Configuration space, sampling

Wood, R. H. Muhlbauer, W. C. F. Thompson, P. T., Systematic errors in free energy perturbation calculations due to a finite sample of configuration space. Sample-size hysteresis, J. Phys. Chem. 1991, 95, 6670-6675... 

When calculating free energies, one generates, either by molecular dynamics or MC, configuration space samples distributed according to a probability distribution function (e.g., the Boltzmann distribution in the case of the Helmholtz free energy). 

Fig. 3.9 Top Tilt (S) and bend angles (0) used to define the structure of the Fe-CO unit in FeP(lm)(CO). Bottom Configurational space sampled by the projection of the...

It should be stressed that (108) is not as accurate as the two-electronic-state approximation given by (74) (for X = 2) because usually the latter is valid over the entire region of nuclear configuration space sampled by xad(R), whereas (108) is only a good approximation in the immediate vicinity of the conical intersection being considered. 

R. H. Wood, W. C. F. Muhlbauer, and P. T. Thompson, ]. Phys. Chem., 95, 6670 (1991). Systematic Errors in Free Energy Perturbation Calculations Due to a Finite Sample of Configuration Space Sample-Size Hysteresis. 

MD, one needs to use multiple time step methods to ensure proper handling of the sprmg vibrations, and there is a possible physical bottleneck in the transfer of energy between the spring system and the other degrees of freedom which must be handled properly [199]. In MC, one needs to use special methods to sample configuration space efficiently [200, 201]. 

Do we expect this model to be accurate for a dynamics dictated by Tsallis statistics A jump diffusion process that randomly samples the equilibrium canonical Tsallis distribution has been shown to lead to anomalous diffusion and Levy flights in the 5/3 < q < 3 regime. [3] Due to the delocalized nature of the equilibrium distributions, we might find that the microstates of our master equation are not well defined. Even at low temperatures, it may be difficult to identify distinct microstates of the system. The same delocalization can lead to large transition probabilities for states that are not adjacent ill configuration space. This would be a violation of the assumptions of the transition state theory - that once the system crosses the transition state from the reactant microstate it will be deactivated and equilibrated in the product state. Concerted transitions between spatially far-separated states may be common. This would lead to a highly connected master equation where each state is connected to a significant fraction of all other microstates of the system. [9, 10]... 

Let us leave, for a moment, the domain of discrete torsion angles and consider torsion-angle moves in a torsion continuum. Much effort has been directed to the development of efficient phase-space sampling methods for MC [17,23,37,128-138]. The simplest off-lattice move - being a pivotal move [128,131] of a single torsion angle at a time - hardly samples configuration... 

---