Expanded ensemble simulations

To achieve uniform sampling of the different canonical ensembles within an expanded ensemble simulation, the weights should ideally obey... 

Chang, J. Sandler, S.I. Determination of liquid-solid transition using histogram reweighting method and expanded ensemble simulations. J. Chem. Phys. 2003, 118, 8930. 

Several factors affect the performance of HPTMC. First, factors that affect the performance of the underling expanded ensemble simulation clearly influence the performance of HPTMC. With regard to HPTMC itself, the frequency and success rate of configuration swaps are the most important factors. A simple rule-of-thumb that we have adopted in these applications is to make the frequency of successful swaps of the same order of magnitude as the frequency of successful particle insertions/removals. Note, however, that simulations of different complex fluids are likely to require some fine-tuning to arrive at optimal parallel tempering algorithms for complex fluids. 

The efficiency of expanded ensemble simulations can be further increased by implementing a configurational-bias scheme for the insertion and deletion processes associated with the segmental coupling-decoupling of the tagged chain [76]. 

Figure 3. Illustration of the transitions between states in a Expanded Ensemble simulation of the chemical potential. The tagged chain of variable length (anisotropic coupling) is depicted in black (solid circles).

FIG. 7 (a) Phase diagram for solutions of polyst5rene in methyicyclohexane. The lines correspond to results of expanded ensemble simulations, and the symbols refer to experimental data [26]. (b) Scaling of the critical volume fraction with chain length. The squares and the circles correspond to literature simulation data [49,50] the diamonds and the triangles correspond to expanded ensemble simulations for a simple cubic lattice and for a bond fluctuation model, respectively [25]. 

Figure 5.7 Evolution of the ordering field, XN, in the course of the expanded ensemble simulation along both branches. The system parameters are identical to Figure 5.5. Smart Monte Carlo moves are used to update the molecular conformations. The local segment motion gives rise to Rouse-like dynamics for all but the very first Monte Carlo steps. Time is measured in units of the Rouse-time of the...

Lyubartsev, A. P., Jacobsson, S. P., Sundholm, G., Laaksonen, A. Water/ octanol systems. A expanded ensemble molecular dynamics simulation smdy of log P parameters. J. Phys. Chem. B 2001, 105, 7775-7782. 

Fenwick, M. K. Escobedo, F. A., Expanded ensemble and replica exchange methods for simulation of protein-like systems, J. Chem. Phys. 2003,119, 11998-12010... 

Extended sampling strategies utilizing this kind of representation appear in the literature with a variety of titles expanded ensemble [23], simulated tempering [24], and temperature scaling [25]. 

A. P. Lyubartsev, A. A. Martsinovski, S. V. Shevkunov and P. N. Vorontsov-Velyaminov (1992) New Approach to Monte-Carlo Calculation of the Free-Energy - Method of Expanded Ensembles. J. Chem. Phys. 96, p. 1776 E. Marinari and G. Parisi (1992) Simulated Tempering - A New Monte-Carlo Scheme. Europhysics Lett. 19, p. 451... 

In order to estimate the free energy many canonical simulations at different temperatures are necessary furthermore, it is often difEcult to define a suitable reference state with a known entropy Sq. Two alternatives can be followed to overcome these difficulties (i) expanded ensemble methods and (ii) multicanonical methods. 

Lyubartsev AP, Jacobsson SP, Sundholm G, Laaksonen A. Solubility of organic compounds in water/octanaol systems. An expanded ensemble molecular dynamics simulation study of log P parameters. J Phys Chem B 2001 105 7775-7782. 

Applications of the expanded-ensemble approach have been reported for the partitioning of polymers between a slit pore and the bulk [52,77,79], and for fluid-fluid equilibria [78-80]. Figure 4 shows results of expanded Gibbs ensemble simulations of phase coexistence in a binary system of Lennard-Jones chains dissolved in their own monomer [80] (cross-inter-... 

The expanded-ensemble method has been shown to be capable of handling molecules with O(102) sites. The obvious disadvantages of the method are that preliminary, iterative simulations are sometimes needed and that, as the number of sites per molecule increases, the number of intermediate states must increase accordingly. 

If a fiVT ensemble simulation can be turned into a ( quasi ) NPT ensemble-type simulation (e.g., a pseudo- FT ensemble), the inverse transformation (a pseudo-NPT ensemble) is also possible. The key relationship for a pseudo-NPT ensemble technique is Eq. (5.1) [78]. Such a reverse strategy can be practical only if molecular insertion and deletion moves can be performed efficiently for the system under study (e.g., by expanded ensemble moves for polymeric fluids). Replacing volume moves by particle insertions can be advantageous for polymeric and other materials that require simulation of a large system (due to the sluggishness of volume moves for mechanical equilibration of the system) such an advantage has been clearly demonstrated for a test system of dense, athermal chains [78]. 

Escobedo and de Pablo have proposed some of the most interesting extensions of the method. They have pointed out [49] that the simulation of polymeric systems is often more troubled by the requirements of pressure equilibration than by chemical potential equilibration—that volume changes are more problematic than particle insertions if configurational-bias or expanded-ensemble methods are applied to the latter. Consequently, they turned the GDI method around and conducted constant-volume phase-coexistence simulations in the temperature-chemical potential plane, with the pressure equality satisfied by construction of an appropriate Cla-peyron equation [i.e., they take the pressure as 0 of Eq. (3.3)]. They demonstrated the method [49] for vapor-liquid coexistence of square-well octamers, and have recently shown that the extension permits coexistence for lattice models to be examined in a very simple manner [71]. 

This chapter is organized as follows. In section 1.1, we introduce our notation and present the details of the molecular and mesoscale simulations the expanded ensemble-density of states Monte Carlo method,and the evolution equation for the tensor order parameter [5]. The results of both approaches are presented and compared in section 1.2 for the cases of one or two nanoscopic colloids immersed in a confined liquid crystal. Here the emphasis is on the calculation of the effective interaction (i.e. potential of mean force) for the nanoparticles, and also in assessing the agreement between the defect structures found by the two approaches. In section 1.3 we apply the mesoscopic theory to a model LC-based sensor and analyze the domain coarsening process by monitoring the equal-time correlation function for the tensor order parameter, as a function of the concentration of adsorbed nanocolloids. We present our conclusions in Section 1.4. 

Expanded Grand Canonical Ensemble Simulation of Polymer Chains Using Configurational Bias... 

In the case of long polymer chains, the insertion or deletion of entire molecules required for grand canonical ensemble simulations is difficult, even when configurational bias techniques are employed. In that case it is beneficial to implement configurational bias moves in the context of an expanded ensemble formalism [17], which essentially allows one to create or delete a smaller number of sites of a molecule (as opposed to an entire chain) in each trial move, thereby increasing the likelihood of acceptance. The... 

Rutledge, G.C. Khare, A.A. Chemical potential of aromatic compounds in pure n-alkanes using expanded ensemble Monte Carlo simulations. J. Phys. Chem. B 2000, 104 (15), 3639-3644. 

---