Generalized valence bond, GVB

A number of types of calculations begin with a HF calculation and then correct for correlation. Some of these methods are Moller-Plesset perturbation theory (MPn, where n is the order of correction), the generalized valence bond (GVB) method, multi-conhgurational self-consistent held (MCSCF), conhgu-ration interaction (Cl), and coupled cluster theory (CC). As a group, these methods are referred to as correlated calculations. 

An MCSCF calculation in which all combinations of the active space orbitals are included is called a complete active space self-consistent held (CASSCF) calculation. This type of calculation is popular because it gives the maximum correlation in the valence region. The smallest MCSCF calculations are two-conhguration SCF (TCSCF) calculations. The generalized valence bond (GVB) method is a small MCSCF including a pair of orbitals for each molecular bond. 

A configuration interaction calculation uses molecular orbitals that have been optimized typically with a Hartree-Fock (FIF) calculation. Generalized valence bond (GVB) and multi-configuration self-consistent field (MCSCF) calculations can also be used as a starting point for a configuration interaction calculation. 

Figure 11-4 Generalized valence bond (GVB) orbitals for one hydrogen of ethyne (left) and of ethane (right) see Section 6-7. The hydrogen and carbon nuclei are located in the X, V plane of the coordinate system at the positions indicated by crosses, the hydrogen nucleus being on the left.

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 ... 

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. 

The recent developments in generalized Valence Bond (GVB) theory have been reviewed by Goddard and co-workers,13 and also the use of natural orbitals in theoretical chemistry,14 15 and the accuracy of computed one-electron properties.18 The Xa method has been reviewed by Johnson,17 and Hurley has discussed high-accuracy calculations on small molecules.18 Several other reviews of interest have appeared in Advances in Quantum Chemistry.17 Localized orbital theory has been reviewed by England, Salmon, and Ruedenberg,19 and the bonding in transition-metal complexes discussed by Brown et a/.20 Finally, the recent developments in computational quantum chemistry have been reviewed by Hall.21... 

Although the emphasis in ab initio calculations in recent years has been on calculations using the MO approach, alternative methods have not been neglected, particularly Valence Bond (VB) methods of various types. Particularly promising has been the work of Goddard and co-workers with the so-called Generalized Valence Bond (GVB) method.13... 

Finally we discuss the Generalized Valence Bond (GVB) method as proposed by Hunt, Hay and Goddard./180,181,182/ This is a method aimed at improving some of the HF procedures, for instance to obtain the correct dissociation limit, and to partially include correlation effects. The basic idea is that the type... 

In certain Instances it may be appropriate to determine the ground state wavefunction using the generalized valence-bond (GVB) technique (21). This is especially true for closed shell anions where the pair of electrons in the highest occupied molecular orbital (HOMO) may be described by the wavefunction... 

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