Excitation energies from an auxiliary-function formulation of time-dependent density-functional response theory with charge conservation constraint

A key feature of the implementation of density-functional theory (DFT) in many quantum chemistry programs is the use of a charge density fitting (CDF) or resolution-of-the-identity (RI) auxiliary basis. One of these, namely the present-day deMon2k (21st century version of densité de Montréal) program, makes particularly heavy use of the CDF algorithm. We report the first fully consistent implementation of time-dependent density-functional theory (TDDFT) response theory into the present-day deMon code, by which we mean both (i) that the static limit yields analytic derivatives which are correct for the numerical method adapted by deMon2k in solving the Kohn-Sham orbital equations and (ii) that the eigenvalue equation appearing in the Casida formulation of TDDFT is properly symmetric. The new implementation is also entirely consistent with using the charge conservation constraint (CCC) in the CDF algorithm. Example calculations on the sodium dimer and tetramer and on para-aminobenzonitrile are given showing that the effect of the CCC on TDDFT excitation energies is minor compared to the importance of choosing an adequate auxiliary basis set.