Exchange correlation energy functionals

Professor Axel Becke of Queens University, Belfast has been very actively involved in developing and improving exchange-correlation energy functionals. For a good recent overview, see ... 

Laming, G. J., Termath, V., Handy, N, C., 1993, A General Purpose Exchange-Correlation Energy Functional ,... 

In principle, the KS equations would lead to the exact electron density, provided the exact analytic formula of the exchange-correlation energy functional E was known. However, in practice, approximate expressions of Exc must be used, and the search of adequate functionals for this term is probably the greatest challenge of DFT8. The simplest model has been proposed by Kohn and Sham if the system is such that its electron density varies slowly, the local density approximation (LDA) may be introduced ... 

Laming, G.J., V. Termath, and N.C. Handy. 1993. A general purpose exchange-correlation energy functional. J. Chem. Phys. 99, 8765. 

The term Exc[p] is called the exchange-correlation energy functional and represents the main problem in the DFT approach. The exact form of the functional is unknown, and one must resort to approximations. The local density approximation (LDA), the first to be introduced, assumed that the exchange and correlation energy of an electron at a point r depends on the density at that point, instead of the density at all points in space. The LDA was not well accepted by the chemistry community, mainly because of the difficulty in correctly describing the chemical bond. Other approaches to Exc[p] were then proposed and enable satisfactory prediction of a variety of observables [9]. 

The third term of Eq (54) is the electronic Hartree potential, whereas the fourth one represents the exchange-correlation potential. This last term is usually obtained from a model exchange-correlation energy functional xc[pl To a first order approximation, the effective KS potential compatible with the electron density p f) given in Eq (51) may be written as ... 

Uniform Density Limit of Exchange-Correlation Energy Functionals... 

Systematic Approaches to the Exchange-Correlation Energy Functional... 

To study the structure of the exchange-correlation energy functional, it is useful to relate this quantity to the pair-correlation function. The pair-correlation function of a system of interacting particles is defined in terms of the diagonal two-particle density matrix (for an extensive discussion of the properties of two-particle density matrices see [30]) as... 

T. van Voorhis and G. E. Scuseria, J. Chem. Phys., 109, 400 (1998). A Novel Form for the Exchange-Correlation Energy Functional. 

The Exchange-Correlation Energy Functional Various Levels of Kohn-Sham DFT... 

We have to consider the calculation of the fourth term, the problem term, in the KS operator of Eq. 7.23, the exchange-correlation potential vXc(r). This is defined as the functional derivative [36, 37] of the exchange-correlation energy functional, fsxc[p(r)], with respect to the electron density functional (Eq. 7.23). The exchange-correlation energy UX( lp(r)], a functional of the electron density function p(r), is a quantity which depends on the function p(r ) and on just what mathematical form the... 

Langreth, D.C. and Mehl, M.J. (1981). Easily implementable nonlocal exchange-correlation energy functional, Phys. Rev. Lett. 47, 446 50. 

---