Classical Simulation of Quantum Energy Flow in Biomolecules

Based on a comparison of classical and quantum-mechanical perturbation theory, the validity of classical nonequilibrium molecular dynamics simulations to describe vibrational energy redistribution in biomolecules is studied. Adopting a small model peptide in aqueous solution as an example, the theory correctly predicts quantum correction factors that need to be applied to the results of classical simulations in order to match the correct quantum results.

Figure 1

Time evolution of the vibrational energy $E_S(t)$ of the amide I mode of NMA in ${\mathrm{D}}_2\mathrm{O}$, reflecting the photoinduced $n=1\to 0$ vibrational energy relaxation of the molecule. Results are obtained from classical nonequilibrium MD simulations (dashed lines) and from a MD-based 10-mode model with cubic couplings, which was solved numerically (full lines) and in classical perturbation theory (dotted lines). Compared are calculations using initial conditions which assign zero-point energy (A) to none of the vibrational modes, (B) to the amide I mode only, and (C) in all modes of NMA.