Fast Overlap Evaluations for Nonadiabatic Molecular Dynamics Simulations: Applications to SF-TDDFT and TDDFT.

Fast overlap integral algorithms for the spin-flip time-dependent density functional theory (SF-TDDFT) and the linear response (LR)-TDDFT were proposed on the basis of determinant factorization (DF) and the truncated Leibnitz formula (TLF). These in turn allow efficient computation of nonadiabatic coupling terms (NACTs) in nonadiabatic molecular dynamics simulations. The TLF(0), TLF(1), and TLF(2) were proposed according to the truncation order. The DF and TLF(1) or TLF(2) provide a four order combined performance improvement to the conventional method without introducing additional errors in the finite difference approximation. On the other hand, the DF and TLF(0) provide a five orders performance improvement making it the most efficient algorithm for NACT calculations so far with errors slightly larger than those of the finite difference approximation. The same techniques can be also applicable to other determinantal wave functions.