Subspace formulation of time-dependent density functional theory for large-scale calculations.

A subspace formulation of time-dependent density functional theory (TDDFT) is proposed for large-scale calculations based on density functional perturbation theory. The formulation is implemented in conjunction with projector augmented-wave method and plane-wave basis set. A key bottleneck of conventional TDDFT method is circumvented by projecting the time-dependent Kohn-Sham eigenvalue equations from a full Hilbert space to a substantially reduced sub-Hilbert space. As a result, both excitation energies and ionic forces can be calculated accurately within the reduced subspace. The method is validated for several model systems and exhibits the similar accuracy as the conventional TDDFT method but at a computational cost of the ground state calculation. The Born-Oppenheimer molecular dynamics can be successfully performed for excited states in C60 and T12 molecules, opening doors for many applications involving excited state dynamics.