The theoretical justifications for these vibrational spectra simulation based on classical MD simulations, including both conventional MD and CMES-MD, is that 1. according to the Fermi's Golden Rule, the Fourier spectrum of quantum autocorrelation functions can be used to calculate transitional frequencies and intensities between energy levels 42 , and 2. the classical autocorrelation functions and the quantum autocorrelation functions match exactly in peak positions and differ only by a universal factor in intensities in the harmonic oscillator model. Although this harmonic approximation justifies the use of classical MD simulations to calculate vibrational spectra, it also leads to the assumption that the fundamental excitations (0 → 1) are the same in energy as those excited states absorptions (e.g. 1 → 2, 2 → 3).