Density-functional theory with effective potential expressed as a direct mapping of the external potential: Applications to atomization energies and ionization potentials

Abstract

In this paper the authors further develop and apply the direct-mapping density functional theory to calculations of the atomization energies and ionization potentials. Single-particle orbitals are determined by solving the Kohn-Sham [Phys. Rev. A. 140, 1133 (1965)] equations with a local effective potential expressed in terms of the external potential. A two-parametric form of the effective potential for molecules is proposed and equations for optimization of the parameters are derived using the exchange-only approximation. Orbital-dependent correlation functional is derived from the second-order perturbation theory in its Moller-Plesset-type zeroth-order approximation based on the Kohn-Sham orbitals and orbital energies. The total atomization energies and ionization potentials computed with the second-order perturbation theory were found to be in agreement with experimental values and benchmark results obtained with ab initio wave mechanics methods.

Highly Excited States from a Time Independent Density Functional Method

“…The potential preserves symmetry properties of the exact eigenstates and has proven to be successful for the ground state calculations of different characteristic atoms and molecules [34,37,38] and for low-lying excited states [1,2]. Therefore it is natural to try this potential for highly excited state calculations.…”

“…. , 7) energies and excitation energies of the Li atom to the HF [38] and "exact" energies obtained with the most accurate configuration interaction wave function using the Hylleraas basis set [41]. It is known that high accuracy of calculation of the transition frequencies for Rydberg states of alkali metal atoms, in particular lithium, is a topical problem of theoretical methods for studying the electronic structure [44].…”

“…Before discussing results of calculations, we should point out that our x-COEP implementation employs a parameterized form of V eff proposed in [36] and further developed in [37,38] where an effective potential is a direct mapping of the external potential V ext and for N-electron atoms takes the form:…”

Subspace effective potential theory for configuration interaction

“… is a mapping of Using symmetry principles and asymptotic conditions it was concluded that is a nonlocal mapping of This mapping gives an approximation which in the following will be denoted by V eff and for molecules where it takes the following form (see Refs. ). where Z k is the charge of the nucleus at and The parameters C and d k have to be determined so that the functional attains its minimum value for the produced by this potential.…”

“… where Z k is the charge of the nucleus at and The parameters C and d k have to be determined so that the functional attains its minimum value for the produced by this potential. This method was applied successfully for the ground state calculations of atoms and molecules, excited state exchange‐only OEP calculations as well as for incorporating static correlation effects . It was also appropriate for core hole excited and ionized states .…”