In this work, we adopt a quantum mechanical approach based on time-dependent density functional theory (TDDFT) to study the optical and electronic properties of alizarin supported on TiO₂ nano-crystallites, as a prototypical dye-sensitized solar cell. To ensure proper alignment of the donor (alizarin) and acceptor (TiO₂ nano-crystallite) levels, static optical excitation spectra are simulated using time-dependent density functional theory in response. The ultrafast photoelectron transfer from the dye to the cluster is simulated using an explicitly time-dependent, one-electron TDDFT ansatz. The model considers the δ-pulse excitation of a single active electron localized in the dye to the complete set of energetically accessible, delocalized molecular orbitals of the dye/nano-crystallite complex. A set of quantum mechanical tools derived from the transition electronic flux density is introduced to visualize and analyze the process in real time. The evolution of the created wave packet subject to absorbing boundary conditions at the borders of the cluster reveal that, while the electrons of the aromatic rings of alizarin are heavily involved in an ultrafast charge redistribution between the carbonyl groups of the dye molecule, they do not contribute positively to the electron injection and, overall, they delay the process.

We present a theoretical study of the electronic and nuclear flux densities of a vibrating ${\text{H}}_{2}$ molecule after an electronic excitation by a short femtosecond laser pulse. The final state, a coherent superposition of the electronic ground state $X{\phantom{\rule{0.16em}{0ex}}}^{1}{$\Sigma${}}_{g}^{+}$ and the electronic excited state $B{\phantom{\rule{0.16em}{0ex}}}^{1}{$\Sigma${}}_{u}^{+}$, evolves freely and permits the partition of the electronic flux density into two competing fluxes: the adiabatic and the transition flux density. The nature of the two fluxes allows us to identify two alternating dynamics of the electronic motion, occurring on the attosecond and the femtosecond time scales. In contradistinction to the adiabatic electronic flux density, the transition electronic flux density shows a dependence on the carrier-envelope phase of the laser field, encoding information of the interaction of the electrons with the electric field. Furthermore, the nuclear flux density displays multiple reversals, a quantum effect recently discovered by Manz et al. [J. Manz, J. F. P\'erez-Torres, and Y. Yang, Phys. Rev. Lett. 111, 153004 (2013)], calling for investigation of the electronic flux density.

A theoretical study of the electronic and nuclear flux densities of a vibrating ${{\mathrm{H}}_2}^{+}$ molecular ion is presented. The time-dependent wave function is represented in the basis of vibronic eigenstates which are numerically obtained from the complete nonrelativistic Hamiltonian without the clamped-nuclei approximation. A one-center expansion in terms of $B$-splines and Legendre polynomials is employed to solve the corresponding eigenvalue equation. The electronic and nuclear flux densities are then calculated from the total wave function through their quantum-mechanical definition. Analysis of the flux densities close to the turning points shows that the nuclear wave packet takes longer time (1.4 fs) to change its direction compared to the electronic one (1 fs).

The predissociation of the ${\mathrm{N}}_2{}^{+}$ molecular ion in the $C {}^2{\mathrm{\Sigma }}_u{}^{+}$ electronic state through the nonadiabatic coupling with the $B {}^2{\mathrm{\Sigma }}_u{}^{+}$ electronic state is studied by solving the Schrödinger equation. The predissociation rates are calculated using Fermi's golden rule and compared with experimental results. We characterize the dynamics by calculating the nuclear probability density $\rho (R,t)$, the nuclear flux density $j(R,t)$, and the two-electron flux density $\mathbf{j}({\mathbf{r}}_1,{\mathbf{r}}_2,t)$. It is found that at the early dynamics, $t\le 100$ fs, Fermi's golden rule breaks down, while a strong correlation between the electronic and nuclear dynamics is observed. Fourier analyses of the probability and flux densities are also presented and yield insight in their frequency dependency.