Modern valence bond theory has been developed by several workers, including Gerratt, Cooper and Raimondi(1997); Li and McWeeny(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. This expansion is optimised to give the lowest energy. This procedure gives good energies without including ionic structures. An atomic orbital is the description of the behavior of an electron in an atom according to quantum mechanics. ... The term orbital has several meanings: in physics and chemistry it is used to describe an atomic electron configuration, see also molecular orbital and atomic orbital. ... In mathematics, linear combinations are a concept central to linear algebra and related fields of mathematics. ... In modern computational chemistry, quantum chemical calculations are typically performed within a finite set of basis functions. ...

For example, in the hydrogen molecule, classic valence bond theory uses two 1s atomic orbitals (a and b) on the two hydrogen atoms respectively and then constructs a covalent structure:- The Hydrogen molecule consists of two Hydrogen atoms, in other words it is a diatomic molecule. ... The valence bond theory considers that the overlapping atomic orbitals of the participating atoms form a chemical bond. ... Electron atomic and molecular orbitals A less formal description of the electrons in atoms can be found at Electron configuration. ... General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ... Covalent bonding is a form of chemical bonding characterized by the sharing of one or more pairs of electrons between atoms, in order to produce a mutual attraction, which holds the resultant molecule together. ...

Φ_C = ((a(1)b(2) + b(1)a(2)) ((α(1)β(2) - β(1)α(2))

and then an ionic structure:- From ancient Greece (Ionic) An Ionian is a member of one of the four great divisions of the ancient Greek people. ...

Φ_I = ((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. Coulson and Fisher pointed out that a completely equivalent function is:- In the most restricted usage in quantum mechanics, the wavefunction associated with a particle such as an electron, is a complex-valued square integrable function ψ defined over a portion of space normalized in such a way that In Max Borns probabilistic interpretation of the wavefunction, the amplitude squared... In mathematics, linear combinations are a concept central to linear algebra and related fields of mathematics. ...

Φ_CF = ((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. 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 the Coulson-Fischer method. In mathematics, linear combinations are a concept central to linear algebra and related fields of mathematics. ... In mathematics, linear combinations are a concept central to linear algebra and related fields of mathematics. ... An atomic orbital is the description of the behavior of an electron in an atom according to quantum mechanics. ... In modern computational chemistry, quantum chemical calculations are typically performed within a finite set of basis functions. ... General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ...

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 optimised using the variation principle 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. In the most restricted usage in quantum mechanics, the wavefunction associated with a particle such as an electron, is a complex-valued square integrable function ψ defined over a portion of space normalized in such a way that In Max Borns probabilistic interpretation of the wavefunction, the amplitude squared... Calculus of variations is a field of mathematics which deals with functions of functions, as opposed to ordinary calculus which deals with functions of numbers. ... In modern computational chemistry, quantum chemical calculations are typically performed within a finite set of basis functions. ...

Valence Bond Programs

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

See also

• Valence bond theory

The valence bond theory considers that the overlapping atomic orbitals of the participating atoms form a chemical bond. ...

References

• 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. 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.