Doubly, triply, and multiply excited states from a constrained optimized effective potential method.

This article further develops and applies a constrained optimized effective potential (COEP) approach for the practical calculations of doubly and multiply excited states of atoms and molecules. The COEP method uses the time-independent theory of pure excited states and implements a simple asymptotic projection method to take orthogonality constraints into account. We show that, in contrast with the common time-dependent density functional method, the COEP methodology is capable of treating doubly, triply, and multiply excited states and can be easily applied to both atoms and molecules. In particular, doubly excited energies of each state are calculated through a constrained minimization procedure including constraints that make its Slater determinantal functions orthogonal to those of the ground and all lower-lying doubly excited states. The performance of the proposed method is examined by calculations of doubly excited state energies for the He atom and H(2) molecule at exchange-only and exchange-correlation level of approximation.