Vibrational dynamics autocorrelation function, corresponding

There are many experiments which determine only specific frequency components of the power spectra. For example, a measurement of the diffusion coefficient yields the zero frequency component of the power spectrum of the velocity autocorrelation function. Likewise, all other static coefficients are related to autocorrelation functions through the zero frequency component of the corresponding power spectra. On the other hand, measurements or relaxation times of molecular internal degrees of freedom provide information about finite frequency components of power spectra. For example, vibrational and nuclear spin relaxation times yield finite frequency components of power spectra which in the former case is the vibrational resonance frequency,28,29 and in the latter case is the Larmour precessional frequency.8 Experiments which probe a range of frequencies contribute much more to our understanding of the dynamics and structure of the liquid state than those which probe single frequency components. 

The dynamics of different modes of molecular librations (hindered rotations) and intramolecular vibrations in supercritical water can now be analyzed in terms of velocity autocorrelation functions for the corresponding projections (Eqns. 22-27) (Kalinichev and Heinzinger 1992, 1995 Kalinichev 1993). The velocity autocorrelation functions calculated for the quantities Qi (Eqns. 25-27) are shown in Figure 19 for two extreme cases of high-density and low-density supercritical water. The Fourier transforms of these functions result in the spectral densities of the corresponding vibrational modes. They are shown in Figure 20 for the supercritical thermodynamic states listed in Table 5. 

At T 0 the sharp lines corresponding to the harmonic modes are broadened by anharmonic effects until, at high temperature, the simple relationship between vibrational density of states and dynamical matrix is lost. In this regime, and especially for large aggregates, MD is the most suitable tool to compute the vibrational spectrum. Standard linear response theory within classical statistical mechanics shows that the spectrum f(co) is given by the Fourier transform of the velocity-velocity autocorrelation function... 

The approximate QD pump probe signal (Fig. 3.47) still yields a good agreement with the experimental and the exact QD theoretical results. The 320 fs oscillation structure dominates in all cases. Moreover, one of the slower pseudorotational vibrations with a period of about 1 ps can also be detected by our approximate QD method. A detailed analysis by means of the Fourier transform of the corresponding autocorrelation function [378] and of the induced wave packet dynamics reveals that this oscillation is caused by a slow pseudorotational vibration in the coordinate (f. As the Fourier spectrum shows the wave packet prepared in the B state is centered around 621 nm, i.e. between the vibrational states = 5 and 6 of the (f mode. The energy distance between these two eigenstates corresponds to a vibrational period of about 1 ps. It is one of the fastest pseudorotational vibrations which can be observed in the absorption spectrum and is the next slower vibration after the Qs mode. This interpretation of the 1 ps oscillation is confirmed by analyzing the induced wave packet dynamics. Here, an accumulation of the... 

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