Generalized valence bond

Short description: Quantum chemistry method extending valence bond theory

Electronic structure methods

Valence bond theory
Coulson–Fischer theory
Generalized valence bond
Modern valence bond
Molecular orbital theory
Hartree–Fock method
Semi-empirical quantum chemistry methods
Møller–Plesset perturbation theory
Configuration interaction
Coupled cluster
Multi-configurational self-consistent field
Quantum chemistry composite methods
Quantum Monte Carlo
Density functional theory
Time-dependent density functional theory
Thomas–Fermi model
Orbital-free density functional theory
Electronic band structure
Nearly free electron model
Tight binding
Muffin-tin approximation
[[Engineering:K·p perturbation k·p perturbation theory]]
Empty lattice approximation
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The generalized valence bond (GVB) is a method in valence bond theory that uses flexible orbitals in the general way used by modern valence bond theory. The method was developed by the group of William A. Goddard, III around 1970.[1][2]

## Theory

The generalized Coulson–Fischer theory for the hydrogen molecule, discussed in Modern valence bond theory, is used to describe every electron pair in a molecule. The orbitals for each electron pair are expanded in terms of the full basis set and are non-orthogonal. Orbitals from different pairs are forced to be orthogonal - the strong orthogonality condition. This condition simplifies the calculation but can lead to some difficulties.

## Calculations

GVB code in some programs, particularly GAMESS (US), can also be used to do a variety of restricted open-shell Hartree–Fock calculations,[3] such as those with one or three electrons in two pi-electron molecular orbitals while retaining the degeneracy of the orbitals. This wave function is essentially a two-determinant function, rather than the one-determinant function of the restricted Hartree–Fock method.

## References

1. ↑ Goddard, W. A., Dunning, T. H., Hunt, W. J. and Hay, P. J. (1973), "Generalized valence bond description of bonding in low-lying states of molecules", Accounts of Chemical Research 6 (11): 368, doi:10.1021/ar50071a002
2. ↑ "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 Cr2 and Mo2", Physical Review Letters 54 (7): 661–664, February 1985, doi:10.1103/PhysRevLett.54.661, PMID 10031583, Bibcode: 1985PhRvL..54..661G.
3. ↑ Muller, Richard P.; Langlois, Jean-Marc; Ringnalda, Murco N.; Friesner, Richard A.; Goddard, William A. (1994), "A generalized direct inversion in the iterative subspace approach for generalized valence bond wave functions", The Journal of Chemical Physics 100 (2): 1226, doi:10.1063/1.466653, Bibcode: 1994JChPh.100.1226M

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