|Electronic structure methods|
|Valence bond theory|
|Generalized valence bond
Modern valence bond
|Molecular orbital theory|
Semi-empirical quantum chemistry methods
Møller–Plesset perturbation theory
Multi-configurational self-consistent field
Quantum chemistry composite methods
Quantum Monte Carlo
Linear combination of atomic orbitals
|Electronic band structure|
|Nearly free electron model
Density functional theory
k·p perturbation theory
Empty lattice approximation
Modern valence bond theory is the application of valence bond theory, with computer programs that are competitive in accuracy and economy with programs for the Hartree–Fock method and other molecular orbital based methods. The latter methods dominated quantum chemistry from the advent of digital computers because they were easier to program. The early popularity of valence bond methods thus declined. It is only recently that the programming of valence bond methods has improved. These developments are due to and described by Gerratt, Cooper, Karadakov and Raimondi (1997); Li and McWeeny (2002); Joop H. van Lenthe and co-workers (2002); Song, Mo, Zhang and Wu (2005); and Shaik and Hiberty (2004).
In its simplest form the overlapping atomic orbitals are replaced by orbitals which are expanded as linear combinations of the atom-based basis functions, forming linear combinations of atomic orbitals (LCAO). This expansion is optimized to give the lowest energy. This procedure gives good energies without including ionic structures.
and then an ionic structure:-
as expanding this out gives a linear combination of the covalent and ionic structures. Modern valence bond theory replaces the simple linear combination of the two atomic orbitals with a linear combination of all orbitals in a larger basis set. The two resulting valence bond orbitals look like an atomic orbital on one hydrogen atom slightly distorted towards the other hydrogen atom. Modern valence bond theory is thus an extension of this Coulson–Fischer method.
There are a large number of different valence bond methods. Most use n valence bond orbitals for n electrons. If a single set of these orbitals is combined with all linear independent combinations of the spin functions, we have spin-coupled valence bond theory. The total wave function is optimized using the variational method by varying the coefficients of the basis functions in the valence bond orbitals and the coefficients of the different spin functions. In other cases only a sub-set of all possible spin functions is used. Many valence bond methods use several sets of the valence bond orbitals. Be warned that different authors use different names for these different valence bond methods.
Several groups have produced computer programs for modern valence bond calculations that are freely available.
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