Canonical ensemble simulation

With the equilibrated system, we began a series of canonical ensemble simulations by placing the umbrella potential center close to the intercalated... 

Wongkoblap et al.307 study Lennard-Jones fluids in finite pores, and compare their results with Grand canonical ensemble simulations of infinite pores. Slit pores of 3 finite layers of hexagonally arranged carbon atoms were constructed. They compare the efficiency of Gibbs ensemble simulations (where only the pore is modelled) with Canonical ensemble simulations where the pore is situated in a cubic cell with the bulk fluid, and find that while the results are mostly the same, the Gibbs ensemble method is more efficient. However, the meniscus is only able to be modelled in the canonical ensemble. 

The specific heat can in turn be obtained in canonical-ensemble simulations from the fluctuations of the internal energy. 

Mehta and Kofke [91] have recently proposed pseudo-ensemble simulations, in which calculations in a nominal ensemble are mimicked by simulation in a different ensemble or, more precisely, in a pseudo-ensemble. Mehta and Kofke implemented pseudo grand-canonical ensemble simulations in which particle deletion and insertion attempts (pertaining to the constant- uGC constraint in the grand-canonical ensemble) were replaced by volume changes. It has been shown [78] that the approach can be restated as one of attempting to transform a fiVT ensemble into a NPT ensemble such a transformation is possible if the equilibrium pressure Peq corresponding to /tGC can be determined that link can be established by the thermodynamic relationship... 

A grand canonical Monte Carlo simulation is somewhat similar to a canonical ensemble simulation. The same translational and rotational moves for the molecules are used, with identical acceptance criteria. Also, moves attempting to introduce an additional water molecule into the system (insertions) or to remove a water from the system (deletions) are included. For an insertion, the position of the new water molecule is selected randomly within the simulation cell, whereas its orientation is chosen in a manner analogous to that used for reorientating a water molecule, that is, using < ) = 6 = ( = 0 and =... 

Panagiotopoulos and coworkers [51] use the same parameters as Larson for the study of phase behavior, but with two different simulation methodologies. The first technique is the Gibbs ensemble method, in which each bulk phase is simulated in a separate cell and molecules are interchanged and volumes adjusted between the two for equilibration of the system [52]. The second is a standard canonical ensemble simulation, like Larson s, but employs the configurational bias Monte Carlo method. The configurational bias Monte Carlo method is much more efficient than the ones based on reptation and other local moves but is not useful if any dynamic information is sought from the simulations. 

The grand canonical ensemble simulations model systems in which the chemical potential (/x), the volume and temperature are held fixed while the number of particles changes. The approach is very useful for simulating phase behavior which requires a constant chemical potential. Grand Canonical Monte Carlo simulation has been used to calculate sorption isotherms for a number of difierent microporous silicate systems. The simulations are used to model the equilibrium between zeolite and sorbate phases and, as such, it provides a natural way of simulating sorption isothermsl ... 

Increment volume or number of particles if NPT or Grand Canonical ensemble simulation... 

FIG. 3 Grand canonical ensemble simulation results at r=300K and chemical potential /1/x = —17.408, which is the value that corresponds to TIP4P water in the bulk (at T = 300 K and P = 1 bar), (a) Normal component of the pressure tensor, (b) Average number of water molecules per clay. 

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... 

Sampling and Analysis We continued the canonical ensemble simulation for another 10 to 20 ns, while the trajectories of the sorbate molecules were written out every 100 fs. The analysis of these trajectories enabled ns to compnte the mean square displacements and therefore the diffusivity. 

Whereas parallel tempering works in the product space of canonical ensembles, simulated tempering virtually dynamically integrates over the temperature space within a single simulation [92,93]. Each inverse temperature in the discrete set P < <. . . fh... < Pi... 

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