Molecular-dynamics at constant

D.A. Gibson and E.A. Carter, Generalized valence bond molecular dynamics at constant temperature, Mol. Phys., 89(1996), 1265-1276. 

H. C. Andersen, J. Chem. Phys., 72, 2384 (1980). Molecular Dynamics at Constant Pressure... 

Figure 9.11 Plot of the mean square displacement (MSD, A ) of water molecules vs time (ps) for 0.6 ns of molecular dynamics at constant pressure. The slope of the curve is 1.2866. Following Einstein s equation, the lateral coefficient of water is one-sixth of this value, i.e., 0.214 AVps or 2.14 X 10 cmVs. In these conditions, the normal value for bulk water is 3.5 x 10 cmVs. In fact a noticeable part of the water is partially trapped into hydration shells around charged moieties like phosphocholines...

Several variations of ordinary MD have been developed. Andersen has proposed "molecular dynamics at constant temperature," in which an MD system is made to represent a canonical system, by altering the momentum of random particles at sequential random Instants of time. The new momentum is picked from a Boltzmann distribution, with a given parameter p. Since the motion of the system is no longer Hamiltonian, this procedure is a statistical sampling method. A combination technique was used by Wood and Erpenbeck, who ran a set of independent MD calculations, with the initial phase of each calculatlon glcked from a canonical, or mlcrocanonical, distribution. Andersen also described molecular dynamics at constant pressure," in which the pressure is a parameter of the Lagranglan, and the system volume fluctuates. 

Mertz JE, Pettitt BM (1994) Molecular dynamics at a constant pH. Int J Supercomput Appl High Perform Comput 8 47-53. 

Excess Kinetic Energy Relaxation Time Constants in "Heme Cooling" Eollowing Ligand Photolysis of CO in Myoglobin Simulated Using Classical Molecular Dynamics at 300 K... 

Being a molecular dynamics technique, GEMD provides dynamical information such as diffusion coefficients in the coexisting phases [5]. Shown in Fig. 3 are the mean squared displacements of the carbon atoms in -hexane, calculated in coexisting phases with GEMD, compared to the results of the constant temperature molecular dynamics at the same conditions. This shows that diffusion coefficients and other dynamical information can be extracted from GEMD simulations, together with the thermodynamic properties. 

Two simulation methods—Monte Carlo and molecular dynamics—allow calculation of the density profile and pressure difference of Eq. III-44 across the vapor-liquid interface [64, 65]. In the former method, the initial system consists of N molecules in assumed positions. An intermolecule potential function is chosen, such as the Lennard-Jones potential, and the positions are randomly varied until the energy of the system is at a minimum. The resulting configuration is taken to be the equilibrium one. In the molecular dynamics approach, the N molecules are given initial positions and velocities and the equations of motion are solved to follow the ensuing collisions until the set shows constant time-average thermodynamic properties. Both methods are computer intensive yet widely used. 

Andersen H C 1980 Molecular dynamics simulations at constant pressure and/or temperature J. Chem. 

As examples of applications, we present the overall accuracy of predicted ionization constants for about 50 groups in 4 proteins, changes in the average charge of bovine pancreatic trypsin inhibitor at pH 7 along a molecular dynamics trajectory, and finally, we discuss some preliminary results obtained for protein kinases and protein phosphatases. 

A typical molecular dynamics simulation comprises an equflibration and a production phase. The former is necessary, as the name imphes, to ensure that the system is in equilibrium before data acquisition starts. It is useful to check the time evolution of several simulation parameters such as temperature (which is directly connected to the kinetic energy), potential energy, total energy, density (when periodic boundary conditions with constant pressure are apphed), and their root-mean-square deviations. Having these and other variables constant at the end of the equilibration phase is the prerequisite for the statistically meaningful sampling of data in the following production phase. 

In a molecular dynamics calculation, you can add a term to adjust the velocities, keeping the molecular system near a desired temperature. During a constant temperature simulation, velocities are scaled at each time step. This couples the system to a simulated heat bath at Tq, with a temperature relaxation time of "r. The velocities arc scaled bv a factor X. where... 

The first molecular dynamics simulation of a condensed phase system was performed by Alder and Wainwright in 1957 using a hard-sphere model [Alder and Wainwright 1957]. In this model, the spheres move at constant velocity in straight lines between collisions. All collisions are perfectly elastic and occur when the separation between the centres of... 

Finite difference techniques are used to generate molecular dynamics trajectories with continuous potential models, which we will assume to be pairwise additive. The essential idea is that the integration is broken down into many small stages, each separated in time by a fixed time 6t. The total force on each particle in the configuration at a time t is calculated as the vector sum of its interactions with other particles. From the force we can determine the accelerations of the particles, which are then combined with the positions and velocities at a time t to calculate the positions and velocities at a time t + 6t. The force is assumed to be constant during the time step. The forces on the particles in their new positions are then determined, leading to new positions and velocities at time t - - 2St, and so on. 

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). 

Once HyperChem calculates potential energy, it can obtain all of the forces on the nuclei at negligible additional expense. This allows for rapid optimization of equilibrium and transition-state geometries and the possibility of computing force constants, vibrational modes, and molecular dynamics trajectories. 

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