Frequency-dependent polarizabilities, hyperpolarizabilities, and excitation energies from time-dependent density-functional theory based on the quasienergy derivative method

A time-dependent density-functional theory for systems in periodic external potentials in time is formulated on the assumption of the existence of the Floquet states from the quasienergy viewpoint. Coupling strength integrati on, which connects a noninteracting system with an interacting system, is i ntroduced by using the time-dependent Hellmann-Feynman theorem. Coupled per turbed time-dependent Kohn-Sham equations are derived from the variational condition to the quasienergy functional with respect to parameters. Explici t expressions for frequency-dependent polarizability and first hyperpolariz ability are given by the quasienergy derivative method. Excitation energies and transition moments are defined from poles and residues of frequency-de pendent polarizabilities, respectively. In contrast to the previous theory, our formulation has the following three advantages: (1) The time-dependent exchange-correlation potential is defined by the functional derivative of the exchange-correlation quasienergy. (2) The formal expression for frequen cy-dependent polarizability, which corresponds to the exact sumover-states expression, can be obtained. (3) Explicit expressions for response properti es which satisfy the 2n+1 rule can be automatically obtained. (C) 1999 Amer ican Institute of Physics. [S0021-9606(99)31031-X].