Nonadiabatic quantum molecular dynamics with hopping. III. Photoinduced excitation and relaxation of organic molecules

Photoinduced excitation and relaxation of organic molecules (${\mathrm{C}}_2{\mathrm{H}}_4$ and ${\mathrm{CH}}_2{\mathrm{NH}}_2^{+}$) are investigated by means of nonadiabatic quantum molecular dynamics with hopping (NA-QMD-H), developed recently [Fischer, Handt, and Schmidt, paper I of this series, Phys. Rev. A 90, 012525 (2014)]. This method is first applied to molecules assumed to be initially ad hoc excited to an electronic surface. Special attention is drawn to elaborate the role of electron-nuclear correlations, i.e., of quantum effects in the nuclear dynamics. It is found that they are essential for a realistic description of the long-time behavior of the electronic relaxation process, but only of minor importance to portray the short-time scenario of the nuclear dynamics. Migration of a hydrogen atom, however, is identified as a quantum effect in the nuclear motion. Results obtained with explicit inclusion of an fs-laser field are presented as well. It is shown that the laser-induced excitation process generally leads to qualitatively different gross features of the relaxation dynamics, as compared to the field-free case. Nevertheless, the nuclear wave packet contains all subtleties of the cis-trans isomerization mechanism as observed without a laser field.

Figure 1

NA-QMD-H electronic state relaxation dynamics of ${\mathrm{CH}}_2{\mathrm{NH}}_2^{+}$, initially excited to the $S_1$ state (left column) and the $S_2$ state (right column). Presented are the electronic excitation energies $E_{\mathrm{ex}}^{\mathrm{el}}\left(t\right)$ (a, b) and the state populations for $S_0$, $S_1$, and $S_2$ (c, d). The ground state populations, calculated with the quantum chemical code newton-x (extracted from Ref. [34]), are also shown for comparison (QC: $S_0$ curves in c and d).

Figure 2

NA-QMD-H nuclear wave packet dynamics of ${\mathrm{CH}}_2{\mathrm{NH}}_2^{+}$, initially excited to the $S_1$ state (left column) and the $S_2$ state (right column). Shown are density plots of the classical trajectories along the C-N bond length $R_{\mathrm{CN}}$ (a, b) and the torsion angle $\theta$ (c, d) as a function of time $t$ (see Ref. [58]). The black curves indicate the maxima of the wave packets.

Figure 3

Electronic state relaxation dynamics of ${\mathrm{C}}_2{\mathrm{H}}_4$, initially excited to the $S_1$ state, calculated with NA-QMD (left column) and NA-QMD-H (right column): Total electronic excitation energies $E_{\mathrm{ex}}^{\mathrm{el}}\left(t\right)$ (a, b) and state populations for $S_0$, $S_1$, and $S_2$ (c, d).

Figure 4

Nuclear dynamics of ${\mathrm{C}}_2{\mathrm{H}}_4$, initially excited to the $S_1$ state, calculated with NA-QMD (left column) and NA-QMD-H (right column). Shown are density plots of the classical trajectories along the C-C bond length $R_{\mathrm{CC}}$ (a, b) and the torsion angle $\theta$ (c, d) as function of time t (see Ref. [58]). The full black lines are the total maxima of the densities. The dashed black lines in panels c and d are side maxima.

Figure 5

Typical trajectory for the excited state relaxation of ethylene calculated with NA-QMD-H: the system is initially in the first excited state $S_1$ with the near-planar geometry of the ground state (first snapshot, $t=0\mathrm{fs}$) and evolves via torsional motion and C-C bond stretching (second snapshot, $t=19\mathrm{fs}$). At later times, hydrogen migration occurs to form ethylidene-like structures (third snapshot, $t=191\mathrm{fs}$), which is a potential precursor for subsequent ${\mathrm{H}}_2$ elimination.

Figure 6

Laser-induced excitation and relaxation dynamics of ${\mathrm{C}}_2{\mathrm{H}}_4$. Shown are, as function of time $t$, the total electronic excitation energy $E_{\mathrm{ex}}^{\mathrm{el}}\left(t\right)$ (a), the state populations for $S_0$, $S_1$, and $S_2$ (b), the nuclear densities along the C-C bond length $R_{\mathrm{CC}}$ (c), and the torsion angle $\theta$ (d).

Figure 7

Potential energy surfaces of ${\mathrm{CH}}_2{\mathrm{NH}}_2^{+}$ for the ground state $S_0$ and the lowest excited states $S_1$ and $S_2$ dependent on the torsion angle $\theta$ calculated using UHF (this work) (black curves) and RHF-CIS (gamess) (red curves). All remaining geometry parameters are kept frozen according to the ground state equilibrium values.

Figure 8

Potential energy surfaces of ${\mathrm{C}}_2{\mathrm{H}}_4$ for the ground state $S_0$ and the lowest excited states $S_1$ and $S_2$ dependent on the torsion angle $\theta$ calculated using UHF (this work) (black curves) and RHF-CIS (gamess) (red curves). All remaining geometry parameters are kept frozen according to the ground state equilibrium values. Note that the $S_2$ state is missing within RHF-CIS due to its doubly excited character.