Asymptotic correction approach to improving approximate exchange-correlation potentials: Time-dependent density-functional theory calculations of molecular excitation spectra

The time-dependent density functional theory (TD-DFT) calculation of excita tion spectra places certain demands on the DFT exchange-correlation potenti al, upsilon (xc), that are not met by the functionals normally used in mole cular calculations. In particular, for high-lying excitations, it is crucia l that the asymptotic behavior of upsilon (xc) be correct. In a previous pa per, we introduced a novel asymptotic-correction approach which we used wit h the local density approximation (LDA) to yield an asymptotically correcte d LDA (AC-LDA) potential [Casida, Casida, and Salahub, Int. J. Quantum Chem . 70, 933 (1998)]. The present paper details the theory underlying this asy mptotic correction approach, which involves a constant shift to incorporate the effect of the derivative discontinuity (DD) in the bulk region of fini te systems, and a spliced asymptotic correction in the large r region. This is done without introducing any adjustable parameters. We emphasize that c orrecting the asymptotic behavior of upsilon (xc) is not by itself sufficie nt to improve the overall form of the potential unless the effect of the de rivative discontinuity is taken into account. The approach could be used to correct upsilon (xc) from any of the commonly used gradient-corrected func tionals. It is here applied to the LDA, using the asymptotically correct po tential of van Leeuwen and Baerends (LB94) in the large r region. The perfo rmance of our AC-LDA upsilon (xc) is assessed for the calculation of TD-DFT excitation energies for a large number of excitations, including both vale nce and Rydberg states, for each of four small molecules: N-2, CO, CH2O, an d C2H4. The results show a significant improvement over those from either t he LB94 or the LDA functionals. This confirms that the DD is indeed an impo rtant element in the design of functionals. The quality of TDLDA/LB94 and T DLDA/AC-LDA oscillator strengths were also assessed in what we believe to b e the first rigorous assessment of TD-DFT molecular oscillator strengths in comparison with high quality experimental and theoretical values. And a co mparison has been given of TDLDA/AC-LDA excitation energies with other TD-D FT excitation energies taken from the literature, namely for the PBE0, HCTH (AC), and TDLDA/SAOP functionals. Insight into the working mechanism of TD- DFT excitation energy calculations is obtained by comparison with Hartree-F ock theory, highlighting the importance of orbital energy differences in TD -DFT. (C) 2000 American Institute of Physics. [S0021-9606(00)30844-3].