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Reverted edit(s) by 50.78.198.129 identified as test/vandalism using STiki

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{{Electronic structure methods}}
'''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);<ref>van Lenthe, J. H.; Dijkstra, F.; Havenith, R. W. A. '''TURTLE - A gradient VBSCF Program Theory and Studies of Aromaticity'''. In Theoretical and Computational Chemistry: Valence Bond Theory; Cooper, D. L., Ed.; Elsevier: Amsterdam, 2002; Vol. 10; pp 79--116.</ref> Song, Mo, Zhang and Wu (2005); and Shaik and Hiberty (2004).<ref>See further reading section.</ref>

In its simplest form the overlapping [[atomic orbitals]] are replaced by orbitals which are expanded as [[linear combination]]s of the atom-based [[Basis set (chemistry)|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.

For example, in the [[hydrogen molecule]], classic [[valence bond theory]] uses two 1s [[atomic orbital]]s (a and b) on the two [[hydrogen]] atoms respectively and then constructs a [[covalent]] structure:-

:<math> \Phi_{C} = </math>(a(1)b(2) + b(1)a(2)) (α(1)β(2) - β(1)α(2))

and then an [[ion]]ic structure:-

:<math> \Phi_{I} = </math>(a(1)a(2) + b(1)b(2)) (α(1)β(2) - β(1)α(2))

The final [[wave function]] is a [[linear combination]] of these two functions. [[Charles Coulson|Coulson]] and [[Inga Fischer-Hjalmars|Fischer]]<ref>C. A. Coulson and I. Fischer,
Phil. Mag. vol 40, p. 386 (1949)</ref>
pointed out that a completely equivalent function is:-

:<math> \Phi_{CF} = </math>((a+kb)(1)(b+ka)(2) + (b+ka)(1)(a+kb)(2)) ((α(1)β(2) - β(1)α(2))

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 (chemistry)|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 theory|Coulson-Fischer method]].

== Spin-coupled theory ==
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 function]]s, we have '''spin-coupled valence bond theory'''. The total [[wave function]] is optimized using the [[variational method]] by varying the coefficients of the [[Basis set (chemistry)|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.

== Valence bond programs ==

Several groups have produced [[Valence bond programs|computer programs]] for modern valence bond calculations that are freely available.

== References ==
<references />

==Further reading==

* J. Gerratt, D. L. Cooper, P. B. Karadakov and M. Raimondi, "Modern Valence Bond Theory", ''Chemical Society Reviews'', '''26''', 87, 1997, and several others by the same authors.
* J. H. van Lenthe, G. G. Balint-Kurti, "The Valence Bond Self-Consistent Field (VBSCF) method", ''Chemical Physics Letters'' '''76''', 138–142, 1980.
* J. H. van Lenthe, G. G. Balint-Kurti, "The Valence Bond Self-Consistent Field (VBSCF) method", ''The Journal of Chemical Physics'' '''78''', 5699–5713, 1983.
* J. Li and R. McWeeny, "VB2000: Pushing Valence Bond Theory to new limits", ''International Journal of Quantum Chemistry'', '''89''', 208, 2002.
* L. Song, Y. Mo, Q. Zhang and W. Wu, "XMVB: A program for ''ab initio'' nonorthogonal valence bond computations", ''Journal of Computational Chemistry'', '''26''', 514, 2005.
* S. Shaik and P. C. Hiberty, "Valence Bond theory, its History, Fundamentals and Applications. A Primer", ''Reviews of Computational Chemistry'', '''20''', 1 2004. A recent review that covers, not only their own contributions, but the whole of modern valence bond theory.

[[Category:Computational chemistry]]
[[Category:Electronic structure methods]]

Central field approximation - Revision history

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