Post-HF-Methods - The Explicit Consideration of theElectron Correlation

Post-HF-Methods - The Explicit Consideration of the Electron Correlation

It is well recognized that refinement of the HF procedure proceeds in two distinct directions. One is extension of the basis set of basis functions used for expansion of the spin-orbitals. The other is the development of methods for taking account of the correlation of electrons that is neglected in the simplest, single-determinant HF treatment. The extension of the basis set would only lead, in the best case of an infinite basis, to the HF limit, which does not include all components of electron correlation. To account for these contributions, a wide variety of methods have been proposed and some are now widely used in practical applications. Ideally, a theoretical model taking electron correlation into consideration should be:^[i]

(1) Well defined, leading to a unique energy for any nuclear configuration and a continuos potential surface

(2) Size consistent, so that when applied to an ensemble of N isolated molecules, calculated energies should be additive, e.g. N = 2 then

E(AA) = 2 E(A).

If this condition is not satisfied, the theory is unlikely to give a good description of the relative energies of molecules of different sizes.

(3) It should be exact (equivalent to full CI) when applied to a two-electron system.

(4) It should be variational, so that the computed energy is an upper bound to the correct energy.

Few theories satisfy all these conditions, even for molecular ground states. HF theory, in its spin-unrestricted form (UHF) with an atom-centered set of basis functions, usually satisfies all four but takes no account of the correlation between electrons of opposite spin. Complete configuration interaction (full CI), within a given basis, would satisfy all conditions, but this is only practical for the very smallest systems. This leads to two additional conditions:

(5) It should be accurate enough to give an adequate approximation to the full CI result.

(6) It should be efficient, so that computation with large basis sets is possible.

No current method satisfies all these criteria; most compromise by introducing different approximations with varying degrees of success.