Many of the non-adiabatic processes in the condensed phase are affected by the interaction with the environment, as exemplified by Marcus theory. However, non-adiabatic molecular dynamics simulations with explicitly including the environment are computationally expensive because of the extended system size, suggesting the need for an efficient scheme applicable to huge systems. In this work, time-derivative non-adiabatic coupling (TDNAC) calculation algorithms were developed in the framework of the divide-and-conquer (DC) time-dependent (TD) density-functional tight-binding (DFTB) method, which is an extension of the TD-DFTB for larger systems based on the fragmentation-based DC scheme. The developed algorithms were incorporated into a fewest-switches trajectory surface hopping (FSSH) routine. The calculated TDNAC and the FSSH results were sufficiently accurate compared to the conventional TD-DFTB results. Use of the DC-TD-DFTB provided a significant reduction in the central processing unit (CPU) time vs that of the TD-DFTB, where the CPU time remained constant irrespective of the total system size. It was also confirmed that the present method is not only efficient but also improves the numerical stability of TDNAC calculations.
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