Exchange-correlation approximation

Becke A D 1995 Exchange-correlation approximations in density-functional theory Modern Eiectronic Structure Theory vol 2, ed D R Yarkony (Singapore World Scientific) pp 1022-46... 

Becke, A. D., 1995, Exchange-Correlation Approximations in Density-Functional Theory in Modem Electronic Structure Theory, Part II, Yarkony, D. R., World Scientific, Singapore. 

Becke AD (1994) Thermochemical tests of a kinetic-energy dependent exchange-correlation approximation, Int. J. Quant. Chem. Symp, 98 625-632... 

This review provides a comprehensive account of the recent progress in constructing practical exchange-correlation approximations of Kohn-Sham density functional theory. The emphasis is on the general techniques of density functional design that have been particularly successful in quantum chemistry. Nearly all density functionals embraced nowadays by computational chemists are discussed. Persistent misconceptions about several widely used functionals are clarified. 

Functionals that combine GGAs or meta-GGAs with exact exchange of Eq. (38) are called hybrids. At present, hybrid functionals outnumber any other group of exchange-correlation approximations. Hybridization has been embraced widely because it greatly improves performance of pure DPT functionals and is easy to implement. 

Becke, A.D. (1985) Local exchange-correlation approximations and first-row molecular dissociation energies. Int. J. Quantum Chem., 27 (5), 585-594. 

Consistency between the exchange-correlation approximations used in the Hamiltonian and in the linear response theory has been realized. The importance of different exchange-correlation approximations is presently under investigation. 

This equation is usually solved self-consistently . An approximate charge is assumed to estimate the exchange-correlation potential and to detennine the Flartree potential from equation Al.3.16. These approximate potentials are inserted in the Kolm-Sham equation and the total charge density is obtained from equation A 1.3.14. The output charge density is used to construct new exchange-correlation and Flartree potentials. The process is repeated nntil the input and output charge densities or potentials are identical to within some prescribed tolerance. 

We have used the basis set of the Linear-Muffin-Tin-Orbital (LMTO) method in the atomic sphere approximation (ASA). The LMTO-ASA is based on the work of Andersen and co-workers and the combined technique allows us to treat all phases on equal footing. To treat itinerant magnetism we have employed the Vosko-Wilk-Nusair parametrization for the exchange-correlation energy density and potential. In conjunction with this we have treated the alloying effects for random and partially ordered phases with a multisublattice generalization of the coherent potential approximation (CPA). 

The explicit form of the functional Fh is of course unknown and in practical applications has to be approximated. In order to facilitate the aeation of these approximations one decomposes Fh into a sum of other functionals that focuses all the unknowns into one component, the exchange-correlation functional, Fxo... 

Just as in the unrestricted Hartree-Fock variant, the Slater determinant constructed from the KS orbitals originating from a spin unrestricted exchange-correlation functional is not a spin eigenfunction. Frequently, the resulting (S2) expectation value is used as a probe for the quality of the UKS scheme, similar to what is usually done within UHF. However, we must be careful not to overstress the apparent parallelism between unrestricted Kohn-Sham and Hartree-Fock in the latter, the Slater determinant is in fact the approximate wave function used. The stronger its spin contamination, the more questionable it certainly gets. In... 

---