Fast Numerical Evaluation of Time-Derivative Nonadiabatic Couplings for Mixed Quantum–Classical Methods

We
have developed a numerical differentiation scheme that eliminates
evaluation of overlap determinants in calculating the time-derivative
nonadiabatic couplings (TDNACs). Evaluation of these determinants
was the bottleneck in previous implementations of mixed quantum–classical
methods using numerical differentiation of electronic wave functions
in the Slater determinant representation. The central idea of our
approach is, first, to reduce the analytic time derivatives of Slater
determinants to time derivatives of molecular orbitals and then to
apply a finite-difference formula. Benchmark calculations prove the
efficiency of the proposed scheme showing impressive several-order-of-magnitude
speedups of the TDNAC calculation step for midsize molecules.