Quantum dynamics and spectroscopy of dihalogens in solid matrices. II. Theoretical aspects and G-MCTDH simulations of time-resolved coherent Raman spectra of Schr\"odinger cat states of the embedded mathrm{I₂ Kr₁₈} cluster

This companion paper to [D. Picconi et al., J. Chem. Phys. 150 (2019)] presents quantum dynamical simulations, using the Gaussian-based multiconfigurational time-dependent Hartree (G-MCTDH) method, of time-resolved coherent Raman four-wave-mixing spectroscopic experiments for the iodine molecule embedded in a cryogenic crystal krypton matrix. These experiments monitor the time-evolving vibrational coherence between two wave packets created in a quantum superposition (i. e. a 'Schr\"odinger cat state') by a pair of pump pulses which induce electronic $B\ ^3\Pi_u\left(0^+\right) \longleftarrow X\ ^1\Sigma_g^+$ transitions. A theoretical description of the spectroscopic measurement is developed, which elucidates the connection between the nonlinear signals and the wave packet coherence. The analysis provides an effective means to simulate the spectra for several different optical conditions with a minimum number of quantum dynamical propagations. The G-MCTDH method is used to calculate and interpret the time-resolved coherent Raman spectra of two selected initial superpositions for a $\mathrm{I_2 Kr_{18}}$ cluster embedded in a frozen Kr cage. The time- and frequency-dependent signals carry information about the molecular mechanisms of dissipation and decoherence, which involve vibrational energy transfer to the stretching mode of the four 'belt' Kr atoms. The details of these processes and the number of active solvent modes depend in a non-trivial way on the specific initial superposition.