Reconstructing Finite-Temperature Velocity Autocorrelation Functions from Short Molecular Dynamics Trajectories

Finite-temperature velocity autocorrelation functions (VACFs) provide a direct connection between molecular dynamics trajectories and vibrational, anharmonic, and relaxation behavior, but their reliable evaluation can require substantial atomistic sampling. In this study, a physics-constrained reduced operator is developed from short stationary molecular dynamics trajectories. The formulation combines a temperature-specific quasiharmonic eigenspectrum with compact corrections for finite-temperature frequency shifts and the loss of modal coherence. A finite-memory extension preserves the equilibrium symmetry and short-time consistency of the correlation function without altering the identified long-time behavior. The method was validated using blind trajectories, repeated data partitions, bootstrap analysis, and independent spectral calculations. For crystalline Si over 300-700 K, the reduced operator reproduces the finite-temperature VACF with an error comparable to the variability among independent molecular dynamics realizations, while retaining physically interpretable spectral trends. The same operator hierarchy can be reidentified for the tested monatomic crystalline systems described by Tersoff, Stillinger-Weber, and embedded-atom potentials. Within this demonstrated scope, the framework converts short atomistic trajectories into a directly evaluable representation of finite-temperature correlation dynamics, providing a practical molecular simulation route for reconstructing VACFs across temperatures and interaction models.