A variational biorthogonal valence bond method

The details of a simple and efficient scheme for performing variational biorthogonal valence bond calculations are presented. A variational bound on the energy functional is obtained through the use of a complete configuration expansion in a well-chosen subset of orbitals. The resultant wave functions are clearly dominated by the covalent (spin-coupled) structures, with a negligible contribution from ionic structures. The orbitals obtained compare favorably with overlap enhanced atomic orbitals obtained by other valence bond approaches. The method is illustrated by calculations on water and dioxygen difluoride. © 1994 by John Wiley & Sons, Inc.     

The orthogonality problem in valence bond calculations

The energy of the π-electron system in benzene has been obtained by means of valence bond calculations using orthogonal and nonorthogonal basis orbitals at different levels of configuration interaction, which shows the influence of the orthogonalization procedures.     

Variational biorthogonal valence bond descriptions of 1,3-dipoles

The variational biorthogonal valence bond method is applied to the π-electrons of six 1,3-dipoles (CH₂N₂, HCNO, CH₂NHO, N₂O, O₃, NO₂). The results are compared with those from other valence bond techniques, including a detailed comparison with the spin-coupled valence bond approach. For CH₂N₂, HCNO, CH₂NHO, and N₂O, zwitterionic structures are predicted and it is shown that the variational biorthogonal valence bond method leads to orbitals and configuration weights which are essentially indistinguishable from those of the spin-coupled valence bond method. However, for O₃ and NO₂ the techniques give contradictory results. The biorthogonal valence method predicts O₃ and NO₂ to be spin-paired diradicals. Evidence from other calculations on O₃ is discussed. © 1994 by John Wiley & Sons, Inc.     

Dynamic correlation for biorthogonal valence bond reference states

Summary The use of biorthogonal valence bond reference functions in evaluating the correlation energy is investigated. Since the method is not variationally bound some care must be taken in defining the reference state to ensure that the variational bound is not violated, some discussion is given to this matter. The procedure adopted here is a matrix element driven configuration interaction scheme. To reduce the computational labour involved, a configuration selection criterion is introduced. The method is tested through its application to the symmetric stretching of HF, H₂O, (² B ₁) NH₂ and the singlet-triplet gap in CH₂. Comparison is made with other methods, including full CI. The results show that the current method is quite promising.     

Computational developments in generalized valence bond calculations

In this article a procedure for generating starting orbitals for generalized valence bond (GVB) calculations is presented. This is achieved by selecting orbitals which correspond to specific bonds or electron pairs. These orbitals can be identified from the localized molecular orbitals, for both occupied and virtual orbitals, which are obtained through a unitary transformation of the Hartree-Fock canonical molecular orbitals using the Boys's localization method. A scheme has also been implemented which achieves optimum convergence of the pairwise orbital optimization. An object-oriented GVB program is developed which automatically generates reliable initial GVB orbitals, leading to proper and fast convergence. © 1996 by John Wiley & Sons, Inc.     

Some valence bond calculations for H2 with 1s and 2p basis sets

Summary The results ofab initio valence bond calculations are reported for H₂, with up to 16 nuclear centred and eight midbond 1s and 2p AOs included in them. The 24 AO calculation, with 116S=0 spin structures, gives an STO-6G energy of –1.17237 a.u., which is close to an MP4 estimate of –1.17256 a.u.     

Ab initio valence bond calculations. I. Methylene

An ab initio valence bond (VB ) method for calculating energies and wave functions for simple electronic systems is described and the results of its application to methylene are given together with extensive comparisons with previous theoretical results.     

The Rydberg states of trans-butadiene from generalized valence bond and configuration interaction calculations

Self-consistent ab initio generalized valence bond (GVB) and configuration interaction (Cl) calculations are presented for the Rydberg states of trans-1,3-butadiene. Five Rydberg series were identified, three optically allowed (np, np, and nf_{z ³}) and two optically forbidden (ns and nd_{z ²}). It is shown that, except for the Λ～ and F? bands (which correspond to the non-valence 1 ¹B _u and the valence 2 ¹A _g states, respectively) all the transitions observed in the ultra-violet (UV) and electron-impact (EI) spectra, and in the two-photon spectra, can be assigned to members of these Rydberg series.     

