Ultrafast Transfer and Transient Entrapment of Photoexcited Mg Electron in $\mathrm{Mg}@{\mathrm{C}}_{60}$

Electron relaxation is studied in endofullerene $\mathrm{Mg}@{\mathrm{C}}_{60}$ after an initial localized photoexcitation in Mg by nonadiabatic molecular dynamics simulations. Two approaches to the electronic structure of the excited electronic states are used: (i) an independent particle approximation based on a density-functional theory description of molecular orbitals and (ii) a configuration-interaction description of the many-body effects. Both methods exhibit similar relaxation times, leading to an ultrafast decay and charge transfer from Mg to ${\mathrm{C}}_{60}$ within tens of femtoseconds. Method (i) further elicits a transient trap of the transferred electron that can delay the electron-hole recombination. Results shall motivate experiments to probe these ultrafast processes by two-photon transient absorption or photoelectron spectroscopy in gas phase, in solution, or as thin films.

Figure 1

(a) $\mathrm{Mg}@{\mathrm{C}}_{60}$ molecular orbital energies (relative to $\mathrm{Mg}@{\mathrm{C}}_{60}$ HOMO) at the DFT/B3LYP level of theory (see text). The Mg $3s\to 3p$ photoexcitation and subsequent CT decay are illustrated. Isosurface plots of Mg $3s$, $\mathrm{LUMO+}20$ (Mg $3p$ type), $\mathrm{LUMO+}17$, and $\mathrm{LUMO+}14$ are shown. (b) Transient electronic state population dynamics following photoexcitation to $\mathrm{LUMO+}20$ for the same simulations; initial excited population decay and transient capture in $\mathrm{LUMO+}14$ are especially marked. The oscillations in time seen correspond to the vibrational motion on the ground state potential energy surface superimposed with the electronic dynamics.

Figure 2

Time evolutions of the decay and transfer population fractions after three initial excitations to (a) $\mathrm{LUMO+}21$, (b) $\mathrm{LUMO+}20$, and (c) $\mathrm{LUMO+}19$, corresponding to Mg $3p$ threefold degenerate orbitals. The decay (${\tau }_{de}$) and transfer (${\tau }_{tr}$) times shown are extracted by curve fittings (see text) and the fit curves for the decay are shown by the dashed lines.

Figure 3

Time evolutions of the population fractions of the trapper state $\mathrm{LUMO+}14$ and the band edge LUMO after initial excitations to (a) $\mathrm{LUMO+}19$, (b) $\mathrm{LUMO+}20$, and (c) $\mathrm{LUMO+}21$. The excited state decays are also shown. The lifetime ($\tau$) and the time ($t_{\max }$) of maximum population of $\mathrm{LUMO+}14$ are extracted by curve fittings; the fit curves are shown as the dashed lines.

Figure 4

Electron density difference (excited minus ground) of $\mathrm{Mg}@{\mathrm{C}}_{60}$ with isodensity value of $\pm 0.0005$ a.u. with positive (golden) and negative (green) values. Results at $t=0$ for ${\mathrm{S}}_{36}$ and ${\mathrm{S}}_{34}$, and the electron transfer for ${\mathrm{S}}_{36}$ in a molecular dynamics trajectory, are shown.