Derivation of the high directional monte carlo sampling scheme and applications to several statistical mechanical and biomolecular systems

Abstract

The motivation for computer simulations of physical systems are manifold. The most important one is that we can obtain an exact answer to a very complex systems without any approximations which are necessary to treat them analytically. Accordingly, they are treated as a reference against which the results of various approximate theories may be compared. And some physical quantities are impossible or difficult to measure in an experiment. If it is the case, then the computer simulation approach may fill the gap between theory and experiment since they can be measured by computer experiments. Particularly, Monte Carlo(MO) method is widely applied to a molecular modeling, drug design as well as to obtain various thermodynamic quantities ranging from simple classical particles to quantum ones or very large macromolecular systems such as proteins and polypeptides. However, the general utility of the method is limited since the computing time greatly increases as the size of the system increases and there are many kinds of slowing down phenomena of convergence rates. Hence, it is worthwhile to explore whether it is possible to accelerate the convergence by more efficient algorithms. In this paper, we develop an efficient algorithm, namely, the High Direction Monte Carlo(HDMC) sampling scheme, which allows to sample more important regions in configurational space. Here, we report some results where the new method is applied to some statistical mechanical systems and biomolecular system. A. Melting of Lennard-Jones Particles Thermal equilibration of 256 Lennard-Jones particles near the critical temperature($T_c$) are simulated by the new method and the conventional one. By monitoring the translational order parameter($S_k$), we identified that our method is far more efficient then the conventional one while there are not bias in the equlibrium distribution of canonical ensembles. B. Equilibration of TIP4P waters And TIP4P water system is simulated using both methods. T...