Phase space equilibration

A sequence of successive configurations from a Monte Carlo simulation constitutes a trajectory in phase space with HyperChem, this trajectory may be saved and played back in the same way as a dynamics trajectory. With appropriate choices of setup parameters, the Monte Carlo method may achieve equilibration more rapidly than molecular dynamics. For some systems, then, Monte Carlo provides a more direct route to equilibrium structural and thermodynamic properties. However, these calculations can be quite long, depending upon the system studied. 

The beauty of the prior approximations is that by assuming a mean-field influence of solvation we can continue to work in a phase space having the same dimensionality as that for the gas phase that being the case, analysis using the tools of TST is mechanically identical for the two phases. When the solvent is not fully equilibrated with the complete reaction path, however, the reacting system can no longer legitimately be described exclusively in terms of solute coordinates. 

By definition, the microcanonical ensemble contains all possible configurations in the 6N-dimensionaI phase space with the same energy and a constant probability of being in each configuration N is the number of particles in the system under consideration. This ensemble describes an isolated system with constant N and V, or constant N and zero external pressure [28]. Constant-energy simulations are not recommended for equilibration because, without the energy flow facilitated by the temperature control methods, the desired temperature cannot be achieved. However, during the data collection phase, if one is... 

A perfect crystal equilibrates very rapidly, following a perturbation from equilibrium, by a collisional energy exchange mechanism requiring of the order of 10 sec. Liquids and defective crystals, on the other hand, equilibrate slowly because of the need for the overall structure to change (to a new distribution of coordination numbers, and a new concentration of defects, respectively). At least at the lower temperatures, the latter processes require the system to explore phase space through an activated diffusion process (see below) for which the time requirements are 10 sec and are also strong functions of temperature. 

Above all, there is need for discussion of, and hopefully agreement on, an operational test for strong-coupling collisions. We have argued here that symmetry in the angular distribution is necessary. Nikitin specifies the need for energy equilibration, and others believe phase-space theory can be applied to charge-transfer reactions where an electron is transferr between the reactants without any momentum transfer. ... 

Other difficulties in molecular simulations arise from the so-called quasi-ergodic problem, i.e., the possibility that the system becomes trapped in a small region of the phase space. To avoid it, whatever the initial conditions, the system should be allowed to equilibrate before starting the simulation, and during the calculation, the bulk properties should be carefully monitored to detect any long-time drift. 

The careful selection of an integration algorithm is not the only means of conserving computer resources in molecular dynamics. In this section we shall discuss two devices that can save a significant amount of computer time during the generation of a phase space trajectory equilibration on subsystems and bookkeeping. 

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