Analysis of perturbed H2O vibrations beyond Fourier transform

New analysis methods for the vibrational dynamics from molecular dynamics are proposed and applied to liquid H$_{2}$O. The internal modes of H$_{2}$O are amplitude-modulated by Langevin dynamics with the frequency of the H$_{2}$O libration (~600 cm$^{-1}$) and its first overtone (~1200 cm$^{-1}$). The carrier signal is frequency-modulated by the variation of the hydrogen bond strength due to thermal motion and by dephasing collisions. The standard power spectra of the bond parameters yield broadened normal modes due to a superposition of several perturbations. Here, the oscillating bond lengths and angles are demodulated by the spline interpolation of the minima or maxima. Additionally, a zero-crossing method is described, which yields the spectrum of the frequency modulated carrier without Fourier transform by directly converting the oscillation periods.