Molecular dynamic computational approach

M. Menon and R. E. AUen, New technique for molecular-dynamics computer simulations Hellmann- Feynman theorem and subspace Hamiltonian approach , Phys. Rev. B33 7099 (1986) Simulations of atomic processes at semiconductor surfaces General method and chemisorption on GaAs(llO) , ibid B38 6196 (1988). 

Nakano A (1997) Parallel multilevel preconditioned conjugate-gradient approach to variable-charge molecular dynamics. Comput Phys Commun 104(l-3) 59-69... 

We have reviewed above the GH approach to reaction rate constants in solution, together with simple models that give a deeper perspective on the reaction dynamics and various aspects of the generalized frictional influence on the rates. The fact that the theory has always been found to agree with Molecular Dynamics computer simulation results for realistic models of many and varied reaction types gives confidence that it may be used to analyze real experimental results. 

Central to the understanding of surface-related phenomena has been the study of gas-surface reactions. A comprehensive understanding of these reactions has proven challenging because of the intrinsic many-body nature of surface dynamics. In terms of theoretical methods, this complexity often forces us either to treat complex realistic systems using approximate approaches, or to treat simple systems with realistic approaches. When one is interested in studying processes of technological importance, the latter route is often the most fruitful. One theoretical technique which embodies the many-body aspect of the dynamics of surface chemistry (albeit in a very approximate manner) is molecular dynamics computer simulation. 

The first step in the theoretical study of this problem is a molecular dynamics computation on the human proteins. Our methodology is described in detail elsewhere [51], but, in brief the starting point for computations were crystal structures solved by Read et al. [52] for homo-tetrameric human heart, h-H4LDH, and muscle, h-M4LDH, isozymes in a ternary complex with NADH and oxamate at 2.1 A and 2.3 A resolution respectively. Numerical analysis of molecular dynamics computations followed our previously published approach [53]. 

Both experiments and theory join in the studies of hydrogen transfer reactions. In general, the approach is of two categories. The first involves the study of prototypical but well-defined molecular systems, either under isolated (microscopic) conditions or in complexes or clusters (mesoscopic) vdth the solvent, in the gas phase or molecular beams. Such studies over the past three decades have provided unprecedented resolution of the elementary processes involved in isolated molecules and en route to the condensed phase. Examples include the discovery of a magic solvent number for acid-base reactions, the elucidation of motions involved in double proton transfer, and the dynamics of acid dissociation in finite-sized clusters. For these systems, theory is nearly quantitative, especially as more accurate electronic structure and molecular dynamics computations become available. 

A . This formulation created a powerful theory which has been translated into an effective computational scheme based on linear algebraic methods. These algebraic methods have become the main agents of quantum molecular dynamical computations, but have blurred the image of the molecular encounter. The algebraic approach has created a new language in which, for example, a chemical reaction is described by a matrix quantity, the state-to-state transition amplitude Su. 

Several molecular dynamics simulation approaches are available, including regular simulation, constrained simulation, and simulated annealing techniques. In addition, the simulated annealing dynamics simulation also was popular in computational chemistry studies of proteins and drug molecules (34.44.45). A common experimental protocol has been widely used in molecular dynamics simulation as following (34.46.47) ... 

M. R. Philpott and J. N. Glosli, in Theoretical and Computational Approaches to Interface Phenomena, H. L. Sellers and J. T. Golab, Eds., Plenum Press, New York, 1994, pp. 75-100. Molecular Dynamics Computer-Simulations of Charged Metal-Electrolyte Interfaces. 

More complicated symmetric second-order schemes can be devised by proceeding almost arbitrarily and maintaining a symmetric composition, but it is not found that alternative approaches improve on the two Verlet schemes, at least for molecular applications. The Verlet methods are seen as the gold-standard for molecular dynamics computations both require only one evaluation of VU q) per iteration (where the velocity Verlet scheme can reuse VU Q) for the next iteration), and offer a second-order symplectic evolution. 

