Metropolis Monte Carlo method, and

In Silicalite. A variety of papers are concerned with sorption of methane in the all-silica pentasil, silicalite. June et al. (87) used a Metropolis Monte Carlo method and MC integration of configuration integrals to determine low-occupancy sorption information for methane. The predicted heat of adsorption (18 kJ/mol) is within the range of experimental values (18-21 kJ/ mol) (145-150), as is the Henry s law coefficient as a function of temperature (141, 142). Furthermore, the center of mass distribution for methane in silicalite at 400 K shows that the molecule is delocalized over most of the total pore volume (Fig. 9). Even in the case of such a small sorbate, the channel intersections are unfavorable locations. 

However, it is normally assumed that the conformers that bind to target sites will be those with a minimum potential energy. Since molecules may have large numbers of such metastable conformers a number of techniques, such as the Metropolis Monte Carlo method and comparative molecular field analysis (CoMFA), have been developed to determine the effect of conformational changes on the effectiveness of docking procedures. 

A similar algorithm has been used to sample the equilibrium distribution [p,(r )] in the conformational optimization of a tetrapeptide[5] and atomic clusters at low temperature.[6] It was found that when g > 1 the search of conformational space was greatly enhanced over standard Metropolis Monte Carlo methods. In this form, the velocity distribution can be thought to be Maxwellian. 

Yashonath etal. (46) used a Metropolis Monte Carlo method to simulate the infinite-dilution adsorption of methane in NaY zeolite. The lattice had a Si/Al ratio of 3.0 and was treated as rigid, whereas methane was modeled... 

Card and Valleau (1970) were the first to apply the Metropolis Monte Carlo method to an electrolytic solution. Their basic assumption was that if... 

Card and Valleau. application of the Metropolis Monte Carlo method, 320 Center, for electrochemistry, at Texas A M University, 26... 

The best-known physically robust method for calculating the conformational properties of polymer chains is Rory s rotational isomeric state (RIS) theory. RIS has been applied to many polymers over several decades. See Honeycutt [12] for a concise recent review. However, there are technical difficulties preventing the routine and easy application of RIS in a reliable manner to polymers with complex repeat unit structures, and especially to polymers containing rings along the chain backbone. As techniques for the atomistic simulation of polymers have evolved, the calculation of conformational properties by atomistic simulations has become an attractive and increasingly feasible alternative. The RIS Metropolis Monte Carlo method of Honeycutt [13] (see Bicerano et al [14,15] for some applications) enables the direct estimation of Coo, lp and Rg via atomistic simulations. It also calculates a value for [r ] indirectly, as a "derived" property, in terms of the properties which it estimates directly. These calculated values are useful as semi-quantitative predictors of the actual [rj] of a polymer, subject to the limitation that they only take the effects of intrinsic chain stiffness into account but neglect the possible (and often relatively secondary) effects of the polymer-solvent interactions. 

Instead of having imaginary time evolution as in DMC, one keeps the entire path in memory and moves it around. PIMC uses a sophisticated Metropolis Monte Carlo method to move the paths. One trades off the complexity of the trial function for more complex ways to move the paths [23]. One gains in this trade-off because the former changes the answer while the latter changes only the computational cost. 

The Metropolis Monte Carlo method attempts to sample a representative set of equilibrium states in a manner that facilitates the calculation of meaningful averages for properties of the system. This method is discussed in the following subsections Basic Aspects of the Metropolis Monte Carlo Method, Monte Carlo Moves, and General Pointers for Conducting Monte Carlo Simulations. 

In an explicit-solvent treatment, one applies the molecular dynamics or the Metropolis Monte Carlo method (Sections 15.12 and 16.6) to a system of a solute molecule (or molecules if a chemical reaction is being studied) surrounded by hundreds or thousands of solvent molecules, and by suitable averaging, one obtains thermodynamic or kinetic properties. The solvent molecules are treated using an empirical force field. Some of the models used to represent water molecules are discussed in Leach, Section 3.13. The solute molecule(s) can be modeled using molecular mechanics or semiempirical quantum mechanics (the QM/MM method of Section 16.6). 

