Coupling factor correlation time calculation

After the coupling factor has been determined, models of molecular interactions can be used to calculate the correlation time, tc, which describes the dynamics of the system. The process of calculating xc from... 

The results presented Irom vibrational relaxation calculations show that the method is numerically very feasible and that the short time approximatiorrs are welljustified as long as the energy difference between the initial and final quantum states is not too small. It is also found that the crossover from the early time quantiun regime to the rate constant regime can be due to either phase decoherence or due to the loss of correlation in the coupling between the states, or to a combination of these factors. The methodology described in Section n.C has been formulated to account for both of these mechanisms. 

Time-temperature superposition software generally has many user-friendly features such as toolbars, icons, and point-and-click mouse interactions. In addition, the automatic shifting capability enables even an inexperienced operator to rapidly generate master curves and evaluate the alternative equations for correlating the data. Plots of the shift factors calculated for the respective equations can be compared to the actual shift factors obtained from both the automatic or the manual curve-fitting routine in the software. Also, TTS can be coupled with the instrument control software to allow completely unattended experimental evaluation and master curve generation once a sample is loaded. 

The mode coupling approximation for m (0 yields a set of equations that needs to be solved self-consistently. Hereby the only input to the theory is the static equilibrium structure factor 5, that enters the memory kernel directly and via the direct correlation function that is given by the Ornstein-Zernicke expression = (1 - l/5,)/p, with p being the average density. In MCT, the dynamics of a fluid close to the glass transition is therefore completely determined by equilibrium quantities plus one time scale, here given by the short-time diffusion coefficient. The theory can thus make rather strong predictions as the only input, namely, the equilibrium structure factor, can often be calculated from the particle interactions, or even more directly can be taken from the simulations of the system whose dynamics is studied. 

All of the modified F12 methods—CCSD(F12 ), CCSD-F12a/b, and CCSD(2) —have in common that the overhead with respect to a conventional method is rather small, when the same basis set is employed. Depending on the system, the rise in computation time (for the CCSD part) is only 10 to 60 per cent. The entire overhead comes from the calculation of the additional integrals including the correlation factor, while the timings for the iterative solution of the coupled-cluster equations remains the same as in a conventional calculation. The slight overhead pays off, however. 

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