Charge-transfer correction for improved time-dependent local density approximation excited-state potential energy curves: Analysis within the two-level model with illustration for H-2 and LiH

Time-dependent density-functional theory (TDDFT) is an increasingly popular approach for calculating molecular excitation energies. However, the TDDFT lowest triplet excitation energy, omega (T), of a closed-shell molecule of ten falls rapidly to zero and then becomes imaginary at large internuclear distances. We show that this unphysical behavior occurs because omega (2)(T ) must become negative wherever symmetry breaking lowers the energy of the ground state solution below that of the symmetry unbroken solution. We use the fact that the Delta SCF method gives a qualitatively correct first trip let excited state to derive a "charge-transfer correction" (CTC) for the ti me-dependent local density approximation (TDLDA) within the two-level model and the Tamm-Dancoff approximation (TDA). Although this correction would n ot be needed for the exact exchange-correlation functional, it is evidently important for a correct description of molecular excited state potential e nergy surfaces in the TDLDA. As a byproduct of our analysis, we show why TD LDA and LDA Delta SCF excitation energies are often very similar near the e quilibrium geometries. The reasoning given here is fairly general and it is expected that similar corrections will be needed in the case of generalize d gradient approximations and hybrid functionals. (C) 2000 American Institu te of Physics. [S0021-9606(00)30941-2].