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Time-dependent density-functional theory (TDDFT) is an increasingly popular approach for calculating molecular excitation energies. However, the TDDFT lowest triplet excitation energy, ωT, 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 ωT2 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.

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The core–valence correlation is introduced into ab initio relativistic pseudopotential calculations by modifying the existing core polarization potential. The salient feature of the method presented here is the use of an l-dependent cutoff parameter (which is related to spherical harmonic functions) for solving the multicenter integrals over the 1/r4 - and r/r3 -type operators. The method is tested on the Rb2 and Cs2 molecules considered as two valence-electron problems. Reliable results for the molecular spectroscopic constants (Re, Te, De, and ωe ) are obtained for the ground state and the lowest excited states. Deviation from the experimental values ranges from 0.05 to 0.1 Å for Re, seldom exceeds 2 cm−1 for ωe, and is of the order of 100 cm−1 for De for most of the excited states.

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