Molecular dynamics method described

The potential model used to test the molecular dynamics method described below was a Lennard-Jones 6, 12 pair potential plus Axilrod-Teller triplet potential. The Lennard-Jones model is given by ... 

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... 

The simulations to investigate electro-osmosis were carried out using the molecular dynamics method of Murad and Powles [22] described earher. For nonionic polar fluids the solvent molecule was modeled as a rigid homo-nuclear diatomic with charges q and —q on the two active LJ sites. The solute molecules were modeled as spherical LJ particles [26], as were the molecules that constituted the single molecular layer membrane. The effect of uniform external fields with directions either perpendicular to the membrane or along the diagonal direction (i.e. Ex = Ey = E ) was monitored. The simulation system is shown in Fig. 2. The density profiles, mean squared displacement, and movement of the solvent molecules across the membrane were examined, with and without an external held, to establish whether electro-osmosis can take place in polar systems. The results clearly estab-hshed that electro-osmosis can indeed take place in such solutions. 

Ryabov, V. A. (1996) Molecular dynamics in curved hyperspace. Physics Letters A. 220(4—5) 258—62. (The author describes a new molecular dynamics method considering the crystal as arranged on a curved hypersurface.)... 

This article is organized as follows. In Section 2 ab initio molecular dynamics methods are described. Specifically, in Section 2.1 we discuss the extended Lagrangian atom-centered density matrix (ADMP) technique for simultaneous dynamics of electrons and nuclei in large clusters, and in Section 2.2 we discuss the quantum wavepacket ab initio molecular dynamics (QWAIMD) method. Simulations conducted and new insights obtained from using these approaches are discussed in Section 3 and the concluding remarks are given in Section 4. 

At even lower temperatures, some unusual properties of matter are displayed. Consequently, new experimental and theoretical methods are being created to explore and describe chemistry in these regimes. In order to account for zero-point energy effects and tunneling in simulations, Voth and coworkers developed a quantum molecular dynamics method that they applied to dynamics in solid hydrogen. In liquid helium, superfluidity is displayed in He below its lambda point phase transition at 2.17 K. In the superfluid state, helium s thermal conductivity dramatically increases to 1000 times that of copper, and its bulk viscosity drops effectively to zero. Apkarian and coworkers have recently demonstrated the disappearance of viscosity in superfluid helium on a molecular scale by monitoring the damped oscillations of a 10 A bubble as a function of temperature. These unique properties make superfluid helium an interesting host for chemical dynamics. 

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. 

As an alternative to the normal-mode method, Monte Carlo and molecular dynamics calculations have been performed on small clusters. Monte Carlo and molecular dynamics methods have the virtue of being exact, within calculable error bars, subject to the constraint of the approximate intermo-lecular interactions that are used. Prior to about six years ago both methods were restricted to systems projjerly described by classical mechanics. This restriction implied that systems for which tunneling or low-temjjerature vibrations were important at best could be treated approximately. 

In most cases, the crystal potential is not known a priori. The usual procedure is to introduce some model potential containing several parameters, which are subsequently found by fitting the calculated crystal properties to the observed data available. This procedure has the drawback that the empirical potential thus obtained includes the effects of the approximations made in the lattice dynamics model, which is mostly the harmonic model. It is very useful to have independent and detailed information about the potential from quantum-chemical ab initio calculations. Such information is available for nitrogen (Berns and van der Avoird, 1980) and oxygen (Wormer and van der Avoird, 1984), and we have chosen the results calculated for solid nitrogen and solid oxygen to illustrate in Sections V and VI, respectively, the lattice dynamics methods described in Sections III and IV. Nitrogen is the simplest typical molecular crystal as such it has received much attention from theorists and... 

To perform the design of new molecules based on the approaches described above, powerful computer-aided tools are required. These include molecular modeling tools for visualization and analysis, extraction of 3D structures from databases, construction of 3D models using force fields [77-79] and molecular dynamics methods, docking of 3D models to protein cavities. These methods have been documented in detail in the previous volumes of this series and in a number of recent review articles [80-87]. These will therefore only be discussed in the context of the case studies presented in this volume. 

Molecular dynamics methods are primarily used for the refinement of structural models (Li et al., 1997) or the analysis of molecular interactions (Cappelli et al., 1996 Kothekar et al., 1998). In both cases the time scales to be simulated are within range of current computing technology. Another application area is the study of allosteric movements of proteins (Tanner et al., 1993). Molecular Dynamics approaches to protein-ligand docking are described in Chapter 7 of Volume I. 

Consider the causal model of explanation. Is notthe molecular dynamics simulation of a molecule a classic example of a simulation of a causal process, and is not the causal model of explanation, hence, a perfect candidate to describe these simulations as explanations To address the first question, I consider the two conceptions of causality discussed above to see if either serves to capture the molecular dynamics method as picturing a causal process. Keep in mind that usually when asking whether a process is causal one cannot look at the process itself, but must rely on a model that simulates it. This is not simply a practical necessity in our example, for instance, it... 

The technique has been described in Section 10.15. In summary, a model of solvation is decided upon. The computer uses Monte Carlo or molecular dynamics methods and a simulation of the solvation pattern emerges. The beauty of the method lies in the capacity to vary the model at will by varying the type and number of interactions considered for each model. This will give a simulation for each set of conditions which can then be compared with each other and with results from all the experimental methods described earlier. In effect the computer is used to help find a model which fits experiment. 

The two major methods for the simulations are the Monte Carlo method (so named for its use of random number generation) and the molecular dynamics method. The Monte Carlo method, as applied to problems of chemistry, was first described by N. Metropolis and his co-workers at the Los Alamos... 

An ingenious method of extending the molecular dynamics approach when incorporating quantum mechanics, is given by the scheme of Car and Parri-nello [255]. Their method combines classical MD with parameter-free quantum mechanics to result in an ab initio molecular dynamics method, sometimes also called dynamical simulated annealing. In this approach, the nuclei are treated as classical objects (the Bom-Oppenheimer approximation is still valid) but the electrons are understood from density-functional theory. As we have seen already, the interactions between the electrons and the nuclei can be described satisfactorily by pseudopotentials (see Section 2.15.2), together with plane-wave basis sets, supercells (see Section 2.18), and periodic boundary conditions. 

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