Molecular dynamics simulation ensemble

Tobias D J, Martyna G J and Klein M L 1993 Molecular dynamics simulations of a protein In the canonical ensemble J. Phys. Chem. 9712959-66... 

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,... 

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). 

Molecular modeling is an indispensable tool in the determination of macromolecular structures from NMR data and in the interpretation of the data. Thus, state-of-the-art molecular dynamics simulations can reproduce relaxation data well [9,96] and supply a model of the motion in atomic detail. Qualitative aspects of correlated backbone motions can be understood from NMR structure ensembles [63]. Additional data, in particular residual dipolar couplings, improve the precision and accuracy of NMR structures qualitatively [12]. 

This section provides an alternative measurement for a material parameter the one in the ensemble averaged sense to pave the way for usage of continuum theory from a hope that useful engineering predictions can be made. More details can be found in Ref. [15]. In fact, macroscopic flow equations developed from molecular dynamics simulations agree well with the continuum mechanics prediction (for instance. Ref. [16]). 

The simulation of a first-order phase transition, especially one where the two phases have a significant difference in molecular area, can be difficult in the context of a molecular dynamics simulation some of the works already described are examples of this problem. In a molecular dynamics simulation it can be hard to see coexistence of phases, especially when the molecules are fairly complicated so that a relatively small system size is necessary. One approach to this problem, described by Siepmann et al. [369] to model the LE-G transition, is to perform Monte Carlo simulations in the Gibbs ensemble. In this approach, the two phases are simulated in two separate but coupled boxes. One of the possible MC moves is to move a molecule from one box to the other in this manner two coexisting phases may be simulated without an interface. Siepmann et al. used the chain and interface potentials described in the Karaborni et al. works [362-365] for a 15-carbon carboxylic acid (i.e. pen-tadecanoic acid) on water. They found reasonable coexistence conditions from their simulations, implying, among other things, the existence of a stable LE state in the Karaborni model, though the LE phase is substantially denser than that seen experimentally. The re-... 

Lyubartsev, A. P., Jacobsson, S. P., Sundholm, G., Laaksonen, A. Water/ octanol systems. A expanded ensemble molecular dynamics simulation smdy of log P parameters. J. Phys. Chem. B 2001, 105, 7775-7782. 

In the canonical ensemble (P2) = 3kBTM and p M. In the microcanonical ensemble (P2) = 3kgT i = 3kBTMNm/(M + Nm) [49]. If the limit M —> oo is first taken in the calculation of the force autocorrelation function, then p = Nm and the projected and unprojected force correlations are the same in the thermodynamic limit. Since MD simulations are carried out at finite N, the study of the N (and M) dependence of (u(t) and the estimate of the friction coefficient from either the decay of the momentum or force correlation functions is of interest. Molecular dynamics simulations of the momentum and force autocorrelation functions as a function of N have been carried out [49, 50]. 

There are two important consequences of this equality for computer simulations of many-body systems. First, it means that statistically averaged properties of these systems are accessible from simulations that are aimed at generating trajectories -e.g., molecular dynamics, or ensemble averages such as Monte Carlo. Furthermore, for sufficiently long trajectories, the time-averaged properties become independent of the initial conditions. Stated differently, it means that for almost all values of qo, Po, the system will pass arbitrarily close to any point x, p, in phase space at some later time. 

Nakajima, N. Nakamura, H. Kidera, A., Multicanonical ensemble generated by molecular dynamics simulation for enhanced conformational sampling of peptides, J. Phys. Chem. B 1997,101, 817-824... 

Temperature effects are included explicitly in molecular dynamics simulations by including kinetic energy terms - the balls representing the atoms are now on the move The principles are simple. In the microcanonical ensemble (NVE) ... 

Similar schemes to the above can be used in molecular dynamics simulations in other ensembles such as those at constant temperature or constant pressure (see Frenkel and Smit, and Allen and Tildesley (Further reading)). A molecular dynamics simulation is computationally much more intensive than an energy minimization. Typically with modern computers the real time sampled in a simulation run for large cells is of the order of nanoseconds (106 time steps). Dynamical processes operating on longer time-scales will thus not be revealed. 

Venable, R. M., Brooks, B. R. and Pastor, R. W. (2000). Molecular dynamics simulations of gel phase lipid bilayers in constant pressure and constant surface area ensembles, J. Chem. Phys., 112, 4822-4832. 

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. 

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