Hartree–Fock calculation for excited states

Abstract

The Hartree–Fock (HF) method, widely used for the calculation of ground state properties, in recent years has been extended for calculating excited states. In this article, we develop an approach, which does not require time consuming calculations and can give a good approximation for the excitation energies. The method is based on the fact that the subspaces of the occupied and virtual orbitals are mutually orthogonal. We test the accuracy of our method by evaluating the excited state wavefunctions and the corresponding energies for the Li, N, F, Ne, and Na atoms and for the BeH and CH molecules, and we found good agreement with configuration interaction and experimental results. © 2012 Wiley Periodicals, Inc.

Double excitations from modified Hartree Fock subsequent minimization scheme

“…One can show this in the same way as Ref. 49 where we proved that the singly excited state is orthogonal to the ground state. …”

“…In a recent paper, 49 we proposed a variational single determinantal approach for singly excited states, based on Unrestricted Hartree-Fock (UHF) equations, 50 where we choose a Slater determinant (SD), by creating a particle in the subspace spanned by the virtual ground state orbitals and a hole in the subspace of occupied ground state orbitals. These orbitals were determined by applying the variational theory, e.g., we minimized the energy of this Slater determinant by varying these orbitals within the ground state occupied and virtual subspaces.…”

Calculation of electronic excited states of molecules using the Helmholtz free-energy minimum principle

“…The GOK principle provided a basis 062501-1 1050-2947/2013/87(6)/062501 (11) ©2013 American Physical Society for the ensemble DFT method [7,8] and its variants which employ the optimized effective potential (exchange only) [9][10][11]. Despite the substantial theoretical investigations of the ensemble variational theories, the practical implementations of the method have been rather scarce and limited to the calculation of excitation energies of atoms and small molecules at equilibrium geometries [12][13][14][15][16].…”

Orthogonality of determinant functions in the Hartree-Fock method for highly excited electronic states

“…It is evident that the existing methods of calculation of the ground state cannot be directly applied for the ESs because of the variational collapse, the problem of which was repeatedly discussed in the literature (see, e.g., [14][15][16][17][18][19][20][21][22][23]). It is known that the exact wave function of an excited state Ψ i , i ≠ 0 should be orthogonal to other functions, including the ground state wave function Ψ 0 .…”

“…One of the approaches explicitly uses the condition of orthogonality of the HF function of a considered ES to the HF functions of all lower-lying states [14,[19][20][21][22]. In a number of papers the practical implementation of this requirement leads to imposing severer conditions on the variational space than is required by the problem itself.…”