This paper presents an evaluation of the performance of time-dependent density-functional response theory ͑TD-DFRT͒ for the calculation of high-lying bound electronic excitation energies of molecules. TD-DFRT excitation energies are reported for a large number of states for each of four molecules: N 2 , CO, CH 2 O, and C 2 H 4 . In contrast to the good results obtained for low-lying states within the time-dependent local density approximation ͑TDLDA͒, there is a marked deterioration of the results for high-lying bound states. This is manifested as a collapse of the states above the TDLDA ionization threshold, which is at Ϫ⑀ HOMO LDA ͑the negative of the highest occupied molecular orbital energy in the LDA͒. The Ϫ⑀ HOMO LDA is much lower than the true ionization potential because the LDA exchange-correlation potential has the wrong asymptotic behavior. For this reason, the excitation energies were also calculated using the asymptotically correct potential of van Leeuwen and Baerends ͑LB94͒ in the self-consistent field step. This was found to correct the collapse of the high-lying states that was observed with the LDA. Nevertheless, further improvement of the functional is desirable. For low-lying states the asymptotic behavior of the exchange-correlation potential is not critical and the LDA potential does remarkably well. We propose criteria delineating for which states the TDLDA can be expected to be used without serious impact from the incorrect asymptotic behavior of the LDA potential.

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This paper presents a comparison between density functional theory local density approximation (LDA) and Hartree–Fock approximation (HFA) calculations of dipole moments, polarizabilities, and first hyperpolarizabilities, using ‘‘comparable’’ basis sets, in order to assess the relative quality of the LDA and the HFA for calculating these properties. Specifically, calculations were done using basis sets of roughly double or triple zeta plus polarization quality, with and without added field-induced polarization (FIP) functions, for the seven small molecules H2, N2, CO, CH4, NH3, H2O, and HF, using the HFA option in the program HONDO8 and the LDA options in the programs DMol and deMon. For the calculations without FIP functions, the results from HONDO8 HFA and deMon LDA, both of which use Gaussian basis sets, are very similar, while DMol, which uses a LDA numerical atomic orbital basis set, gives substantially better results. Adding FIP functions does much to alleviate these observed basis set artifacts and improves agreement with experiment. With FIP functions, the results from the two sets of LDA calculations (deMon and DMol) are very similar to each other, but differ markedly from the HFA results, and the LDA results are in significantly better agreement with experiment. This is particularly true for the hyperpolarizabilities. This appears to be the first detailed study of DFT calculations of molecular first hyperpolarizabilities. We note that closer attention to numerical details of the finite field calculation of β⇊ is necessary than would usually be the case with traditional ab initio methods. A proof that the Hellmann–Feynman theorem holds for Kohn–Sham calculations is included in the Appendix.

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