An approximate diatomics in molecules formulation of generalized valence bond theory

The slow computational speed of the generalized valence bond perfect pairing method (GVB-PP) has been an impediment to its routine use. We have addressed this problem by employing a diatomics in molecules Hamiltonian derived from a second quantization perturbation approach. This results in all three- and four-centered two-electron integrals being dropped from the traditional GVB-PP calculation. For moderate sized molecules, as for example C20 computed with a double zeta + polarization basis, there is on average a fifty-fold decrease in computational times. In this article, we present the theory behind our approach and analyze the accuracy and speed of this approximate GVB-PP method for several cases where density functional methods have produced ambivalent results.     

The valence bond description of conjugated molecules. II. A very simple method to approximate the structural weights of a fully correlated valence bond wavefunction

A very simple method to get the same structural weights as those provided by a fully correlated valence bond function is proposed. It applies to the ground states of delocalized systems, and only requires the knowledge of the occupied molecular orbitals. The SCF wavefunction is projected on a valence bond basis, and the SCF weights thus obtained are multiplied by some sets of multipliers which are transferable from one molecule to another. Some numerical examples are displayed, showing a very satisfying agreement between the structural weights thus estimated and the ones resulting from a rigorous calculation.     

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.     

Program for predicting interatomic distances in crystals by the bond valence method

The program is a computer realization of the bond valence method (BVM), used to predict bond lengths in crystal structures from topological data. Using object-oriented programming made it possible to analyze structures of any complexity (up to 6480 crystal chemical positions). Hardware and software requirements: i486DX processor, operating system Windows 3.1/95, 4M RAM, and about 2M disk space. The program was developed at the Crystallography and Crystal Chemistry Department, Geological Faculty, Moscow State University. Translated fromZhumal Strukturnoi Khimii, Vol. 39, No. 4, pp. 708–713, July–August, 1998.     

Parameterization of the approximate valence bond (AVB) method to describe potential energy surface in the reaction catalyzed by HIV‐1 protease

The approximate valence bond (AVB) method was parameterized to obtain the potential energy surface for ongoing classical and further quantum classical molecular dynamics simulations describing the enzymatic reaction of the human immunodeficiency virus type 1 protease (HIV‐1 PR). The parameterized AVB method allows to describe the complete enzymatic reaction, including a proton transfer between a water molecule and an aspartic acid, nucleophilic attack of a hydroxy anion on the substrate peptide bond, conformational changes of an intermediate, two proton transfers between the intermediate and aspartic acids, and cleavage of the intermediate into reaction products. The AVB method was parameterized based on density functional theory (DFT) calculations performed for small molecular systems. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 86–103, 2001     

Breathing orbital valence bond method in diffusion Monte Carlo: C-H bond dissociation of acetylene

This study explores the use of breathing orbital valence bond (BOVB) trial wave functions for diffusion Monte Carlo (DMC). The approach is applied to the computation of the carbon-hydrogen (C-H) bond dissociation energy (BDE) of acetylene. DMC with BOVB trial wave functions yields a C-H BDE of 132.4 +/- 0.9 kcal/mol, which is in excellent accord with the recommended experimental value of 132.8 +/- 0.7 kcal/mol. These values are to be compared with DMC results obtained with single determinant trial wave functions, using Hartree-Fock orbitals (137.5 +/- 0.5 kcal/mol) and local spin density (LDA) Kohn-Sham orbitals (135.6 +/- 0.5 kcal/mol).     

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.     

An approximate valence force field for benzenetricarbonylchromium

An approximate valence force field has been calculated for benzenetricarbonylchromium, using data from (C₆H₆)Cr(CO)₃ and (C₆D₆)Cr(CO)₃. Significant changes were found in a number of benzene internal force constants on complexation, which were consistent with a bonding model for benzenetricarbonylchromium in which the benzene ring acts as a net electron donor to the Cr atom.     

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.     

VBEFP: a valence bond approach that incorporates effective fragment potential method

An ab initio explicit solvation valence bond (VB) method, called VBEFP, is presented. The VBEFP method is one type of QM/MM approach in which the QM part of system is treated within the ab initio valence bond scheme and the solvent water molecules are accounted by the effective fragment potential (EFP) method, which is a polarized force field approach developed by Gordon et al. (J. Chem. Phys. 1996, 105, 1968). This hybrid method enables one to take the first-solvation shell and heterogeneous solvation effects into account explicitly with VB wave function. Therefore, the nature of chemical bonding and the mechanism of chemical reactions with explicit solvent environments can be explored at the ab inito VB level. In this paper, the hydrated metal-ligand complexes [M(2+)L](H(2)O)(n) (M(2+): Mg(2+), Zn(2+); L: NH(3), CH(2)O) are studied by the VBEFP method. Resonance energy and bond order are computed, and the influence of the solvent coordination and hydrogen bonding to the metal-ligand bonding are explored in the paper.     

