Direct configurational averaging

EFFECTIVE PAIR INTERACTIONS IN RANDOM ALLOYS BY DIRECT CONFIGURATIONAL AVERAGING... 

Rate constants, based on potential profiles such as those displayed in Figure 7, were evaluated with use of the WKB expression. The ingredients for the evaluation of k(R), the barrier height above the reactant well eigenvalue and the well frequency, were obtained by solution of the Schrodinger equation for these potential surfaces. We also developed a survival probability MD scheme to account for the interference between solvation dynamics and proton transfer, and then compared the two predictions. The survival probability decays reasonably exponentially. The rate constant obtained from the survival probability scheme is about 50% smaller than the rate constant obtained by direct configuration averaging. The value of 0.25 ps and shows that this... 

DCA direct configurational averaging GFT glass-forming tendency... 

This prescription transforms the effective Hamiltonian to a tridiagonal form and thus leads directly to a continued fraction representation for the configuration averaged Green function matrix element = [G i]at,. This algorithm is usually continued... 

It is interesting to examine the bead-spring models to see what flow-induced configurational changes would be required in order to develop N2 values of the proper magnitude and sign. In the Rouse model, the components of the stress tensor are related directly to averages of the internal coordinates of the beads. For the simplest case of the elastic dumbbell ... 

Thus, unlike molecular dynamics or Langevin dynamics, which calculate ensemble averages by calculating averages over time, Monte Carlo calculations evaluate ensemble averages directly by sampling configurations from the statistical ensemble. 

The comparison with experiment can be made at several levels. The first, and most common, is in the comparison of derived quantities that are not directly measurable, for example, a set of average crystal coordinates or a diffusion constant. A comparison at this level is convenient in that the quantities involved describe directly the structure and dynamics of the system. However, the obtainment of these quantities, from experiment and/or simulation, may require approximation and model-dependent data analysis. For example, to obtain experimentally a set of average crystallographic coordinates, a physical model to interpret an electron density map must be imposed. To avoid these problems the comparison can be made at the level of the measured quantities themselves, such as diffraction intensities or dynamic structure factors. A comparison at this level still involves some approximation. For example, background corrections have to made in the experimental data reduction. However, fewer approximations are necessary for the structure and dynamics of the sample itself, and comparison with experiment is normally more direct. This approach requires a little more work on the part of the computer simulation team, because methods for calculating experimental intensities from simulation configurations must be developed. The comparisons made here are of experimentally measurable quantities. 

Notice that the averaging is done over the number of particles N and to, but not the number of configurations M. Since an MD simulation produces a set of time-connected configurations, the number of a given configuration is directly related to the simulation time. 

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