Generation of explicit electron correlation functional by means of local scaling transformations

Abstract

We discuss in the present work the treatment of electron correlation within the context of the local scaling transformation version of density functional theory. This is done by resorting to a locally scaled transcorrelated Hamiltonian of Boys and Handy [S. F. Boys and N. C. Handy, Proc. Roy. Soc. A310, 43 (1969)] which describes electron correlation effects as arising from the action of effective two- and three-particle terms on a single Slater determinant. The expectation value of the locally scaled correlated wave function is expressed in terms of the factor Aviles-Hartog-Tolhoek (FAHT) cluster expansion, and the explicit form of the correlation functional is given up to second order. In particular, an explicit analytic functional is obtained for the effective two-body term. This functional contains ρ5/3, ρ4/3, and ρ2/3 as universal factors. Numerical calculations using the locally scaled correlation wave function are performed for two-electron atoms for which various types of orbitals and correlation factors are tested. The numerical results for the correlation energy of these two-electron systems attest as to the adequacy of the present locally scaled-generated functionals. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 439–450, 1998