Monte Carlo techniques, simulations small molecules

Molecular Simulations Molecular simulations are useful for predicting properties of bulk fluids and solids. Molecular dynamics (MD) simulations solve Newton s equations of motion for a small number (on the order of 10 ) of molecules to obtain the time evolution of the system. MD methods can be used for equilibrium and transport properties. Monte Carlo (MC) simulations use a model for the potential energy between molecules to simulate configurations of the molecules in proportion to their probability of occurrence. Statistical averages of MC configurations are useful for equilibrium properties, particularly for saturated densities, vapor pressures, etc. Property estimations using molecular simulation techniques are not illustrated in the remainder of this section as commercial software implementations are not generally available at this time. 

The proposed approach may also be useful in simulating thermochromatography in vacuum columns, chromathermography and other separation techniques in open columns. Moreover, repeated Monte Carlo experiments with small number of molecules serve to visualize the uncertainties imposed by poor statistics. They are very helpful in evaluating Bayesian confidence intervals for the parameters measured in the experiment performed in non-ideal conditions, when any attempt to obtain an analytical solution fails completely. This will be discussed and illustrated in Sect. 6.2. 

There are two main methods in this field. One is Molecular Dynamics and the other is Monte Carlo. Additional simulation methods are either closely related to one or the other aforementioned methods or they apply on spatial scales far beyond the molecular scale. Molecular Dynamics techniques model a small amount of material (system sizes usually are on the nm-scale) based on the actual equations of motion of the atoms or molecules in this system. Usually this is done on the basis of mechanical inter- and intra-particle potential functions. In certain cases however quantum mechanics in needed. Monte Carlo differs from Molecular Dynamics in that its systems do not follow their physical dynamics. Monte Carlo estimates thermodynamic quantities via intelligent statistical sampling of (micro)states. Capabilities and applications of both methods overlap widely. But they both also have distinct advantages depending on the problem at hand. Here we concentrate on Monte Carlo—which is the more thermodynamic method of the two. 

A molecular dynamics simulation samples the phase space of a molecule (defined by the position of the atoms and their velocities) by integrating Newton s equations of motion. Because MD accounts for thermal motion, the molecules simulated may possess enough thermal energy to overcome potential barriers, which makes the technique suitable in principle for conformational analysis of especially large molecules. In the case of small molecules, other techniques such as systematic, random. Genetic Algorithm-based, or Monte Carlo searches may be better suited for effectively sampling conformational space. 

Molecular mechanics calculations are an attempt to understand the physical properties of molecular systems based upon an assumed knowledge of the way in which the energy of such systems varies as a function of the coordinates of the component atoms. While this term is most closely associated with the conformational energy analyses of small organic molecules pioneered by Allinger (1), in their more general applications molecular mechanics calculations include energy minimization studies, normal mode calculations, molecular dynamics (MD) and Monte Carlo simulations, reaction path analysis, and a number of related techniques (2). Molecular mechanics... 

Molecular modeling applied to polymers is, in principle, an extension of the concepts applied to small molecules. Readers familiar with energy minimization with empirical force fields (MM2, etc.), Monte Carlo, or molecular dynamics techniques for simulations already know a significant part of what is required to model polymer systems. What we present here is a description of the various techniques available for the simulation of polymers. The discussion is mostly limited to homopolymers, although we briefly mention some exciting topics outside this area. 

The first molecular simulations were performed almost five decades ago by Metropolis et al. (1953) on a system of hard disks by the Monte Carlo (MC) method. Soon after, hard spheres (Rosenbluth and Rosenbluth, 1954) and Lennard-Jones (Wood and Parker, 1957) particles were also studied by both MC and molecular dynamics (MD). Over the years, the simulation techniques have evolved to deal with more complex systems by introducing different sampling or computational algorithms. Molecular simulation studies have been made of molecules ranging from simple systems (e.g., noble gases, small organic molecules) to complex molecules (e.g., polymers, biomolecules). 

The dielectric rotational relaxation spectrum of two glass forming small molecules both in the bulk and in 4 nm porous Vycor glass have been measured. Theoretical studies have been conducted using Monte Carlo simulation techniques on short polymer chains to study the effect of confinement on glass formation as a polymer system is cooled fix>m the melt using different rates of coding. 

Investigation of the motion of adsorbed molecules, which give mechanisms and rates of re-orientation and diffusion, require alternative approaches. For systems that contain highly mobile species. Molecular Dynamics (MD) techniques are widely used. However, for many adsorbates the timescales of motion are much longer than can feasibly be simulated, so that MD is only relevant either for small molecules or at high temperatures. In order to simulate slower diffusion, the process must be considered in terms of rare events with significant activations. The activated processes are then usefully treated by transition state theory, and the associated processes treated over extended timescales and volumes by, for example, Kinetic Monte Carlo (KMQ techniques. 

---