where the overlap functions are defined in eq (12). These functions can be obtained with two different methods, the determinant-derivative 48 (DD) and the orbital-derivative 49-50 (OD) approaches. In both cases, they depend upon the calculations of atomic orbital overlap integrals between different time steps. OD overlap calculations are much faster than calculations of DD overlaps. However, OD overlaps are limited to single excitations, while DD overlaps can deal with any excitation rank. These same overlap functions are used for local diabatization (Section 3.4).