Autocorrelation functions environments

Our experimental measurements of the orientation autocorrelation function on sub-nanosecond time scales are consistent with the theoretical models for backbone motions proposed by Hall and Helfand(ll) and by Bendler and Yaris(12). The correlation functions observed in three different solvents at various temperatures have the same shape within experimental error. This implies that the fundamental character of the local segmental dynamics is the same in the different environments investigated. Analysis of the temperature dependence of the correlation function yields an activation energy of 7 kJ/mole for local segmental motions. 

Aimed at characterizing the local environment of atoms, these descriptors are calculated by applying the autocorrelation function to encode spatial information relative to each single ith atom in a molecule as [Nohair, Zakarya et al., 2002 Nohair and Zakarya, 2003]... 

Next we examine whether these vibrations are unique in the enzymatic environment or they are inherent in the substrates. In the left panel of Fig. 18 we compare the calculation in the enzyme with a simulation of the substrates in aqueous solution, in the absence of hPNP. The spectrum of the 0-5 —0-4 distance autocorrelation function of the classical MD of solvated substrates showed a peak at 330 cm-1, and of the unsolvated substrates at 285 cm-1, i.e. distinct from the peaks in the presence of the enzyme, revealing that hPNP is directly affecting the way in which these oxygens naturally vibrate. 

The time autocorrelation function can be written as a transition dipole correlation function, a form that is equally useful for an inhomogeneously broadened spectrum. This is the form that is extensively used to discuss the spectral effects of the environment (32-34). The dipole correlation function also provides for the novice an intuitively clear prescription as to how to compute a spectrum using classical dynamics. For the expert it points out limitations of this, otherwise very useful, approximation. The required transformation is to rewrite the spectrum so that the time evolution is carried by the dipole operator rather than by the bright state wave packet. The conceptual advantage is that it is easier to imagine what the classical limit will be because what is readily provided by classical mechanics trajectory computations is the time dependence of the coordinates and momenta and hence, of functions thereof. In other words, in our mind it is easier to... 

Triplet crossing (Figure 2.11(b)) modulates the fluorescence output of the molecule causing blinking on a characteristic timescale and therefore generates fluctuations that can be observed in the autocorrelation function [42]. However, the photophysics of the triplet state of common dye molecules are very poorly understood and measurements of the rates and degrees of population are inconsistent [38]. In particular, the environment of the dye molecule has been shown to... 

Pig.3. The energy autocorrelation function of the non-bonded interactions (electrostatic and Van der Waals) of the tyrosine residue L162 with the protein environment are depicted. The time correlation function is calculated for 3 different temperatures according to Eqs. (10-13). 

For systems in homogeneous environments and in the absence of cross-correlations between different chains, crr 1) is reduced to the autocorrelation function of the end-to-end vector. 

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