Molecular dynamics volume

Bartell and co-workers have made significant progress by combining electron diffraction studies from beams of molecular clusters with molecular dynamics simulations [14, 51, 52]. Due to their small volumes, deep supercoolings can be attained in cluster beams however, the temperature is not easily controlled. The rapid nucleation that ensues can produce new phases not observed in the bulk [14]. Despite the concern about the appropriateness of the classic model for small clusters, its application appears to be valid in several cases [51]. 

In equilibrium statistical mechanics, one is concerned with the thennodynamic and other macroscopic properties of matter. The aim is to derive these properties from the laws of molecular dynamics and thus create a link between microscopic molecular motion and thennodynamic behaviour. A typical macroscopic system is composed of a large number A of molecules occupying a volume V which is large compared to that occupied by a molecule ... 

An initial and desired final configuration of a system can be used by the targeted molecular dynamics (TMD) method (Schlitter et al., 1993) to establish a suitable pathway between the given configurations. The resulting pathway, can then be employed during further SMD simulations for choosing the direction of the applied force. TMD imposes time-dependent holonomic constraints which drive the system from one known state to another. This method is also discussed in the chapter by Helms and McCammon in this volume. 

B. J. Leimkuhler, S. Reich, and R. D. Skeel. Integration methods for molecular dynamics. In J. P. Mesirov, K. Schulten, and D. W. Sumners, editors, Mathematical Approaches to Biomolecvlar Structure and Dynamics, volume 82 of IMA Volumes in Mathematics and Its Applications, pages 161-186, New York, New York, 1996. Springer-Verlag. 

E. Barth, M. Mandziuk, and T. Schlick. A separating framework for increasing the timestep in molecular dynamics. In W. F. van Gunsteren, P. K. Weiner, and A. J. Wilkinson, editors. Computer Simulation of Biomolecular Systems Theoretical and Experimental Applications, volume III, chapter 4, pages 97-121. ESCOM, Leiden, The Netherlands, 1997. 

Leimkuhler, B. J., Reich, S., Skeel, R. D. Integration Methods for Molecular Dynamics. In IMA Volumes in Mathematics and its Applications. Eds. Mesirov, J., Schulten, K., Springer-Verlag, Berlin 82 (1995)... 

P. Nettesheim, and S. Reich Symplectic raultiple-time-stepping integrators for quantum-classical molecular dynamics. (1998) (this volume)... 

M. Hochbruck and Ch. Lubich. A bunch of time integrators for quan-tum/classical molecular dynamics, this volume. 

Molecular dynamics simulations can produce trajectories (a time series of structural snapshots) which correspond to different statistical ensembles. In the simplest case, when the number of particles N (atoms in the system), the volume V,... 

The correct treatment of boundaries and boundary effects is crucial to simulation methods because it enables macroscopic properties to be calculated from simulations using relatively small numbers of particles. The importance of boundary effects can be illustrated by considering the following simple example. Suppose we have a cube of volume 1 litre which is filled with water at room temperature. The cube contains approximately 3.3 X 10 molecules. Interactions with the walls can extend up to 10 molecular diameters into the fluid. The diameter of the water molecule is approximately 2.8 A and so the number of water molecules that are interacting with the boundary is about 2 x 10. So only about one in 1.5 million water molecules is influenced by interactions with the walls of the container. The number of particles in a Monte Carlo or molecular dynamics simulation is far fewer than 10 -10 and is frequently less than 1000. In a system of 1000 water molecules most, if not all of them, would be within the influence of the walls of the boundary. Clecirly, a simulation of 1000 water molecules in a vessel would not be an appropriate way to derive bulk properties. The alternative is to dispense with the container altogether. Now, approximately three-quarters of the molecules would be at the surface of the sample rather than being in the bulk. Such a situation would be relevcUit to studies of liquid drops, but not to studies of bulk phenomena. 

Just as one may wish to specify the temperature in a molecular dynamics simulation, so may be desired to maintain the system at a constant pressure. This enables the behavior of the system to be explored as a function of the pressure, enabling one to study phenomer such as the onset of pressure-induced phase transitions. Many experimental measuremen are made under conditions of constant temperature and pressure, and so simulations in tl isothermal-isobaric ensemble are most directly relevant to experimental data. Certai structural rearrangements may be achieved more easily in an isobaric simulation than i a simulation at constant volume. Constant pressure conditions may also be importai when the number of particles in the system changes (as in some of the test particle methoc for calculating free energies and chemical potentials see Section 8.9). 

The rate of chemical diffusion in a nonfiowing medium can be predicted. This is usually done with an equation, derived from the diffusion equation, that incorporates an empirical correction parameter. These correction factors are often based on molar volume. Molecular dynamics simulations can also be used. 

The original molecular dynamics (MD) technique was used only to study the namral time evolution of a classical system of N particles in a volume V. In such simulations, the total... 

In a normal molecular dynamics simulation with repeating boundary conditions (i.e., periodic boundary condition), the volume is held fixed, whereas at constant pressure the volume of the system must fluemate. In some simulation cases, such as simulations dealing with membranes, it is more advantageous to use the constant-pressure MD than the regular MD. Various schemes for prescribing the pressure of a molecular dynamics simulation have also been proposed and applied [23,24,28,29]. In all of these approaches it is inevitable that the system box must change its volume. 

An algorithm for performing a constant-pressure molecular dynamics simulation that resolves some unphysical observations in the extended system (Andersen s) method and Berendsen s methods was developed by Feller et al. [29]. This approach replaces the deterministic equations of motion with the piston degree of freedom added to the Langevin equations of motion. This eliminates the unphysical fluctuation of the volume associated with the piston mass. In addition, Klein and coworkers [30] present an advanced constant-pressure method to overcome an unphysical dependence of the choice of lattice in generated trajectories. 

By far the most common methods of studying aqueous interfaces by simulations are the Metropolis Monte Carlo (MC) technique and the classical molecular dynamics (MD) techniques. They will not be described here in detail, because several excellent textbooks and proceedings volumes (e.g., [2-8]) on the subject are available. In brief, the stochastic MC technique generates microscopic configurations of the system in the canonical (NYT) ensemble the deterministic MD method solves Newton s equations of motion and generates a time-correlated sequence of configurations in the microcanonical (NVE) ensemble. Structural and thermodynamic properties are accessible by both methods the MD method provides additional information about the microscopic dynamics of the system. 

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