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.

This paper is dedicuted to Professor Sigeru Huzirlugu or1 the occasion of his 65th birthdayNATHALIE GODBOUT, DENNIS R. SALAHUB, JAN ANDZELM, and ERICH WIMMER. Can J. Chem. 70, 560 (1992). Gaussian-type orbital and auxiliary basis sets have been optimized for local spin density functional calculations. This first paper deals with the atoms boron through neon. Subsequent papers will provide a list through xenon. The basis sets have been tested for their ability to give equilibrium geometries, bond dissociation energies, hydrogenation energies, and dipole moments. These results indicate that the present optimization technique yields reliable basis sets for molecular calculations.

Standard density functional theory (DFT) is augmented with a damped empirical dispersion term. The damping function is optimized on a small, well balanced set of 22 van der Waals (vdW) complexes and verified on a validation set of 58 vdW complexes. Both sets contain biologically relevant molecules such as nucleic acid bases. Results are in remarkable agreement with reference high-level wave function data based on the CCSD(T) method. The geometries obtained by full gradient optimization are in very good agreement with the best available theoretical reference. In terms of the standard deviation and average errors, results including the empirical dispersion term are clearly superior to all pure density functionals investigated-B-LYP, B3-LYP, PBE, TPSS, TPSSh, and BH-LYP-and even surpass the MP2/cc-pVTZ method. The combination of empirical dispersion with the TPSS functional performs remarkably well. The most critical part of the empirical dispersion approach is the damping function. The damping parameters should be optimized for each density functional/basis set combination separately. To keep the method simple, we optimized mainly a single factor, s(R), scaling globally the vdW radii. For good results, a basis set of at least triple-zeta quality is required and diffuse functions are recommended, since the basis set superposition error seriously deteriorates the results. On average, the dispersion contribution to the interaction energy missing in the DFT functionals examined here is about 15 and 100% for the hydrogen-bonded and stacked complexes considered, respectively.

We report the implementation of time-dependent density-functional response theory (TD-DFRT) for molecules using the time-dependent local density approximation (TDLDA). This adds exchange and correlation response terms to our previous work which used the density-functional theory (DFT) random phase approximation (RPA) [M. E. Casida, C. Jamorski, F. Bohr, J. Guan, and D. R. Salahub, in Theoretical and Computational Modeling of NLO and Electronic Materials, edited by S. P. Karna and A. T. Yeates (ACS, Washington, D.C., in press)], and provides the first practical, molecular DFT code capable of treating frequency-dependent response properties and electronic excitation spectra based on a formally rigorous approach. The essentials of the method are described, and results for the dynamic mean dipole polarizability and the first eight excitation energies of N2 are found to be in good agreement with experiment and with results from other ab initio methods.

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