Molecular dynamics Verlet algorithms

Helmut Grubmuller, Helmut Heller, Andreas Windemuth, and Klaus Schulten. Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions. Mol. Sim., 6 121-142, 1991. 

Grubmiiller, H., Heller, H., Windemuth, A., Schulten, K. Generalized Verlet Algorithm for Efficient Molecular Dynamics Simulations with Long-range Interactions. Molecular Simulation 6 (1991) 121-142... 

In our calculations we make use of several standard techniques of molecular dynamics simulations. The integration of the equations of motions is done by the velocity form of the Verlet-algorithm with a time step of 1.5 The temperature is controlled... 

On-the-fly molecular dynamics have been employed in order to simulate the photochemistry of carbonyl-containing compounds. The on-the-fly mechanism implemented in the MNDO program is the velocity-Verlet algorithm. Here an additional aspect of the usage of a computational cheap semiempirical method is visible. In order to provide realistic relative yields of different photochemical reactions, a large enough sample of trajectories is needed. For these systems, a substantial amount of trajectories (around 100) has been calculated for a relatively long timescale (up to 100 ps). 

A very simple implementation of a molecular dynamics trajectory calculation is achieved by using a velocity Verlet algorithm to calculate the... 

RestrirteH Open-shell Hartree-Fock (ROHFl Solvation Models (SMx), 397 Trajectory, 3 /6 Verlet algorithm, for molecular dynamics, 384... 

A variety of algorithms have been used for integrating the equations of motion in molecular dynamics simulations of macromolecules. Most widely employed are the algorithms due to Gear91 and Verlet.90 The algorithm introduced by Verlet in his initial studies of the dynamics of Lennard-Jones fluids is derived from the two Taylor expansions,... 

Molecular dynamics simulation investigations of Lennard-Jones huids were continued by Verlet [9] and in the course of his studies he introduced several important techniques that have continued to be in use to the present day. The now-famous Verlet algorithm for integrahng Newton s equations of motion was hrst presented in this paper. In this algorithm the positions of the particles are updated according to the following scheme if F(ry) is the force on particle i due to particle j, the position of particle i at time t + h can be found from the positions at two earlier times using. 

Marry, V., Ciccotti, G. Trotter derived algorithms for molecular dynamics with constraints velocity Verlet revisited. J. Comput. Phys. 222, 428 40 (2007). doi 10.1016/j.jcp.2006.07. 

In practice molecular dynamics is run with finite time steps. Using the equations above would therefore lead to the introduction of inaccuracies (Biesiadecki and Skeel 1993). A number of algorithms have been developed to overcome this difficulty. One of the most widely used is the Verlet Leapfrog Algorithm (VLA), modified from Verlet s original algorithm (Verlet 1967) which uses the velocity at the mid-step v( + /2 ). 

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