On the relation between adiabatic time dependent density functional theory (TDDFT) and the ΔSCF-DFT method. Introducing a numerically stable ΔSCF-DFT scheme for local functionals based on constricted variational DFT

In Delta SCF density functional theory studies of a i -> a transition one performs separate fully self-consistent field calculations on the ground state configuration (i)(n) (n = 1,2) and the excited state configuration (i)(n - 1)a. The excitation energy for the transition i -> a is subsequently determined as the Kohn-Sham energy difference Delta E-i -> a = E[i(n - 1)a] - E[i(n)] between the ground state (i)(n) and the excited state configuration (i)(n - 1)a. The Delta SCF scheme has been applied extensively and works well for lower energy excitations provided that they can be represented by a single orbital replacement or transition i -> a. However, for excitations of higher energy Delta SCF tends to become numerically unstable with a variational collapse to transitions of lower energy. We demonstrate here a numerically stable Delta SCF scheme for local functionals that is guaranteed not to collapse on excited configurations of lower energy as well as the ground state. The new scheme is based on constricted variational density functional theory in which the canonical ground state orbitals are allowed to relax (R-CV(infinity)-DFT). Since it is restricted to a single orbital replacement i -> a it is termed SOR-R-CV(infinity)-DFT.