  In this work, we simulate the electron dynamics in molecular systems with the
Time-Dependent Density Matrix Renormalization Group (TD-DMRG) algorithm. We
leverage the generality of the so-called tangent-space TD-DMRG formulation and
design a computational framework in which the dynamics is driven by the exact
non-relativistic electronic Hamiltonian. We show that, by parametrizing the
wave function as a matrix product state, we can accurately simulate the
dynamics of systems including up to 20 electrons and 32 orbitals. We apply the
TD-DMRG algorithm to three problems that are hardly targeted by
time-independent methods: the calculation of molecular (hyper)polarizabilities,
the simulation of electronic absorption spectra, and the study of ultrafast
ionization dynamics.
