Description of electronic excited states using electron correlation operator.

The electron correlation energy in a chemical system is defined as a difference between the energy of an exact energy for a given Hamiltonian, and a mean-field, or single determinant, approximation to it. A promising way to model electron correlation is through the expectation value of a linear two-electron operator for the Kohn-Sham single determinant wavefunction. For practical reasons, it is desirable for such an operator to be universal, i.e., independent of the positions and types of nuclei in a molecule. The correlation operator models the effect of electron correlation on the interaction energy in a electron pair. We choose an operator expanded in a small number of Gaussians as a model for electron correlation, and test it by computing atomic and molecular adiabatic excited states. The computations are performed within the Δ Self-Consistent Field (ΔSCF) formalism, and are compared to the time-dependent density functional theory model with popular density functionals. The simplest form of the correlation operator contains only one parameter derived from the helium atom ground state correlation energy. The correlation operator approach significantly outperforms other methods in computation of atomic excitation energies. The accuracy of molecular excitation energies computed with the correlation operator is limited by the shortcomings of the ΔSCF methodology in describing excited states.