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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.