Generalized valence bond wave functions

F. W. Bobrowicz and W. A. Goddard III, Self-Consistent Field Equations for Open-Shell Hartree-Fock and Generalized Valence Bond Wave Functions, in Modem Theoretical Chemistry, vol. 3, H. F. Schaeffer III Ed., Plenum, New York, 1977... 

Goodgame, M. M., and W. A. Goddard III (1985). Modified generalized valence-bond method a simple correction for the electron correlation missing in generalized valence-bond wave functions prediction of double-well states for Crj and Moj. Phys. Rev. Lett. 54, 661-64. 

Procedures for Generalized Valence Bond Wave Functions. 

Drowicz F W and W A Goddard IB 1977. The Self-Consistent Field Equations for Generalized Valence Bond and Open-Shell Hartree-Fock Wave Functions. In Schaeffer H F III (Editor). Modem Theoretical Chemistry III, New York, Plenum, pp. 79-127. 

Such a "general form of wave function is easily written explicitly for each set of values of N, S, and MS- Any appropriate form of approximate wave functions, like determinantal functions composed of one-electron functions ( molecular spin orbitals ), the "bond eigenfunctions" used in the valence bond approach, and so on, is shown to fulfil this requirement. 

Most of the commonly used electronic-structure methods are based upon Hartree-Fock theory, with electron correlation sometimes included in various ways (Slater, 1974). Typically one begins with a many-electron wave function comprised of one or several Slater determinants and takes the one-electron wave functions to be molecular orbitals (MO s) in the form of linear combinations of atomic orbitals (LCAO s) (An alternative approach, the generalized valence-bond method (see, for example, Schultz and Messmer, 1986), has been used in a few cases but has not been widely applied to defect problems.)... 

Amovilli et al. [20] presented a method to carry out VB analysis of complete active space-self consistent field wave functions in aqueous solution by using the DPCM approach [3], A Generalized Valence Bond perfect pairing (GVB-PP) level... 

The generalized valence bond (GVB) method was the earliest important generalization of the Coulson—Fischer idea to polyatomic molecules (13,14). The method uses OEOs that are free to delocalize over the whole molecule during orbital optimization. Despite its general formulation, the GVB method is usually used in its restricted form, referred to as GVB SOPP, which introduces two simplifications. The first one is the perfect-pairing (PP) approximation, in which only one VB structure is generated in the calculation. The wave function may then be expressed in the simple form of Equation 9.1, as a product of so-called geminal two-electron functions ... 

GVB Generalized valence bond. A theory that employs CF orbitals to calculate electronic structure with wave functions in which the electrons are formally coupled in a covalent manner. The simplest level of the theory is GVB PP (PP-perfect pairing), in which all the electrons are paired into bonds, as in the Lewis structure of the molecule. 

They showed that the dimerized bond should be considered as a singlet diradical. Therefore, a qualitatively correct description of the dimer requires at least a generalized valence bond, GVB-PP132, or a two configuration self-consistent field (TCSCF)33 wave function. More recently, Paulus29 performed a more exhaustive multi-reference analysis of silicon clusters and reconfirmed this conclusion. 

From the conceptual point of view, there are two general approaches to the molecular structure problem the molecular orbital (MO) and the valence bond (VB) theories. Technical difficulties in the computational implementation of the VB approach have favoured the development and the popularization of MO theory in opposition to VB. In a recent review [3], some related issues are raised and clarified. However, there still persist some conceptual pitfalls and misinterpretations in specialized literature of MO and VB theories. In this paper, we attempt to contribute to a more profound understanding of the VB and MO methods and concepts. We briefly present the physico-chemical basis of MO and VB approaches and their intimate relationship. The VB concept of resonance is reformulated in a physically meaningful way and its point group symmetry foundations are laid. Finally it is shown that the Generalized Multistructural (GMS) wave function encompasses all variational wave functions, VB or MO based, in the same framework, providing an unified view for the theoretical quantum molecular structure problem. Throughout this paper, unless otherwise stated, we utilize the non-relativistic (spin independent) hamiltonian under the Bom-Oppenheimer adiabatic approximation. We will see that even when some of these restrictions are removed, the GMS wave function is still applicable. 

Fig. 6. Average relativistic effective core potential and relativistic effective core potential energy curves for two states of Bi2. HF, Hartree-Fock GVB(pp), eight-configuration perfect-pairing generalized valence bond FVCI, full-valence Cl based on the GVB(pp) wave functions FV7R, full-valence Cl plus single and double promotions to virtual MOs relative to seven-dominant configurations. (The FVCI and FV7R calculations include the REP-based spin-orbit operator.)...

FIGURE 6.37 The electron density for the if/g and ifil wave functions in the simple valence bond model for H2. (a) The electron density pg for if/g and Pu for calculated analytically as described in the text, (b) Three-dimensional isosurface of the electron density for the ipg wave function, as calculated numerically by Generalized Valence Bond Theory (GVB). 

Hartke, B. and E. A. Carter (1992). Ab Initio Molecular Dynamics with Correlated Molecular Wave Functions Generalized Valence Bond Molecular Dynamics and Simulated Annealilng. J. Chem. Phvs. 97(9) 6569-6578. 

---