Computational methods, molecular simulation

Contemporary computer-assisted molecular simulation methods and modern computer technology has contributed to the actual numerical calculation of solvent effects on chemical reactions and molecular equilibria. Classical statistical mechanics and quantum mechanics are basic pillars on which practical approaches are based. On top of these, numerical methods borrowed from different fields of physics and engineering and computer graphics techniques have been integrated into computer programs running in graphics workstations and modem supercomputers (Zhao et al., 2000). 

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). 

Molecular modeling uses computational methods to simulate the properties of chemical and biological systems. Many molecular modeling tools are commercially available to predict the physical properties of solids with reasonable accuracy. These tools may be applied to the chiral drugs to explain the experimental observations at the molecular level and to predict the properties based on the crystal structure or the molecular structure. 

J.A. McCleverty and T.J. Meyer, eds (2004) Comprehensive Coordination Chemistry II, Elsevier, Oxford Volume 2 contains a section Theoretical Models, Computational Methods, and Simulation consisting of a series of articles covering computational methods including molecular mechanics, semi-empirical SCF MO methods, and density functional theory. 

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. 

In principle, mesoscale methods can provide a means for connecting one type of simulation to another. For example, a molecular simulation can be used to describe a lipid. One can then derive the parameters for a lipid-lipid potential. These parameters can then be used in a simulation that combines lipids to form a membrane, which, in turn, can be used to compute parameters describing a membrane as a flexible sheet. Such parameters could be used for a simulation with many cells in order to obtain parameters that describe an organ, which could be used for a whole-body biological simulation. Each step, in theory, could be modeled in a different way using parameters derived not from experiment but from a more low-level form of simulation. This situation has not yet been realized, but it is representative of one trend in computational technique development. 

Monte Carlo (MC) techniques for molecular simulations have a long and rich history, and have been used to a great extent in studying the chemical physics of polymers. The majority of molecular modeling studies today do not involve the use of MC methods however, the sampling capabiUty provided by MC methods has gained some popularity among computational chemists as a result of various studies (95—97). Relevant concepts of MC are summarized herein. 

Computational methods have played an exceedingly important role in understanding the fundamental aspects of shock compression and in solving complex shock-wave problems. Major advances in the numerical algorithms used for solving dynamic problems, coupled with the tremendous increase in computational capabilities, have made many problems tractable that only a few years ago could not have been solved. It is now possible to perform two-dimensional molecular dynamics simulations with a high degree of accuracy, and three-dimensional problems can also be solved with moderate accuracy. 

However, theories that are based on a basis set expansion do have a serious limitation with respect to the number of electrons. Even if one considers the rapid development of computer technology, it will be virtually impossible to treat by the MO method a small system of a size typical of classical molecular simulation, say 1000 water molecules. A logical solution to such a problem would be to employ a hybrid approach in which a chemical species of interest is handled by quantum chemistry while the solvent is treated classically. 

Owing to the increasing efficiency of computational methods, it has become possible to investigate base pairs in the gas phase and solution simulated by super-molecular approaches with up to six water molecules [98IJQ37, 98JPC(A) 10374, 98JPC(B)9109, 99JST107]. In the cytosine-isocytosine Watson-Crick base pair. 

Most liquid phase molecular simulations with explicit atomic polarizabilities are performed with MD rather than MC techniques. This is due to the fact that, despite its general computational simplicity, MC with explicit polarization [173, 174] requires that Eq. (9-21) be solved every MC step, when even one molecule in the system is moved, and the number of configurations in an average Monte Carlo computation is orders of magnitude greater than in a MD simulation. For nonpolarizable, pairwise-additive models, MC methods can be efficient because only the... 

Beginning with values of ]r) and ]v) at time 0, one calculates the new positions and then the new velocities. This method is second-order in At, too. For additional details, see Allen, M. R, and D. J. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford (1989) Frenkel, D., and B. Smit, Understanding Molecular Simulation, Academic Press (2002) Haile, J. M., Molecular Dynamics Simulation, Wiley (1992) Leach, A. R., Molecular Modelling Principles and Applications, Prentice-Hall (2001) Schlick, T., Molecular Modeling and Simulations, Springer, New York (2002). 

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