Multiresolution quantum chemistry in multiwavelet bases: time-dependent density functional theory with asymptotically corrected potentials in local density and generalized gradient approximations

A multiresolution solver for fully numerical linear response calculations of excitation states via the time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) is presented. The linear response method Yanai et al. previously reported [J. Chem. Phys., submitted] was limited to the Tamm–Dancoff approximation and could only use the Hartree–Fock exchange and the local-spin density approximation (LSDA) with a crude asymptotic correction. The present development enables us to perform full TD-HF/DFT calculations employing generalized gradient approximation (GGA) exchange-correlation potentials as well as hybrid ones. The linear response of TD-HF/DFT is computed by means of iteratively solving the coupled integral equations with the Green's functions. In this study, Tozer and Handy's asymptotic correction (AC) is applied to existing DFT exchange-correlations, and is found numerically stable and efficient. Furthermore, the new hybrid exchange-correlation functional CAM-B3LYP, which was recently proposed by Yanai et al. [Chem. Phys. Lett. 393, 51 (2004)], is implemented. The implementation requires a new separated representation of the integral kernel for the Coulomb-attenuated potential. We demonstrate linear response calculations free of basis set error for the excited states of Be, N2, C2H4 and C6H6 using LSDA, HCTH, CAM-B3LYP and PBE0 exchange-correlation functionals. The mean absolute errors of the C6H6 calculations with HCTH and CAM-B3LYP are 0.12 and 0.18 eV, respectively. The second derivative of exchange-correlation functionals is represented fully numerically at O(N) computation cost.