Molecular dynamics numerical experiments

The method of molecular dynamics (numerical modeling of the dynamic type) combines both theoretical and experimental approaches. The method specifies the interaction potentials of molecules (atoms), the temperature as a chaotic distribution of velocities, and the laws of motion (in our case, the integration of Newton s laws for each molecule). At the same time, molecular dynamic simulation is an experiment, which enables one to observe the behavior of molecules (atoms) with a resolution of up to 10" s in the time domain and up to 10 m in the space domain, which can t be realized in any other experiment. 

A dynamic numerical experiment was used to study the molecular mechanism of the Rehbinder effect using molecular dynamic simulation [71-74]. A numerical experiment allows one to observe tine details of the process being modeled. However, the experiment is limited in terms of the size of the system (up to 10 particles) and the observation time (for argon this time is 10" ° s). Consequently, processes involving a large number of particles, or processes that take place over periods significantly exceeding the maximum time of dynamic-type numerical experiments, can t be modeled. 

Verlet, L. Computer experiments on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev. 165 (1967) 98-103. Ryckaert, J.-P., Ciccotti,G., Berendsen, H.J.C. Numerical integration of the cartesian equations of motion of a system with constraints Molecular dynamics of n-alkanes. Comput. Phys. 23 (1977) 327-341. 

Verlet, L. Computer Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules. Physical Review 159 (1967) 98-103 Janezic, D., Merzel, F. Split Integration Symplectic Method for Molecular Dynamics Integration. J. Chem. Inf. Comput. Sci. 37 (1997) 1048-1054 McLachlan, R. I. On the Numerical Integration of Ordinary Differential Equations by Symplectic Composition Methods. SIAM J. Sci. Comput. 16 (1995) 151-168... 

This paper is meant as a contribution to systematize the quantum-classical modeling of molecular dynamics. Hence, we are interested in an extended theoretical understanding of the models rather than to further contribute to the bunch of numerical experiments which have been performed on certain models by applying them to particular molecular systems. Thus, we will carefully review the assumptions under which our models are known to approximate the full quantum dynamical (QD) evolution of the system. This knowledge... 

In his early survey of computer experiments in materials science , Beeler (1970), in the book chapter already cited, divides such experiments into four categories. One is the Monte Carlo approach. The second is the dynamic approach (today usually named molecular dynamics), in which a finite system of N particles (usually atoms) is treated by setting up 3A equations of motion which are coupled through an assumed two-body potential, and the set of 3A differential equations is then solved numerically on a computer to give the space trajectories and velocities of all particles as function of successive time steps. The third is what Beeler called the variational approach, used to establish equilibrium configurations of atoms in (for instance) a crystal dislocation and also to establish what happens to the atoms when the defect moves each atom is moved in turn, one at a time, in a self-consistent iterative process, until the total energy of the system is minimised. The fourth category of computer experiment is what Beeler called a pattern development... 

At present we are far from an understanding of the protein folding process. Even numerical methods as e.g. molecular dynamics simulations do not lead to realistic predictions. Experiments on the folding process have been performed initially on the millisecond time-scale. It was only recently that new techniques - temperature jump or triplet-triplet quenching experiments - allowed a first access to the nanosecond time domain [2-4]. However, the elementary reactions in protein folding occur on the femto- to picosecond time-scale (femtobiology). In order to allow experiments in this temporal range we developed a new... 

One has to emphasize that Eqs. (82) and (83) do not involve the Born-Oppenheimer approximation although the nuclear motion is treated classically. This is an important advantage over the quantum molecular dynamics approach [47-54] where the nuclear Newton equations (82) are solved simultaneously with a set of ground-state KS equations at the instantaneous nuclear positions. In spite of the obvious numerical advantages one has to keep in mind that the classical treatment of nuclear motion is justified only if the probability densities (R, t) remain narrow distributions during the whole process considered. The splitting of the nuclear wave packet found, e.g., in pump-probe experiments [55-58] cannot be properly accounted for by treating the nuclear motion classically. In this case, one has to face the complete system (67-72) of coupled TDKS equations for electrons and nuclei. 

The understanding of bulk polymer dynamics involves new and difficult questions such as the relative importance of intra and inter chain constraints, or the relation between molecular motions and the complicated mechanical behavior of these materials. Numerous experiments on bulk polymers using ESR or... 

We will not deal here with the subject of EPR spectroscopy of the solid state. In this field of investigation a kind of delta-like approach such as that recently proposed to deal with molecular dynamics in the liquid state has developed naturally. According to the European Molecular Liquid Group (EMLG), the symbol A symbolizes the cooperative efforts of computer simulation, experiment, and theory. Knak Jensen and Hansen, for instance, carried out a computer simulation of the dynamics of N identical spins placed in a rigid simple cubic lattice subject to an external magnetic field Bq. a further example of numerical study is the paper of Sur and Lowe. Free-induction decay measurements,on the other hand, represent the experimental comer of this ideal triangle, the theoretical comer of which is, of course, expressed by the theoretical papers mentioned above. 

Computational methods are increasingly valuable supplements to experiments and theories in the quest to understand complex liquids. Simulations and computations can be aimed at either molecular or microstructural length scales. The most widely used molecular-scale simulation methods are molecular dynamics. Brownian dynamics, and Monte Carlo sampling. Computations can also be performed at the continuum level by numerical solutions of field equations or by Stokesian dynamics methods, described briefly below. 

Recent numerical experiments by the method of molecular dynamics have shown that, for a chain model consisting of particles joined by ideally rigid bonds, the Van der Waals interactions of chain units cause only a little change in the dependence of relaxation times on the wave vector of normal modes of motions, i.e. in the character and shape of the relaxation spectrum. It was found that for the model chain the important relationship... 

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