Monte Carlo calculations, simulated

Recently, molecular dynamics and Monte Carlo calculations with quantum mechanical energy computation methods have begun to appear in the literature. These are probably some of the most computationally intensive simulations being done in the world at this time. 

Molecular dynamics calculations are more time-consuming than Monte Carlo calculations. This is because energy derivatives must be computed and used to solve the equations of motion. Molecular dynamics simulations are capable of yielding all the same properties as are obtained from Monte Carlo calculations. The advantage of molecular dynamics is that it is capable of modeling time-dependent properties, which can not be computed with Monte Carlo simulations. This is how diffusion coefficients must be computed. It is also possible to use shearing boundaries in order to obtain a viscosity. Molec-... 

OPES (Optimized Potentials for Liquid Simulations) is based on a force field developed by the research group of Bill Jorgensen now at Yale University and previously at Purdue University. Like AMBER, the OPLS force field is designed for calculations on proteins and nucleic acids. It introduces nonbonded interaction parameters that have been carefully developed from extensive Monte Carlo liquid simulations of small molecules. These nonbonded interactions have been added to the bonding interactions of AMBERto produce anew force field that is expected to be better than AMBER at describing simulations where the solvent is explic-... 

For reasons of space and because of their prime importance, we focus here on free energy calculations based on detailed molecular dynamics (MD) or Monte Carlo (MC) simulations. However, several other computational approaches exist to calculate free energies, including continuum dielectric models and integral equation methods [4,14]. 

The essential influence of surface roughening is also present in this model. Grand canonical Monte Carlo calculations were used to generate adatom populations at various temperatures up to Chemical potentials corresponding to those in the bulk LJ crystal were used, and these produced adatom densities that increased with temperature and roughly approximated the values observed in Ising model simulations below T. ... 

RAT grinding operations. This surface layer was removed except for a remnant in a second grind. Spectra - both 14.4 keV and 6.4 keV - were obtained on the undisturbed surface, on the bmshed surface and after grinding. The sequence of spectra shows that nanophase Oxide (npOx) is eiu-iched in the surface layer, while olivine is depleted. This is also apparent from a comparison of 14.4 keV spectra and 6.4 keV spectra [332, 346, 347]. The thickness of this surface layer was determined by Monte-Carlo (MC)-Simulation to about 10 pm. Our Monte Carlo simulation program [346, 347] takes into account all kinds of absorption processes in the sample as well as secondary effects of radiation scattering. For the MC-simulation, a simple model of the mineralogical sample composition was used, based on normative calculations by McSween [355]. 

Monte Carlo calculations have been carried out to simulate the spin transition behaviour in both mono- and dinuclear systems [197]. The stepwise transition in [Fe(2-pic)3]Cl2-EtOH as well as its modification by metal dilution and application of pressure have been similarly modelled by considering short- and long-range interactions [52, 198, 199]. An additional study of the effect of metal dilution was successfully simulated with the Monte Carlo treatment considering direct and indirect inter-molecular interactions [200]. A very recent report deals with the application of the Monte Carlo method to mimic short- and long-range interactions in cooperative photo-induced LS—>HS conversion phenomena in two- and three-dimensional systems [201],... 

It is also straightforward to carry out Monte Carlo simulations with a constant number of particles, temperature and pressure (the NPTensemble). In such simulations, in addition to random moves of the atoms or molecules random changes in the volume of the simulation cell are also attempted, and in the Metropolis step O(Z) + pV replaces < >(Z). Monte Carlo calculations, both NVT and NPT, have thus been extremely useful in establishing equations of state. 

In a statistical Monte Carlo simulation the pair potentials are introduced by means of analytical functions. In the election of that analytical form for the pair potential, it must be considered that when a Monte Carlo calculation is performed, the more time consuming step is the evaluation of the energy for the different configurations. Given that this calculation must be done millions of times, the chosen analytic functions must be of enough accuracy and flexibility but also they must be fastly computed. In this way it is wise to avoid exponential terms and to minimize the number of interatomic distances to be calculated at each configuration which depends on the quantity of interaction centers chosen for each molecule. A very commonly used function consists of a sum of rn terms, r being the distance between the different interaction centers, usually, situated at the nuclei. In particular, non-bonded interactions are usually represented by an atom-atom centered monopole expression (Coulomb term) plus a Lennard-Jones 6-12 term, as indicated in equation (51). 

During the last few years the progress of computational techniques has made it possible to simulate the dynamic behavior of whole ensembles consisting of several hundred molecules. In this way the limitations of the statistical approach can be at least partly overcome. Two kinds of methods — molecular dynamics and Monte Carlo calculations — were applied to liquids and liquid mixtures and brought new insight into their structure and properties. Even some important characteristics of systems as complicated as associated liquids like water could be... 

Obviously this picture might be supported and supplemented by according data from different experimental investigations, or it might be modified to fit these data. Interactions within the basic hydrated structures, as well as their energetics, are obtainable from gas-phase solvation experiments or from accurate MO calculations. For the simulation of real solutions, dynamic calculations will be inevitable. There is, however, a demand for acceptable effective potentials to be used in molecular dynamics, or in Monte Carlo calculations. 

More recently, Pound and co-workers compared both the classical theory and their own modified proposal to the exact results obtained by a Monte-Carlo simulation study of small clusters [65] thermodynamic functions for such clusters (size from 13 to 87 entities) were calculated, showing a better agreement between the Monte-Carlo calculations and the authors theory. 

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