Monte Carlo methods condensed phases

Detailed calculations on the condensed phases of biphenyl have been carried out by the variable shape isothermal-isobaric ensemble Monte Carlo method. The study employs the Williams and the Kitaigorodskii intermolecular potentials with several intramolecular potentials available from the literature. Thermodynamic and structural properties including the dihedral angle distributions for the solid phase at 300 K and 110 K are reported, in addition to those in the liquid phase. In order to get the correct structure it is necessary to carry out calculations in the isothermal-isobaric ensemble. Overall, the Williams model for the intermolecular potential and Williams and Haigh model for the intramolecular potential yield the most satisfactory results. In contrast to the results reported recently by Baranyai and Welberry, the dihedral angle distribution in the solid state is monomodal or weakly bimodal. There are interesting correlations between the molecular planarity, the density and the intermolecular interaction. 

Recent years have seen the extensive application of computer simulation techniques to the study of condensed phases of matter. The two techniques of major importance are the Monte Carlo method and the method of molecular dynamics. Monte Carlo methods are ways of evaluating the partition function of a many-particle system through sampling the multidimensional integral that defines it, and can be used only for the study of equilibrium quantities such as thermodynamic properties and average local structure. Molecular dynamics methods solve Newton s classical equations of motion for a system of particles placed in a box with periodic boundary conditions, and can be used to study both equilibrium and nonequilibrium properties such as time correlation functions. 

Detailed calculations on the condensed phases of biphenyl have been carried out by the variable shape isothermal-isobaric ensemble Monte Carlo method. 

Fig. 1. The phase diagram of condensed hydrogen computed by the quantum Monte Carlo methods. Here r is the average proton separation. The calculations treated both electrons and protons quantum mechanically except that the protons are required to have a average fee structure in the metaiiic phase and the centers of the molecules are restrained in the molecular phase. The molecular curve agrees well with experiment to 0.5 Mbar and the transition is predicted to occur around 5 Mbar. (Figure courtesy of D. M. Ceperley and B. J. Alder). 

This chapter is written for the reader who would like to learn how Monte Carlo methods are used to calculate thermodynamic properties of systems at the atomic level, or to determine which advanced Monte Carlo methods might work best in their particular application. There are a number of excellent books and review articles on Monte Carlo methods, which are generally focused on condensed phases, biomolecules or electronic structure the-ory. " The purpose of this chapter is to explain and illustrate some of the special techniques that we and our colleagues have found to be particularly... 

The above results apply to the ideal gas of molecules. The objects addressed in the context of molecular modeling of complex systems are known in the form of macroscopic samples, mostly in the condensed phase. Thus the intermolecular degrees of freedom significantly contribute to the thermodynamical and other properties due to intermolecular interactions. For taking these latter into account the Monte-Carlo (MC) or molecular dynamics (MD) techniques are applied to model systems containing from hundreds to thousands of molecules and correspondingly tens and hundreds of thousands of atoms. These two approaches represent two more modem contexts where a demand for efficient methods of calculation of molecular potential... 

The principal drawback of the DFT method is that it is computationally intensive relative to the classical adsorption models, although it is still much less compute-intensive than full Monte Carlo molecular simulation. A semianalytic adsorption model that retains computational efficiency while accounting for gas-solid potential interactions in micropores was originally proposed by Horvath and Kawazoe [12], In the Horvath-Kawazoe or HK method, a pore filling correlation is obtained by calculating the mean heat of adsorption (/> required to transfer an adsorbate molecule from the gas phase to the condensed phase in a slit pore of width // ... 

Because of the time-consuming nature of full dynamical (or Monte Carlo) treatments of the thermodynamic properties of molecules as large as proteins, simplified approaches have been used to obtain approximate results. In what follows, a series of methods is described in increasing order of sophistication. The first section treats classical vacuum calculations, which are concerned with the evaluation of the system energy. Next, methods that take into account internal flexibility and harmonic fluctuations are outlined. Finally, techniques for calculating the free energies in condensed phases are presented. 

Due to the difficulties of QM methods to describe correctly condensed phase behavior. Van der Waals parameters and atomic point charges of molecular models are often adjusted to reproduce experimental data on macroscopic properties of the liquid state. Usually, they are fitted to thermodynamic properties determined by means of molecular dynamics (MD) or Monte Carlo (MC) simulations. 

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