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This paper reviews the linearized path integral approach for computing timedependent properties of systems that can be approximated using a mixedquantum-classical description. This approach is applied to studying vibrationalpure dephasing of ground state molecular iodine in a rare gas matrix. TheFeynman-Kleinert optimized harmonic approximation for the full system densityoperator is used to sample initial conditions for the bath degrees of freedom.This extremely efficient approach is compared with alternative initialcondition sampling techniques at low temperatures where classical initialcondition sampling yields dephasing rates that are nearly an order of magnitudetoo slow compared with quantum initial condition sampling and experimentalresults.

Quantum initial condition sampling for linearized density matrix dynamics: Vibrational pure dephasing of iodine in krypton matrices