Diagrammatic valence bond studies on hemocyanin

Summary The Diagrammatic Valence Bond studies on the active sites of hemocyanin, consisting of two Cu(I) ions and an oxygen molecule, are performed to find out the stable geometrical pattern and electronic structure. Different parameters used in this theoretical approach are taken from existing literature on highT _c superconductors. Attempts have been made to find out the differences in electronic structure of [Cu₂O₂]⁺² and [Cu₂O₂N₄]⁺² as it is observed that coordination of nitrogen ligand do affect electronic structure i.e. spin excitation gaps and charge and spin density distribution. A comparison of our results with earlier theoretical results are also presented.     

A practical valence bond method: a configuration interaction method approach with perturbation theoretic facility

The previously developed valence bond configuration interaction (VBCI) method (Wu, W.; Song, L.; Cao, Z.; Zhang, Q.; Shaik, S., J. Phys. Chem. A, 2002, 105, 2721) that borrows the general CI philosophy of the MO theory, is further extended in this article, and its methodological features are improved, resulting in three accurate and cost-effective procedures: (a) the effect of quadruplet excitation is incorporated using the Davidson correction, such that the new procedure reduces size consistency problems, with due improvement in the quality of the computational results. (b) A cost-effective procedure, named VBCI(D, S), is introduced. It includes doubly excited structures for active electrons and singly excited structures for inactive pairs. The computational results of VBCI(D, S) match those of VBCISD with much less computational effort than VBCISD. (c) Finally, a second-order perturbation theory is utilized as a means of configuration selection, and lead to considerable reduction of the computational cost, with little or no loss in accuracy. Applications of the new procedures to bond energies and barriers of chemical reactions are presented and discussed.     

Paired-permanent approach to valence bond theory

A new function called paired-permanent is defined and widely discussed, and a practicable procedure for evaluations of paired-permanents is proposed, which is similar to the Laplace method for determinants. Using the concept of paired-permanents, an efficient algorithm is presented for evaluating the Hamiltonian and overlap matrix elements in the spin-free form of valence bond (VB) theory. With the new algorithm, a spin-free wavefunction is simply written as a paired-permanent, and an overlap matrix element may be obtained by evaluating a corresponding paired-permanent. Meanwhile, the Hamiltonian matrix element is expressed in terms of the summation of the products of electronic integrals and the corresponding sub-paired-permanents     

Protonated water clusters described by an empirical valence bond potential

The properties of low-lying stationary points on the potential energy surfaces of singly protonated water clusters (H(2)O)(n)H(+), are investigated using an empirical valence bond potential. Candidate global minima are reported for n=2-4, 8, and 20-22. For n=8, the variation in the energies and structures of low-lying minima with the number of valence bond states included in the model is studied. For n=4 and 8, disconnectivity graphs are also reported and are compared to results for the equivalent neutral water clusters as described by the rigid TIP3P potential. For the larger clusters, n=20-22, the structural properties of the low energy minima are compared with recently published spectroscopic data on these systems. The observed differences between the n=20 and n=21 systems are qualitatively reproduced by the model potential, but the similarities between the n=21 and n=22 systems are not.     

Application of the valence bond mixing configuration diagrams to hypervalency in trihalide anions: a challenge to the Rundle-Pimentel model

The X(3)(-) hypercoordinated anions (H, F, Cl, Br, I) are studied by means of the breathing-orbital valence bond ab initio method. The valence bond wave functions describe the different X(3)(-) complexes in terms of only six valence bond structures and yield energies relative to the two exit channels, X(2) + X(-) and X(2)(-) + X(*), in very good agreement with reference CCSD(T) calculations. Although H(3)(-) is unstable and dissociates to H(2) + H(-), all the trihalogen anions are stable intermediates, Br(3)(-) and I(3)(-) being more stable than F(3)(-) and Cl(3)(-). As a challenge to the traditional Rundle-Pimentel model, the different energies of the hypercoordinated species relative to the normal-valent dissociation products X(2) + X(-) are interpreted in terms of valence bond configuration mixing diagrams and found to correlate with a single parameter of the X(2) molecule, its singlet-triplet energy gap. Examination of the six-structure wave functions show that H(3)(-), Cl(3)(-), Br(3)(-), and I(3)(-) share the same bonding picture and can be mainly described in terms of the interplay of two Lewis structures. On the other hand, F(3)(-) is bonded in a different way and possesses a significant three-electron bonding character that is responsible for the dissociation of this complex to F(2)(-) + F(*), instead of the more stable products F(2) + F(-). This counterintuitive preference for the thermodynamically disfavored exit channel is found to be an experimental manifestation of the large charge-shift resonance energy that generally characterizes fluorine-containing bonds.