The Single-Determinant Approximation with a Local Potential for Excited States

The specific features of the calculations of the electronic structure in the approximation of a local exchange potential that is identical for all the electrons involved are considered. An optimized effective potential method is proposed for calculating the energies of excited electronic states of the same symmetry. A single-particle Schroedinger equation is derived for an excited state whose orbitals are described by a single-determinant wave function orthogonal to the ground state. The equations determining the local potential for excited states are obtained within the variational approach. The solution to these equations is analyzed in the framework of the parameterized representation of the effective potential. The efficiency of the proposed method is demonstrated by calculating the energies of three excited states of the same symmetry for a HeH molecule. The difference between the results obtained by the Hartree-Fock method and the method proposed in this paper is equal, on average, to 0.05%. A comparison with the results obtained from precise calculations based on the configuration interaction method shows that the accuracy in determining the energy of the excited states by the optimized effective potential method is comparable to the accuracy in calculating the energy of the ground state.