Multi-configuration time-dependent density-functional theory based on range separation

Multi-configuration range-separated density-functional theory is extended to the time-dependent regime. An exact variational formulation is derived. The approximation, which consists in combining a long-range Multi-Configuration-Self-Consistent Field (MCSCF) treatment with an adiabatic short-range density-functional (DFT) description, is then considered. The resulting time-dependent multi-configuration short-range DFT (TD-MC-srDFT) model is applied to the calculation of singlet excitation energies in H2, Be and ferrocene, considering both short-range local density (srLDA) and generalized gradient (srGGA) approximations. In contrast to regular TD-DFT, TD-MC-srDFT can describe double excitations. As expected, when modeling long-range interactions with the MCSCF model instead of the adiabatic Buijse-Baerends density-matrix functional as recently proposed by Pernal [K. Pernal, J. Chem. Phys. 136, 184105 (2012)], the description of both the 1^1D doubly-excited state in Be and the 1^1\Sigma^+_u state in the stretched H2 molecule are improved, although the latter is still significantly underestimated. Exploratory TD-MC-srDFT/GGA calculations for ferrocene yield in general excitation energies at least as good as TD-DFT/CAM-B3LYP, and superior to wave-function (TD-MCSCF, symmetry adapted cluster-configuration interaction) and TD-DFT results based on LDA, GGA, and hybrid functionals.