Excited electronic states from a generalization of the extended Koopmans theorem

Abstract

Inspired by the extended Koopmans theorem, we demonstrate that excited electronic states can efficiently and very accurately be computed from the ground-state density correlators. That this is possible in principle does not come as a surprise. However, what correlator order is needed is an important question. There are a number of methods that differ in the way in which higher-order correlators, which are very expensive to evaluate, are treated: the equation-of-motion approach, also known as the random phase approximation, the cumulant, and the Hermitian operator methods. Here it is shown that there exists, in fact, a close connection between the extended Koopmans theorem and the equation-of-motion approach. A dramatic improvement over the conventional linear-response calculations is numerically demonstrated for a paradigmatic molecular system and explained by comparing with the equation-of-motion approach for a single-determinant reference state and for the case of composite excitations. Our approach opens prospects for systematic improvements of the adiabatic approximation of the time-dependent density functional theory by exploiting properties of the correlated ground state.