Here, S is the overlap matrix with respect to the adiabatic electronic basis where H is a diagonal matrix. This overlap can be constructed in a three-step process, starting with the computation of the overlap of the atomic orbitals. This step is widely used in quantum chemistry computations and numerical code is readily available. Afterward, these overlaps can be combined with the molecular orbitals coefficients to obtain the overlap between different molecular orbitals, which are then used to construct different Slater determinants. As a final step, these Slater determinants and their corresponding configuration interaction (CI) coefficients are combined to produce the overlap between different adiabatic electronic states. The CI coefficients that are required for this step are obtained from the transition density matrix, since in wave function methods where a single determinant represents the ground state, the one-particle transition density matrix corresponds to the CI vector. To reduce computational effort, the CI vector can be truncated by sorting the CI coefficients in descending order and retaining only those configurations for which the cumulative sum of squares of the preceding CI coefficients exceeds a specified threshold. This LVC Hamiltonian may also be extended by an additional term, accounting for the interaction with an external electric field, ⃗ E(t), in dipole approximation (dipole vector matrix elements ⃗ d mn )