Quantum dynamics and spectroscopy of dihalogens in solid matrices. I. Efficient simulation of the photodynamics of the embedded $\mathrm{I_2 Kr_{18}}$ cluster using the G-MCTDH method

Abstract

The molecular dynamics following the electronic $B\ ^3\Pi_u\left(0^+\right) \longleftarrow X\ ^1\Sigma_g^+$ photoexcitation of the iodine molecule embedded in solid krypton are studied quantum mechanically using the Gaussian variant of the multiconfigurational time-dependent Hartree method (G-MCTDH). The accuracy of the Gaussian wave packet approximation is validated against numerically exact MCTDH simulations for a fully anharmonic seven-dimensional model of the $\mathrm{I_2 Kr_{18}}$ cluster in a crystal Kr cage. The linear absorption spectrum, time-evolving vibrational probability densities, and $\mathrm{I_2}$ energy expectation value are accurately reproduced by the numerically efficient G-MCTDH approach. The reduced density matrix of the chromophore is analyzed in the coordinate, Wigner and energy representations, so as to obtain a multifaceted dynamical view of the guest-host interactions. Vibrational coherences extending over the bond distance range $ 2.7\,\mbox{\AA} < R_\mathrm{I-I} < 4.0\,\mbox{\AA}$ are found to survive for several vibrational periods, despite extensive dissipation. The present results prepare the ground for the simulation of time-resolved coherent Raman spectroscopy of the $\mathrm{I_2}$-krypton system addressed in a companion paper.