Density functional methods

Although density functional theory (DFT) has been around for many years, it is only recently (since 1990) that its application to chemical problems has become popular. In the first stage of DFT, the energy is expressed as a functional of the density of a uniform electron gas (E([rho])). This is then modified to express the electron density around molecules.

Despite its simple origins, DFT works very well in most cases. For about the same cost of doing a Hartree-Fock calculation, DFT includes a significant fraction of the electron correlation. Note that DFT is not a Hartree-Fock method, nor is it (strictly speaking) a post-Hartree-Fock method! The wave function is constructed in a different way (the spin and spatial parts are different to those developed in Hartree-Fock theory) and the resulting orbitals are often referred to as "Kohn-Sham" orbitals. Nevertheless, the same SCF procedure is used as in Hartree-Fock theory.

The choice of the functional is the only limitation of the DFT method. At the present time, there is no systematic way of choosing the functional and the most popular ones in the literature have been derived by careful comparison with experiment. Some of the most common methods you may come across are:

BP86 - developed by Becke and Perdew in 1986

BLYP - developed by Becke, Lee, Yang and Parr

B3LYP - a modification of BLYP in which a three-parameter functional developed by Axel Becke is used, mixing the Hartree-Fock exchange term with the DFT term. This is an example of a hybrid DFT method.

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