Parameterized valence bond calculations for benzenoid hydrocarbons using clar structure

SCF (Dewar-de Llano) calculations are used to parameterize a valence bond theory with a basis of Clar structures. A precise correlation of calculated resonance energies is found (corr. coeff. 0.9998). Graphtheoretic algorithms for carrying out the calculations are illustrated. It is suggested that this theoretical approach would be useful in considering structure and reactivity problems in very large polycyclic benzenoid aromatic hydrocarbons.     

Ab initio valence bond calculations. X. Vertical valence ionization potentials of allene and butatriene

The ground and vertical valence ionized states of allene and butatriene have been studied in the ab initio valence bond framework using the 6–31G basis set after contraction and introducing the core–valence shell separation. The final wave functions have been analyzed in terms of VB structures by means of population analysis.     

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.     

A diagrammatic valence bond method for configuration interaction calculations in atoms and molecules

A diagrammatic valence bond method based on Rumer-Pauling rules for configuration interaction calculations is described. The advantages of this method are that it is simple and flexible and is expected to be computationally efficient as the basis functions can be coded as increasing integers. Evaluation of Hamiltonian matrix elements involves simple bit manipulations and binary searches. The basis, being represented pictorially, should also help in utilizing spatial symmetries for further block-diagonalizing the Hamiltonian matrix. The eigenfunctions of the Hamiltonian can also be used to compute matrix elements between different electronic states.     

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.     

New algorithm for nonorthogonal ab initio valence bond calculations II: Subgraph-driven method

The permanent method for nonorthogonal VB calculations is extensively developed, and the so-called subgraph-driven procedure is proposed. To achieve high efficiency, the summation of a huge number of permanents is treated as a whole system, and the intermediate quantities, the contracted-cofactors of various orders, are introduced for the systematic summation. These intermediate quantities can be characterized by pairing graphs of 2n elements (n = 1, 2, ... 1/2N – 2). Some test calculations for systems of up to 20 electrons are performed. The practice shows that this method is highly efficient, and the CPU time increases in a quite moderate way with the increasing number of electrons.On leave from Chemistry Department, Xiamen University, 361005 Xiamen, PR China.     

Gradients in valence bond theory

A gradient method for very general valence bond (VB) wavefunctions is presented. This method introduces the electronic energy as a Lagrange multiplier, and evaluates the contributions of the derivatives of the normalisation and of the first- and second-order cofactors present in the VB energy expression. The correctness of the method is illustrated with classic and breathing-orbital VB calculations on the HF molecule.     

The application of cholesky decomposition in valence bond calculation

The Cholesky decomposition (CD) technique, used to approximate the two‐electron repulsion integrals (ERIs), is applied to the valence bond self‐consistent field (VBSCF) method. Test calculations on ethylene, C_2nH_2n+2, and C_2nH_4n?2 molecules (n = 1–7) show that the performance of the VBSCF method is much improved using the CD technique, and thus, the integral transformation from basis functions to VB orbitals is no longer the bottleneck in VBSCF calculations. The errors of the CD‐based ERIs and of the total energy are controlled by the CD threshold, for which a value of 10^?6 ensures to control the total energy error within 10^?6 Hartree. © 2016 Wiley Periodicals, Inc.     

Ab initio valence bond calculations. XI. Pyridine: Ground and ionized states

The ab initio valence bond method has been used to study the ground and the lowest vertical valence ionized states of pyridine. On the basis of our calculations the first two ionization potentials are assigned to π and n electron removals, respectively. The final wave functions have been interpreted in terms of valence bond structures by means of an appropriate population analysis.     

Ab initio valence bond calculations and the spin-paired diradical character of S 4 2+

The results of some ab initio valence bond calculations, with STO-6G basis sets for the s and p orbitals, are reported for the ground state of cyclic S ₄ ²⁺ . The sum of the weights for two long-bond (or spin-paired diradical) structures is approximately 50% of the total.