where V (t) is set to -E 0 sin(ωt) • μ(t) or the expression for the delta perturbation (Eq. ( )). It is worth mentioning that both of these different choices for the electric field give different but complementary viewpoints of quantum dynamics, as will be explained in both the tutorial and example sections that follow. To more easily understand this entire procedure, the following pseudocode flowchart shows the sequential steps for carrying out an RT-TDDFTB electron dynamics calculation. In summary, the RT-TDDFTB algorithm commences by reading the following files from a ground-state DFTB+ calculation: the non-self-consistent Hamiltonian matrix (H 0 ), the self-consistent Hamiltonian matrix (H SCC ), the single-electron density matrix in the molecular orbital representation (ρ MO ), and the overlap matrix (S). Next, the inverse of the overlap matrix (S -1 ) is computed, and H SCC is diagonalized. The diagonalization of this matrix gives the one-electron reduced density matrix of the ground state in the atomic