Local-scaling transformation version of density functional theory: Application to atoms and diatomic molecules

Abstract

Applications of the local-scaling transformation version of density functional theory, LS-DFT, to atoms and diatomic molecules are presented. In the case of atoms, explicit kinetic- and exchange-energy functionals for first- and second-row atoms at the Hartree–Fock level are constructed. The emphasis given in LS-DFT to the symmetry problem, namely, to the inclusion of spin and angular momentum restrictions in energy density functionals, is illustrated by the construction of explicit energy functionals (at the Hartree–Fock level) for the 1S, 3P and 1D terms of the 1s22s22p2 configuration of the carbon atom. Also, applications of LS-DFT that go beyond the Hartree–Fock method are presented. In this respect, the decomposition of the electron correlation energy into its dynamical and nondynamical parts is analyzed for the case of four-electron atoms and ions. It is shown that a “reference wave function”—differing from the exact one only in the dynamical correlation energy component—can always be found. Based on this wave function, the correlation energy is partitioned into “long-range” and “short-range” contributions. A method based on a cluster-expansion technique is advanced for the purpose of treating the dynamical “short-range” correlation component. In the case of diatomic molecules, the derivation of coupled first-order integral equations for density transformations of prolate-spheroidal coordinates is discussed. Applications of these density transformations to molecular orbitals involving single ζ atomic functions are carried out and a comparison is made between the energies coming from the original and the locally scaled orbitals. Also, the minimization of the kinetic energy at fixed Hartree–Fock density is discussed as this procedure is equivalent to solving the Kohn–Sham x-only equations. Finally, some extensions of LS-DFT to polyatomic systems (molecules and solids) are discussed. In particular, the possibility of generating a molecular energy density functional as a collection of atom-centered functionals and of applying nonisotropic density transformations to solids is considered. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 155–183, 1999