Long-time correlation decay, slow relaxation

As in the study of water dynamics, the power spectrum density is useful to detect the long-time correlation or to detect decay slow energy transfers between optical and acoustic modes in the model given in Eq. (11). The relaxation inside optical modes is much faster than that in acoustic modes, since the frequency spectrum in optical modes is sharply localized and almost resonant while the spectrum is broadly spread in acoustic modes. 

It is reasonable to expect that for dense fluids the decay of the memory function at intermediate and long times is dominated by those mode correlations which have the longest relaxation times. The sluggishness of the structural relaxation processes typical of dense liquids suggests that the slow decay of the memory function at long times is basically due to couplings to wavevector-dependent density modes of the form... 

The relaxation dynamics (W7 in Fig. 38) is the response of the environment around Trp7 to its sudden shift in charge distribution from the ground state to the excited state. Under this perturbation, the response can result from both the surrounding water molecules and the protein. We separately calculated the linear-response correlation functions of indole-water, indole-protein, and the sum of the two. The results for isomer 1, relative to the time-zero values, are shown in Fig. 42a. The linear response correlation function is accumulated from a 6-ns interval indicated in Fig. 41a during which the protein was clearly in the isomer 1 substate. All three correlation functions show a significant ultrafast component 63% for the total response, 50% for indole-water, and nearly 100% for indole-protein. A fit to the total correlation function beyond the ultrafast inertial decrease requires two exponential decays 1.4 ps (3.6kJ/mol) and 23 ps (2.0kJ/mol). Despite the 6-ns simulation window for isomer 1, the 23-ps long component is not well determined on account of the noise apparent in the linear response correlation function (Fig. 42a) between 30 and 140 ps. The slow dynamics are mainly observed in the indole-water relaxation and the overall indole-protein interactions apparently make nearly no contributions to the slowest relaxation component. 

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