Exponential model molecular dynamics simulation

Even if we consider a single solvent, e g., water, at a single temperature, say 298K, depends on the solute and in fact on the coordinate of the solute which is under consideration, and we cannot take xF as a constant. Nevertheless, in the absence of a molecular dynamics simulation for the solute motion of interest, XF for polar solvents like water is often approximated by the Debye model. In this model, the dielectric polarization of the solvent relaxes as a single exponential with a relaxation time equal to the rotational (i.e., reorientational) relaxation time of a single molecule, which is called Tp) or the Debye time [32, 347], The Debye time may be associated with the relaxation of the transverse component of the polarization field. However the solvent fluctuations and frictional relaxation occur on a faster scale given by [348,349]... 

The Gruen—Marcelja model could relate the hydration force to the physical properties of the surfaces by assuming that the polarization of water near the interface is proportional to the surface dipole density.9 This assumption led to the conclusion that the hydration force is proportional to the square of the surface dipolar potential of membranes (in agreement with the Schiby—Ruckenstein model),6 a result that was confirmed by experiment.10 However, subsequent molecular dynamics simulations revealed that the polarization of water oscillated in the vicinity of an interface, instead of being monotonic.11 Because the Gruen—Marcelja model was particularly built to explain the exponential decay of the polarization, it was clearly invalidated by the latter simulations. Other conceptual difficulties of this model have been also reported.12 13... 

So far we have employed the exponential model for the memory kernel appearing in the GLE for the density correlation functions. In [60] the model based on the mode-coupling theory described in Sec. 5.2.4is applied to the calculation of the longitudinal current spectra of the same diatomic liquid as discussed here. It is found that the essential features of the results remained the same as far as the collective dynamics is concerned. It is also demonstrated that the results are in fair agreement with those determined from the molecular dynamics simulation. 

We may look at atomic clusters as particularly apt and useful models to study virtually every aspect of what we call, diffusely, complexity. Simulations are particularly powerful means to carry out such studies. For example, we can follow trajectories for very long times with molecular dynamics and thereby evaluate the global means of the exponential rates of divergence of neighboring trajectories. This is the most common way to evaluate those exponents, the Liapunov exponents. The sum of these is the Kolmogorov entropy, one gross measure of the volume of phase space that the system explores, and hence one... 

However, despite of the great importance of quantum mechanical potentials from the purely theoretical point of view, simple effective two-body potential functions for water seem at present to be preferable for the extensive simulations of complex aqueous systems of geochemical interest. A very promising and powerful method of Car-Parrinello ah initio molecular dynamics, which completely eliminates the need for a potential interaction model in MD simulations (e.g., Fois et al. 1994 Tukerman et al. 1995, 1997) still remains computationally extremely demanding and limited to relatively small systems N < 100 and a total simulation time of a few picoseconds), which also presently limits its application for complex geochemical fluids. On the other hand, it may soon become a method of choice, if the current exponential growth of supercomputing power will continue in the near future. 

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