## Introduction

Because many details of the dynamics and structure of chemical systems cannot be directly observed, molecular simulation methods such as molecular dynamics (MD) [1-31, molecular mechanics (MM) [4], and classical and quantum Monte Carlo [5,6] are extremely valuable tools for making sense of experimental results. In the context of nanotechnology, molecular simulation is crucial for studying the feasibility of proposed directions of research and development [7]. With the rapid improvement in computing power and algorithms, the capabilities and range of applicability of molecular simulation have dramatically increased over the past decade.

This article describes work performed at Oak Ridge National Laboratory on the development of molecular simulation methods. Our group has optimized molecular simulation methods particularly suitable for systems with highly interconnected bond networks. One area of improvement is in the calculation of forces and second derivatives common to many types of simulation [8-11]. Another is a method for automatically keeping track of bend, torsion, and other interactions in any bond network [12]. A more recent development is the development of internal coordinate quantum Monte Carlo (ICQMC) [13], a method for the calculation of vibrational energy levels and wavefunctions of systems with many atoms.

This work has begun to yield fruit in the study of quantum- classical correspondence in many body systems. Although considerable work has gone into this area for few body systems, comparatively little work has been done for many body systems. Results so far indicate that classical MD simulations can grossly overestimate vibrational motion in many body systems due to the leakage of zero point energy into high amplitude vibrational modes. Although this problem is mitigated by geometric constraints or by approximations that reduce the number of degrees of freedom (such as collapsed atoms), comparison of classical and quantum simulations underscore the need for the determination of the limits of classical simulation. Although such studies have led to two schemes for correcting the zero point energy problem in few body systems, there are many challenges in extending these methods to larger systems.

It should be noted that this problem is much less of an issue in, for example, classical Monte Carlo calculations, where successive iterations do not correspond to a progression of time steps. Similar considerations apply to molecular mechanics calculations. The consequences for the MD simulation of liquids, which are unbounded, are also much less severe than for chemically bound systems.

The next section describes improvements in general methods for calculating potential energy first and second derivatives, which are applicable to almost all molecular simulations. After this, the recently developed ICQMC method is described, followed by a discussion of classical and quantum results in the simulation of polymer chains and of carbon nanotubes.

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