Molecular dynamics (MD) methods are nearly as old as the Metropolis Monte Carlo method. The first applications of MD techniques for molecular simulation were made to simple fluids. Simulations for complex liquids such as water followed, and the first MD simulation of a biomacromolecule was performed over 10 years ago. Since then, the MD technique has been used extensively in the study of biomolecules, and the increased utility of this technique parallels closely the development of computer resources. 

The C stack calculation involved the positions (more precisely, the weighted averages of the probability distributions of the atomic nuclei) of five water clusters around a cytidine molecule (and five clusters in the planes above and below) computed by dementi s group with the aid of the Metropolis-Monte Carlo method. The five water clusters together contain 37 water molecules (see Figure 7.1). If three of their planes are selected, one has to construct the resultant effective potential of 111 water molecules. This was carried out with the help of the first (point-charge) version of the MCF method (see Section 6.2.1). 

With the advent of fast computers, numerical simulations of liquid structure have become practical. There are two principal simulation methods, h Monte Carlo method and molecular dynamics. The Monte Carlo method is so named because it uses a random number generator, reminiscent of the six-sided random number generators (dice) used in gambling casinos, such as those in Monte Carlo. This method was pioneered by Metropolis. ... 

Monte Carlo Studies in Polyelectrolyte Solutions Structure and Thermodynamics on Monte Carlo studies in polyelectrolyte solutions structure and thermodynamics, this chapter discussing about, Monte Carlo studies of polyelectrolytes, theoretical approach of Monte Carlo studies, application level of Monte Carlo in polyelectrolyte, authors of this chapter are also trying to discuss more with many topics, such as coarse-grain model for poly electrolyte and small ions, ideal gas and excess contribution to the partition function of the system, metropolis Monte Carlo method, Monte Carlo trial moves, conformational and persistence length of a single polyelectrolyte chain, counterions condensation and end-chain effects and morphology of polyelectrolyte complex. 

The Metropolis method is the simplest importance sampling Monte Carlo method and for this reason it is a good starting point for the simulation of a complex system. However, it is also one of the least efficient methods and thus one will often have to face the question of how to improve the efficiency of the sampling. One of the most frequently used tricks is to employ a modified statistical ensemble within the simulation mn and to reweight the obtained statistics after the simulation. The simulation is performed in an artificial generalized ensemble. 

The Andersen thermostat is very simple. After each time step Si, each monomer experiences a random collision with a fictitious heat-bath particle with a collision probability / coll = vSt, where v is the collision frequency. If the collisions are assumed to be uncorrelated events, the collision probability at any time t is Poissonian,pcoll(v, f) = v exp(—vi). In the event of a collision, each component of the velocity of the hit particle is changed according to the Maxwell-Boltzmann distribution p(v,)= exp(—wv /2k T)/ /Inmk T (i = 1,2,3). The width of this Gaussian distribution is determined by the canonical temperature. Each monomer behaves like a Brownian particle under the influence of the forces exerted on it by other particles and external fields. In the limit i —> oo, the phase-space trajectory will have covered the complete accessible phase-space, which is sampled in accordance with Boltzmann statistics. Andersen dynamics resembles Markovian dynamics described in the context of Monte Carlo methods and, in fact, from a statistical mechanics point of view, it reminds us of the Metropolis Monte Carlo method. 

To model the fluidity of the membrane, tethers can be flipped between the two possible diagonals of two adjacent triangles. A number xjfNh of bond-flip attempts is performed with the Metropolis Monte Carlo method [173] at time intervals AtBF. where Nh = 3 Nmh - 2) is the number of bonds in the network, and 0 < yr < 1 is a parameter of the model. Simulation results show that the vertices of a dynamically triangulated membrane show diffusion, i.e., the squared distance of two initially neighboring vertices increases linearly in time. 

---