Water bonds Monte Carlo methods

By the 1970s, larger computers permitted the statistical mechanical treatment of molecules with complicated (other than spherical) potentials. By using potentials similar to MM2, molecular dynamics and Monte Carlo methods were developed, and calculations could be carried out on whole assemblies of molecules. A successful simulation of the molecular dynamics of water by Rahman and Stillinger allowed the calculation of properties such as dielectric constants. The hydrogen bonding structure of water was finally revealed. Thus, some early approximate developments had begun to pay off. 

A trick to accelerate the simulation is to impose order parameters relevant to the description of the crystalline state to drive the system towards nucleation. This method was applied to the study of water nucleation and carbon dioxide hydrate formation using a conventional Monte Carlo method. ° ° Stein-hardt s bond-orientational order parameters Q and W , based on quadratic and third-order invariants formed from bond spherical harmonics (Y/ ,(0, (p)), were employed. These order parameters allow quantitative measures of the local symmetry in liquids and glasses. The rotationally invariant orientational order parameters are defined as ... 

However, the solvent molecules are not fixed and their contributions can be treated only in an averaged manner, except in the case where a water molecule is bound to the protein by a strong hydrogen bond. Theories to describe solvent interactions are presented in Chapter 3 (Sections 3.4 and 3.5). As already mentioned, recent approaches use either molecular dynamics or Monte Carlo methods. 

Equation (4-5) can be directly utilized in statistical mechanical Monte Carlo and molecular dynamics simulations by choosing an appropriate QM model, balancing computational efficiency and accuracy, and MM force fields for biomacromolecules and the solvent water. Our group has extensively explored various QM/MM methods using different quantum models, ranging from semiempirical methods to ab initio molecular orbital and valence bond theories to density functional theory, applied to a wide range of applications in chemistry and biology. Some of these studies have been discussed before and they are not emphasized in this article. We focus on developments that have not been often discussed. 

We treat, in this chapter, mainly solid composed of water molecules such as ices and clathrate hydrates, and show recent significant contribution of simulation studies to our understanding of thermodynamic stability of those crystals in conjunction with structural morphology. Simulation technique adopted here is not limited to molecular dynamics (MD) and Monte Carlo (MC) simulations[l] but does include other method such as lattice dynamics. Electronic state as well as nucleus motion can be solved by the density functional theory[2]. Here we focus, however, our attention on the ambient condition where electronic state and character of the chemical bonds of individual molecules remain intact. Thus, we restrict ourselves to the usual simulation with intermolecular interactions given a priori. 

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