Volume molecular dynamic simulation

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]. 

J. D. Turner, P. K. Weiner, H. M. Chun, V. Lupi, S. Gallion, and U. C. Singh. Variable reduction techniques applied to molecular dynamics simulations. In W. F. van Gunsteren, P. K. Weiner, and A. J. Wilkinson, editors. Computer Simulation of Biomolecular Systems Theoretical and Experimental Applications, volume 2, chapter 24. ESCOM, Leiden, The Netherlands, 1993. 

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. 

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. 

Studies of the effect of permeant s size on the translational diffusion in membranes suggest that a free-volume model is appropriate for the description of diffusion processes in the bilayers [93]. The dynamic motion of the chains of the membrane lipids and proteins may result in the formation of transient pockets of free volume or cavities into which a permeant molecule can enter. Diffusion occurs when a permeant jumps from a donor to an acceptor cavity. Results from recent molecular dynamics simulations suggest that the free volume transport mechanism is more likely to be operative in the core of the bilayer [84]. In the more ordered region of the bilayer, a kink shift diffusion mechanism is more likely to occur [84,94]. Kinks may be pictured as dynamic structural defects representing small, mobile free volumes in the hydrocarbon phase of the membrane, i.e., conformational kink g tg ) isomers of the hydrocarbon chains resulting from thermal motion [52] (Fig. 8). Small molecules can enter the small free volumes of the kinks and migrate across the membrane together with the kinks. 

The strong point of molecular dynamic simulations is that, for the particular model, the results are (nearly) exact. In particular, the simulations take all necessary excluded-volume correlations into account. However, still it is not advisable to have blind confidence in the predictions of MD. The simulations typically treat the system classically, many parameters that together define the force field are subject to fine-tuning, and one always should be cautious about the statistical certainty. In passing, we will touch upon some more limitations when we discuss more details of MD simulation of lipid systems. We will not go into all the details here, because the use of MD simulation to study the lipid bilayer has recently been reviewed by other authors already [31,32]. Our idea is to present sufficient information to allow a critical evaluation of the method, and to set the stage for comparison with alternative approaches. 

Figure 8 Compressibility factor P/fiksT versus density p = pa3 of the hard-sphere system as calculated from both free-volume information (Eq. [8]) and the collision rate measured in molecular dynamics simulations. The empirically successful Camahan-Starling84 equation of state for the hard-sphere fluid is also shown for comparison. (Adapted from Ref. 71).

This volume of Modem Aspects covers a wide spread of topics presented in an authoritative, informative and instructive manner by some internationally renowned specialists. Professors Politzer and Dr. Murray provide a comprehensive description of the various theoretical treatments of solute-solvent interactions, including ion-solvent interactions. Both continuum and discrete molecular models for the solvent molecules are discussed, including Monte Carlo and molecular dynamics simulations. The advantages and drawbacks of the resulting models and computational approaches are discussed and the impressive progress made in predicting the properties of molecular and ionic solutions is surveyed. 

The sizes of the dendrimers have been determined by calculating the molecular volumes, as defined by the van der Waals radii of the atoms, and by calculating the radii of gyration for several configurations of the dendrimers, as obtained from a molecular dynamics simulation at room temperature. The solvent influence on the calculated radii was estimated by scaling the nonbonded interactions between the atoms. Molecular volumes and average radii for ensembles of 500 conformations of the BAB-dendr-(NH2)D dendrimers have been collected in Table 26.2. 

We now present results from molecular dynamics simulations in which all the chain monomers are coupled to a heat bath. The chains interact via the repiflsive portion of a shifted Lennard-Jones potential with a Lennard-Jones diameter a, which corresponds to a good solvent situation. For the bond potential between adjacent polymer segments we take a FENE (nonhnear bond) potential which gives an average nearest-neighbor monomer-monomer separation of typically a 0.97cr. In the simulation box with a volume LxL kLz there are 50 (if not stated otherwise) chains each of which consists of N -i-1... 

Figure 1. Density profiles for a droplet confined to a finite volume as predicted by YBG theoiy (solid line) are compared with the results of molecular dynamics simulations (7) ( ). The reduced temperature, kT/e=0.71, is near the triple point. The total number of atoms in each of the tems is indicated.

Figure 1 The shear stress relaxation function, C(t), obtained from a molecular dynamics simulation of500 SRP spheres at a reduced temperature of 1.0 and effective volume fraction of 0.45. Note that n = 144 and 1152 (from Equation (1)) cases are superimposable with the analytic function of Equation (4) ( Algebraic on the figure) for short times, t (or nt here)...

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