculations

A pictorial representation of the algorithm using successive expansion method for the nonorthogonal VB calculations is given. With the help of this representation and the graph analysis, the efficiency of this algorithm is improved and theN! problem is reduced by a factor of about (N!)^1/2. Anab initio VB program for valence bond self-consistent-field (VBSCF) calculations has been implemented based on this algorithm. Some VBSCF calculations have been performed for systems of up to 14 electrons. The statistics of the CPU time of the calculations indicate that this new group-theoretical approach is quite practical.     

AIM and NPA studies of the role of polarization in electronic structures

Atomic charges, as measured by Atoms in Molecule (AIM) or Natural Population Analyses (NPA), of the enolate anions of acetaldehyde and crotonaldehyde and of pentadienyl anion and cation show both charge transfer and polarization effects. In general, normal resonance structures and "curved arrow" symbolism give good representations of π-electron distributions, but back-polarizations in the σ-system complicate these electronic structures and can obscure the correspondence to resonance symbols. Twisting a vinyl group to orthogonality disrupts the π-system, but the vinyl group retains significant charge transfers and polarizations. The role of polarization is also demonstrated by the effect of external positive and negative charges on the electronic structure of ethylene. The π-electronic changes again are straightforward but are changed significantly by σ-polarizations. The polarizability of ethane is about half that of ethylene.     

Evaluation of a new procedure for quantum-chemical estimates of constants of isotropic hyperfine coupling with protons in free radicals

A new procedure for quantum-chemical estimates of the constants of isotropic hyperfine coupling (IHFC) with protons using the orbital spin populations calculated in the basis set of symmetrically orthogonalized (according to Löwdin) atomic orbitals is tested taking 16 well-studied simplest π-electron and σ-electron radicals as examples. The most probable reasons for and possible ways of correcting large deviations of calculated IHFC constants from experimental values are considered. The efficiency of the semiempirical MNDORU scheme, which makes it possible to consistently estimate the delocalization and spin-polarization contributions to the constants of IHFC with protons in free radicals, is demonstrated.     

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.     

A new algorithm for inactive orbital optimization in valence bond theory

This paper presents an efficient algorithm for energy gradients in valence bond self-consistent field (VBSCF) method with non-orthogonal orbitals. The frozen core approximation method is extended to the case of non-orthogonal orbitals. The expressions for the total energy and its gradients are presented by introducing auxiliary orbitals, where inactive orbitals are orthogonal, while active orbitals are non-orthogonal themselves but orthogonal to inactive orbitals. It is shown that our new algorithm has a low scaling of (N _a + 1)m ⁴, where N _a and m are the numbers of the active orbitals and basis functions, respectively, and is more efficient than the existing VBSCF algorithms.     

An efficient algorithm for complete active space valence bond self‐consistent field calculation

This article describes a novel algorithm for the optimization of valence bond self‐consistent field (VBSCF) wave function for a complete active space (CAS), so‐called VBSCF(CAS). This was achieved by applying the strategies adopted in the optimization of CASSCF wave functions to VBSCF(CAS) wave functions, using an auxiliary orthogonal orbital set that generates the same configuration space as the original nonorthogonal orbital set. Theoretical analyses and test calculations show that the VBSCF(CAS) method shares the same computational scaling as CASSCF. The test calculations show the current capability of VBSCF method, which involves millions of VB structures. © 2012 Wiley Periodicals, Inc.     

有机及金属有机苯乙炔树状分子体系的非线性光学性质的理论研究

应用密度泛函理论研究了一系列有机及金属有机苯乙炔树状分子的激发态性质和非线性光学性质。计算的电子吸收光谱显示这些树状分子均在低能区域有一个最强的吸收;此外,金属有机体系的吸收光谱和有机体系相比发生了明显的红移。响应性质的计算结果表明共轭体系的扩展和金属有机基团的引入都使得苯乙炔树状分子的非线性光学极化率显著增加,尤其是含Ru体系,其β和γ值呈数量级增长。对于有机体系和含Pd体系,发生在共轭体系内部的π→π*电荷跃迁是产生分子一阶和二阶超极化率的主要原因。而含Ru体系相当大的非线性响应则主要起源于Ru的轨道到共轭体系的π*的跃迁,同时与Ru相邻的C≡C到共轭体系的π→π*跃迁起着辅助贡献。     

Investigating the possibility of simultaneously finding an electron-hole and an electron-pair in a molecule: Delocalization,competition of ionic vs. covalent character,and related effects in push–pull ethylenes

This work examines the possibility of finding an electron-hole and an electron-pair simultaneously in a π-system substituted by an electron-donating (NH₂) and/or electron-withdrawing (NO₂) group. The contributions of various ionic [(+), ( ↑ ↓ )] structures are calculated from ab initio SCF –CI wave functions, using a recently developed general multielectron population analysis. The molecules studied are two monosubstituted ethylenes, aminoethylene and nitroethylene, and a disubstituted ethylene, the 2-nitroethenamine (push–pull ethylene) in its two configurational forms. The influence of the NH₂ and/or NO₂ group in delocalization and ionic (vs. covalent) character of the C?C double bond are investigated, along with examining the experimental chemist formalism of electron-pair “displacements” in several resonance structures. Analysis of mutual dependence of an electron-hole and an electron-pair, at short and long distances, leads to the conclusion that a push–pull π-system can stimulate the simultaneous existence of an electronhole and an electron-pair even for nonvicinal positions. The relationship between the electronpair distributions and contributions of the corresponding structures are also examined; the effects of electronic correlation are analyzed as well. © 1992 John Wiley & Sons, Inc.     

On the construction of diabatic and adiabatic potential energy surfaces based on ab initio valence bond theory

A theoretical model is presented for deriving effective diabatic states based on ab initio valence bond self-consistent field (VBSCF) theory by reducing the multiconfigurational VB Hamiltonian into an effective two-state model. We describe two computational approaches for the optimization of the effective diabatic configurations, resulting in two ways of interpreting such effective diabatic states. In the variational diabatic configuration (VDC) method, the energies of the diabatic states are variationally minimized. In the consistent diabatic configuration (CDC) method, both the configuration coefficients and orbital coefficients are simultaneously optimized to minimize the adiabatic ground-state energy in VBSCF calculations. In addition, we describe a mixed molecular orbital and valence bond (MOVB) approach to construct the CDC diabatic and adiabatic states for a chemical reaction. Note that the VDC-MOVB method has been described previously. Employing the symmetric S(N)2 reaction between NH(3) and CH(3)NH(3)(+) as a test system, we found that the results from ab initio VBSCF and from ab initio MOVB calculations using the same basis set are in good agreement, suggesting that the computationally efficient MOVB method is a reasonable model for VB simulations of condensed phase reactions. The results indicate that CDC and VDC diabatic states converge, respectively, to covalent and ionic states as the molecular geometries are distorted from the minimum of the respective diabatic state along the reaction coordinate. Furthermore, the resonance energy that stabilizes the energy of crossing between the two diabatic states, resulting in the transition state of the adiabatic ground-state reaction, has a strong dependence on the overlap integral between the two diabatic states and is a function of both the exchange integral and the total diabatic ground-state energy.