Vibrational Energy Relaxation: A Benchmark for Mixed Quantum-Classical Methods

We investigate the ability of mixed quantum-classical methods to capture the dynamics of vibrational energy relaxation. Several methods, including surface hopping, and Ehrenfest and symmetrical quasiclassical (SQC) dynamics, are benchmarked for the exactly solvable model problem of a harmonic oscillator bilinearly coupled to a bath of harmonic oscillators. Results show that, very often, one can recover accurate vibrational relaxation rates and detailed balance using simple mixed quantum-classical approaches. A few anomalous results do appear, however, especially regarding Ehrenfest and SQC dynamics.