Time-dependent optimized effective potential

Given an expression for the quantum mechanical action A[φjσ] of an N-electron system as a functional of N time-dependent spin orbitals, we present a method of constructing the variationally best local time-dependent single-particle potentials vσ(rt) which, when inserted in time-dependent single-particle Schrödinger equations for the spin-up and spin-down electrons yield orbitals {φjσ(rt)} that make A[φjσ] stationary. We also propose a simplification of this scheme leading to a time-dependent generalization of the static optimized effective potentials recently introduced by Krieger, Li, and Iafrate [Phys. Lett. A 146, 256 (1990)]