Molecular dynamics algorithms

Tuckerman, M.E., Berne, B.J., Rossi, A. Molecular dynamics algorithm for multiple time scales systems with long range forces. J. Chem. Phys. 94 (1991) 6811-6815. 

Mark E. Tuckerman, Glenn J. Martyna, and Bruce J. Berne. Molecular dynamics algorithm for condensed systems with multiple time scales. J. Chem. Phys., 93(2) 1287-1291, Jul. 1990. 

Given this effective potential, it is possible to define a constant temperature molecular dynamics algorithm such that the trajectory samples the distribution Pg(r ). The equation of motion then takes on a simple and suggestive form... 

D. E. Humphreys, R. A. Friesner, and B. J. Berne. A multiple-time-step molecular dynamics algorithm for macromolecules. J. Phys. Cfiem., 98(27) 6885-6892,... 

Wisdom, J. The Origin of the Kirkwood Gaps A Mapping for Asteroidal Motion Near the 3/1 Commensurability. Astron. J. 87 (1982) 577-593 Tuckerman, M., Martyna, G. J., Berne, J. Reversible Multiple Time Scale Molecular Dynamics. J. Chem. Phys. 97 (1992) 1990-2001 Tuckerman, M., Berne, J. Vibrational Relaxation in Simple Fluids Comparison of Theory and Simulation. J. Chem. Phys. 98 (1993) 7301-7318 Humphreys, D. D., Friesner, R. A., Berne, B. J. A Multiple-Time Step Molecular Dynamics Algorithm for Macromolecules. J. Chem. Phys. 98 (1994) 6885-6892... 

Tuckerman, M., Martyna, G. J., Berne, J. Molecular Dynamics Algorithm for Condensed Systems with Multiple Time Scales. J. Chem. Phys. 93 (1990) 1287-1291... 

Yoshida, H. Recent Progress in the Theory and Application of Symplectic Integrators. Celestial Mechanics and Dynamical Astronomy 56 (1993) 27-43 Trobec, R., Merzel, F., Janezic, D. On the Complexity of Parallel Symplectic Molecular Dynamics Algorithms. J. Chem. Inf. Comput. Sci. 37 (1997) 1055-1062... 

Darve, E. Wilson, M.A. Pohorille, A., Calculating free energies using a scaled-force molecular dynamics algorithm, Mol. Simul. 2002, 28, 113-144... 

Straub, J.E. Andricioaei, I., Computational methods inspired by Tsallis statistics Monte Carlo and molecular dynamics algorithms for the simulation of classical and quantum systems, Braz. J. Phys. 1999, 29, 179-186... 

Baranyai, A. Cummings, P. T., On the molecular dynamics algorithm for Gibbs ensemble simulation, Mol. Simul. 1996,17, 21-25... 

REM has already been used in many applications in protein systems [76-91]. Other molecular simulation fields have also been studied by this method in various ensembles [92-96]. Moreover, REM was applied to cluster studies in quantum chemistry field [97]. The details of molecular dynamics algorithm have been worked out for REM in [77]. This led to a wide application of REM in the protein folding and related problems (see, e.g., [98-115]). 

In the original implementation of the replica-exchange method (REM) [67-69], Monte Carlo algorithm was used, and only the coordinates q (and the potential energy function E(q)) had to be taken into account. In molecular dynamics algorithm, on the other hand, we also have to deal with the momenta p. We proposed the following momentum assignment in (4.45) (and in (4.46)) [77] ... 

T. Schlick, Comput. Chem., 15,251 (1991). New Approaches to Potential Energy Minimization and Molecular Dynamics Algorithms. 

M. E. Tuckerman, B. J. Berne, and A. Rossi, J. Chem. Phys., 94, 1465 (1991). Molecular Dynamics Algorithm for Multiple Time Scales Systems with Disparate Masses. 

In this work, we have approaehed the understanding of proton transport with two tasks. In the first task, deseribed above, we have sought to identify the moleeular-level stmeture of PFSA membranes and their relevant interfaees as a funetion of water content and polymer architecture. In the second task, described in this Section, we explain our efforts to model and quantify proton transport in these membranes and interfaces and their dependence on water content and polymer architecture. As in the task I, the tool employed is molecular dynamics (MD) simulation. A non-reactive algorithm is sufficient to generate the morphology of the membrane and its interfaces. It is also capable of providing some information about transport in the system such as diffusivities of water and the vehicular component of the proton diffusivity. Moreover, analysis of the hydration of hydronium ion provides indirect information about the structural component of proton diffusion, but a direct measure of the total proton diffusivity is beyond the capabilities of a non-reactive MD simulation. Therefore, in the task II, we develop and implement a reactive molecular dynamics algorithm that will lead to direct measurement of the total proton diffusivity. As the work is an active field, we report the work to date. 

Coarse-Grained Reactive Molecular Dynamics Algorithm... 

F. Mueller-Plathe, Comput. Phys. Commun., 61, 285 (1990). Parallellizing a Molecular Dynamics Algorithm on a Multi-Processor Workstation. 

T. Schlick and W. Olson, Workshop on High Performance Computing and Grand Challenges in Structural Biology, Florida State University, Tallahassee, FL, Jan. 24-27, 1992. A Molecular Dynamics Algorithm and Its Applications to Supercoiled DNA. 

These methods can be combined with geometry optimization as well as with molecular dynamics algorithms, with forces obtained from the gradients of the total quantum energy [10]. This equally applies to all quantum methods, quoted in the following. 

Similiar problems are known in classical MD simulations, where intramolecular and intermolecular dynamics evolve on different time scales. One possible solution to this problem is the method of multiple time scale propagators which is describede in section 5. Berne and co-workers [21] first used different time steps to integrate the intra- and intermolecular degrees of freedom in order to reduce the computational effort drastically. The method is based on a Trotter-factorization of the classical Liouville-operator for the time evolution of the classical system, resulting in a time reversible propagation scheme. The multiple time scale approach has also been used to speed up Car-Parrinello simulations [20] and ab initio molecular dynamics algorithms [21]. 

S. Plimpton and B. Hendrickson, Parallel Molecular Dynamics Algorithms for Simulation of Molecular Systems, in Mattson [110], 114-132. 

D. C. Rapaport, Hardware Issues in Molecular Dynamics Algorithm Design, in Computer Modelling of Fluids Polymers and Solids, C. R. A. Cat-low et al., eds., Kluwer Academic Publishers Group, 1990, 249-267. 

The simplest model potentials that form liquid crystals are the hard ellipsoid fluid and the hard cylinder fluid [4]. Linear and angular momenta are constant between collisions so that very efficient molecular dynamics algorithms can be devised. Unfortunately, when transport coefficients are calculated external fields and thermostats are often applied. That means that the particles accelerate between collisions. The advantages of using hard body fluids is conse-... 

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