Molecular dynamics ensembles

Evans D J and Morriss G P 1983 The Isothermal Isobaric molecular dynamics ensemble Phys. Lett. A 98 433-6... 

W. G. Hoover, Molecular Dynamics, Springer-Verlag, New York, 1986 W. G. Hoover, Constant-Pressure Equations of Motion, Phys. Rev. A 34 (1986y) 2499-2500 D. J. Evans and G. P. Morriss, The Isothermal/Isobaric Molecular Dynamics Ensemble, Phys. Lett. 98A (1983) 433-436 G. J. Martyna, D. J. Tobias and M. L. Klein, Constant Pressure Molecular Dynamics Algorithms, J. Chem. Phys. 101 (1994) 4177-4189. 

Evans, D.J. and Morriss, G.P. (1983).Isothermal isobaric molecular dynamics ensemble. Chem. Phys., 77, 63—6. 

As noted in Section 2, the molecular dynamics ensemble is characterized by fixed values of N, V, E and M. All states consistent with these values are equiprobable. According to the quasi-ergodic hypothesis, the trajectory x (t) starting from x should, except possibly for a set of initial phases of zero... 

For a finite system with periodic boundary conditions, one readily finds the molecular dynamics ensemble average low-density collision rate to be... 

Iliis exact result for the low-density collision rate in the molecular dynamics ensemble differs slightly in 0(N ) from the approximate expression given by Hoover and Alder... 

Evans DJ, Moiriss GP (1983) The isothermal isobaric molecular dynamics ensemble. Phys Lett A 98 433 36... 

Microcanonical parallel tempering has been extended to the molecular dynamics ensemble by introducing the appropriate center of mass and angular momentum constraints, the details of which can be found elsewhere. " ... 

Nos e S 1984 A molecular dynamics method for simulations In the canonical ensemble Mol. Phys. 52 255-68... 

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... 

Monte Carlo simulations generate a large number of confonnations of tire microscopic model under study that confonn to tire probability distribution dictated by macroscopic constrains imposed on tire systems. For example, a Monte Carlo simulation of a melt at a given temperature T produces an ensemble of confonnations in which confonnation with energy E. occurs witli a probability proportional to exp (- Ej / kT). An advantage of tire Monte Carlo metliod is tliat, by judicious choice of tire elementary moves, one can circumvent tire limitations of molecular dynamics techniques and effect rapid equilibration of multiple chain systems [65]. Flowever, Monte Carlo... 

Nose, S. A molecular dynamics method for simulations in the canonical ensemble. Mol. Phys. 52 (1984) 255-268 ibid. A unified formulation of the constant temperature molecular dynamics method. J. Chem. Phys. 81 (1984) 511-519. 

Fig. 5. To generate an ensemble using Molecular Dynamics or Monte-Carlo simulation techniques the interaction between all pairs of atoms within a given cutoff radius must be considered. In contrast, to estimate changes in free energy using a stored trajectory only those interactions which are perturbed need be determined making the approach highly efficient.

Other methods which are applied to conformational analysis and to generating multiple conformations and which can be regarded as random or stochastic techniques, since they explore the conformational space in a non-deterministic fashion, arc genetic algorithms (GA) [137, 1381 simulation methods, such as molecular dynamics (MD) and Monte Carlo (MC) simulations 1139], as well as simulated annealing [140], All of those approaches and their application to generate ensembles of conformations arc discussed in Chapter II, Section 7.2 in the Handbook. 

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). 

Ensemble Distance Geometry, Ensemble Molecular Dynamics and Genetic Algorithms... 

In a related way, ensemble molecular dynamics derives a pharmacophore using restrained molecular dynamics for a collection of molecules. A force field model is set up so that none of the atoms in each molecule sees the atoms in ainy other molecule. This enables the molecules to be overlaid in space. A restraint term is included in the potential, which forces the appropriate atoms or functional groups to be overlaid in space. 

Thus, unlike molecular dynamics or Langevin dynamics, which calculate ensemble averages by calculating averages over time, Monte Carlo calculations evaluate ensemble averages directly by sampling configurations from the statistical ensemble. 

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