Exact non-adiabatic coupling vectors for the time-dependent density functional based tight-binding method.

We report on non-adiabatic coupling vectors between electronic excited states for the time-dependent-density functional theory based tight-binding (TD-DFTB) method. The implementation includes orbital relaxation effects that have been previously neglected and covers also the case of range-separated exchange-correlation functionals. Benchmark calculations with respect to first principles TD-DFT highlight the large dependence of non-adiabatic couplings on the functional. Closer investigations of the topology around a conical intersection between excited states show that TD-DFTB delivers near-exact values of the Berry phase, which paves the way for consistent non-adiabatic molecular dynamics simulations for large systems.