Charge-transfer correction for improved time-dependent local density approximation excited-state potential energy curves: Analysis within the two-level model with illustration for H2 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 often falls rapidly to zero and then becomes imaginary at large internuclear distances. We show that this unphysical behavior occurs because ${\omega }_T^2$ 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 ΔSCF method gives a qualitatively correct first triplet excited state to derive a “charge-transfer correction” (CTC) for the time-dependent local density approximation (TDLDA) within the two-level model and the Tamm-Dancoff approximation (TDA). Although this correction would not be needed for the exact exchange–correlation functional, it is evidently important for a correct description of molecular excited state potential energy surfaces in the TDLDA. As a byproduct of our analysis, we show why TDLDA and LDA ΔSCF excitation energies are often very similar near the equilibrium geometries. The reasoning given here is fairly general and it is expected that similar corrections will be needed in the case of generalized gradient approximations and hybrid functionals.