A distinctly different approach, which has witnessed much progress recently, is large scale Monte Carlo and molecular dynamics computer simulations [4]. These studies provide many insights regarding the physics of model polymer fluids, and also valuable benchmarks against which approximate theory can be tested. However, an atomistic, off-lattice treatment of high polymer fluids and alloys remains immensely expensive, if not impossible, from a computational point of view. 

Sivanesan D, Rajnarayanan RV, Doherty J, Pattabiraman N (2005) In-silico screening using flexible ligand binding pockets a molecular dynamics-based approach. J Comput-Aided Mol Des 19(4) 213-228. doi 10.1007/sl0822-005-4788-9... 

A rather different approach for polar molecules has recently been explored by Bossis and Brot. This is to calculate correlation functions for dipole, in an inner spherical region which is part of a larger spherical region the motivation being to gain some idea of how well such simulations can approximate the inner sphere function in the Rirkwood Fr hlich (KF) equation (21) which strictly should be evaluated in the double limits Rj, I /Rj eO. Molecular dynamics computer simulations have so far been done (35) for a two-dimensional system, i.e. disks rather than spheres, for 324 molecules in most cases with a Lennard-Jones 12-6 radial plus rigid dipole pair potential, with the system confined within an outer radius R = 13.2 0- by a soft dish potential barrier. 

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. 

Tuckerman M E and Hughes A 1998 Path integral molecular dynamics a computational approach to quantum statistical mechanics Classical and Quantum Dynamics In Condensed Phase Simulations ed B J Berne, G Ciccotti and D F Coker (Singapore World Scientific) pp 311-57... 

The method of molecular dynamics (MD), described earlier in this book, is a powerful approach for simulating the dynamics and predicting the rates of chemical reactions. In the MD approach most commonly used, the potential of interaction is specified between atoms participating in the reaction, and the time evolution of their positions is obtained by solving Hamilton s equations for the classical motions of the nuclei. Because MD simulations of etching reactions must include a significant number of atoms from the substrate as well as the gaseous etchant species, the calculations become computationally intensive, and the time scale of the simulation is limited to the... 

In Chapter VI, Ohm and Deumens present their electron nuclear dynamics (END) time-dependent, nonadiabatic, theoretical, and computational approach to the study of molecular processes. This approach stresses the analysis of such processes in terms of dynamical, time-evolving states rather than stationary molecular states. Thus, rovibrational and scattering states are reduced to less prominent roles as is the case in most modem wavepacket treatments of molecular reaction dynamics. Unlike most theoretical methods, END also relegates electronic stationary states, potential energy surfaces, adiabatic and diabatic descriptions, and nonadiabatic coupling terms to the background in favor of a dynamic, time-evolving description of all electrons. 

The classical microscopic description of molecular processes leads to a mathematical model in terms of Hamiltonian differential equations. In principle, the discretization of such systems permits a simulation of the dynamics. However, as will be worked out below in Section 2, both forward and backward numerical analysis restrict such simulations to only short time spans and to comparatively small discretization steps. Fortunately, most questions of chemical relevance just require the computation of averages of physical observables, of stable conformations or of conformational changes. The computation of averages is usually performed on a statistical physics basis. In the subsequent Section 3 we advocate a new computational approach on the basis of the mathematical theory of dynamical systems we directly solve a... 

Since 5 is a function of all the intermediate coordinates, a large scale optimization problem is to be expected. For illustration purposes consider a molecular system of 100 degrees of freedom. To account for 1000 time points we need to optimize 5 as a function of 100,000 independent variables ( ). As a result, the use of a large time step is not only a computational benefit but is also a necessity for the proposed approach. The use of a small time step to obtain a trajectory with accuracy comparable to that of Molecular Dynamics is not practical for systems with more than a few degrees of freedom. Fbr small time steps, ordinary solution of classical trajectories is the method of choice. 

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