This paper presents an optimized effective potential (OEP) approach based on density functional theory (DFT) for individual excited states that implements a simple method of taking the necessary orthogonality constraints into account. The amended Kohn-Sham (KS) equations for orbitals of excited states having the same symmetry as the ground one are proposed. Using a variational principle with some orthogonality constraints, the OEP equations determining a local exchange potential for excited states are derived. Specifically, local potentials are derived whose KS determinants minimize the total energies and are simultaneously orthogonal to the determinants for states of lower energies. The parametrized form of an effective DFT potential expressed as a direct mapping of the external potential is used to simplify the OEP integral equations. A performance of the presented method is examined by exchange-only calculations of excited state energies for simple atoms and molecules.
Distributed basis sets of s-type Gaussian functions are determined by invoking the variation principle for the Hartree-Fock ground states of the H 2 , LiH, and BH molecules at their respective experimental equilibrium geometries. The calculated energy expectation values supported by these finite basis sets are compared with finite difference Hartree-Fock energies reported by Kobus et al. A distributed basis set of 54 s-type Gaussian functions distributed along the internuclear axis is shown to support an accuracy of 0.05 Hartree for the Hartree-Fock ground-state energy of the H 2 molecule while a similar set containing 50 functions leads to an accuracy of 0.8 Hartree for the ground-state energy of the LiH molecule. For the BH ground state, a Hartree-Fock energy in error by 1.7 Hartree is supported by a variationally optimized distributed basis set of 65 s-type Gaussian functions distributed along the internuclear axis. The parameters, that is, the exponents and positions, defining the variationally optimized distributed basis sets are presented and discussed.
An alternative approach to problems in quantum chemistry which can be written as an eigenvalue equation with orthogonality restrictions imposed on eigenvectors is reviewed. The basic tenets of a simply implemented asymptotic projection method for taking the necessary orthogonality constraints into account are presented. The eigenvalue equation for a modified operator is derived and the equivalence of the original and modified problem is rigorously demonstrated. The asymptotic projection method is compared with the conventional approach to constrained variational problems based on the elimination of off-diagonal Lagrange multipliers and with other methods. A general procedure for application of the method to excited state problems is demonstrated by means of calculations of excited state energies and excitation energies for the one-electron molecular systems, H + 2 and H ++ 3 .
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.