A quadratically convergent VBSCF method

A quadratically convergent valence bond self-consistent field method is described where the simultaneous optimisation of orbitals and the coefficients of the configurations (VB structures) is based on a Newton-Raphson scheme. The applicability of the method is demonstrated in actual calculations. The convergence and efficiency are compared with the Super-CI method. A necessary condition to achieve convergence in the Newton-Raphson method is that the Hessian is positive definite. When this is not the case, a combination of the Super-CI and Newton-Raphson methods is shown to be an optimal choice instead of shifting the eigenvalues of the Hessian to make it positive definite. In the combined method, the first few iterations are performed with the Super-CI method and then the Newton-Raphson scheme is switched on based on an internal indicator. This approach is found computationally a more economical choice than using either the Newton-Raphson or Super-CI method alone to perform a full optimisation of the nonorthogonal orbitals

Generation of Kekulé Valence Structures and the Corresponding Valence Bond Wave Function

Abstract: 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

The effect of syn-anti isomerism on the lowest valence transitions of 1,1′-bicyclohexylidene. An ab initio MRDCI investigation

Conformational effects on the ground-state and excited-state properties of 1,1′-bicyclohexylidene were studied. The energy difference between the two conformers anti- (anti-1a) and syn-1,1′-bicyclohexylidene (syn-1b) was determined at the RHF/6-31G, MP2/6-31G//RHF/6-31G, RHF/6-311G * * //RHF/6-31G and MP2/6-311G * * //RHF/6-31G levels of theory. Syn-1b is lower in energy by 0.051 kcal/mol at the MP2/6-311G * * //RHF/6-31G level. The valence transitions of syn-1b were calculated using the MRDCI method using its 6-31G geometry and molecular orbitals. In contrast to the predicted UV data of anti-1a for which two absorptions are found, only one absorption for syn-1b, a π→π * transition at ~6.0 eV, is discernible. The next transition with appropriate oscillator strength is at ~7.8 eV (π→σ *). Inclusion of polarization functions on the carbon atoms hardly affects the calculated transition energies, oscillator strengths and CI vectors

Resonance and Aromaticity:An Ab Initio Valence Bond Approach

Resonance energy is one of the criteria to measure aromaticity. The effect of the use of different orbital models is investigated in the calculated resonance energies of cyclic conjugated hydrocarbons within the framework of the ab initio Valence Bond Self-Consistent Field (VBSCF) method. The VB wave function for each system was constructed using a linear combination of the VB structures (spin functions), which closely resemble the Kekule valence structures, and two types of orbitals, that is, strictly atomic (local) and delocalized atomic (delocal) p-orbitals, were used to describe the pi-system. It is found that the Pauling-Wheland's resonance energy with nonorthogonal structures decreases, while the same with orthogonalized structures and the total mean resonance energy (the sum of the weighted off-diagonal contributions in the Hamiltonian matrix of orthogonalized structures) increase when delocal orbitals are used as compared to local p-orbitals. Analysis of the interactions between the different structures of a system shows that the resonance in the 6 pi electrons conjugated circuits have the largest contributions to the resonance energy. The VBSCF calculations also show that the extra stability of phenanthrene, a kinked benzenoid, as compared to its linear counterpart, anthracene, is a consequence of the resonance in the pi-system rather than the H-H interaction in the bay region as suggested previously. Finally, the empirical parameters for the resonance interactions between different 4n+2 or 4n pi electrons conjugated circuits, used in Randic's conjugated circuits theory or Herdon's semi-emprical VB approach, are quantified. These parameters have to be scaled by the structure coefficients (weights) of the contributing structures