Generalized valence bond wave

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. 

Anderson AG, Goddard WA (2010) Generalized valence bond wave fiuictions in quantum Monte Carlo. J Chem Phys 132(16) 1641 lO-(lO)... 

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. 

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. 

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. 

The choice of reference space for MRCI calculations is a complex problem. First, a multieonfigurational Hartree-Fock (MCSCF) approach must be chosen. Common among these are the generalized valence-bond method (GVB) and the complete active space SCF (CASSCF) method. The latter actually involves a full Cl calculation in a subspace of the MO space—the active space. As a consequence of this full Cl, the number of CSFs can become large, and this can create very long Cl expansions if all the CASSCF CSFs are used as reference CSFs. This problem is exacerbated when it becomes necessary to correlate valence electrons in the Cl that were excluded from the CASSCF active space. It is very common to select reference CSFs, usually by their weight in the CASSCF wave function. Even more elaborate than the use of a CASSCF wave function as the reference space is the seeond-order Cl, in which the only restriction on the CSFs is that no more than two electrons occupy orbitals empty in the CASSCF wave function. Such expansions are usually too long for practical calculations, and they seldom produce results different from a CAS reference space MRCI. 

Murphy RB, Pollard WT, Friesner RA. Pseudospectral localized generalized Moller-Plesset methods with a generalized valence bond reference wave function theory and calculation of conformational energies. J Chem Phys 1997 106 5073-5084. 

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