Dynamic Simulator

Since the development of grazing incidence x-ray diffraction, much of the convincing evidence for long-range positional order in layers has come from this technique. Structural relaxations from distorted hexagonal structure toward a relaxed array have been seen in heneicosanol [215]. Rice and co-workers combine grazing incidence x-ray diffraction with molecular dynamics simulations to understand several ordering transitions [178,215-219]. 

Small metal clusters are also of interest because of their importance in catalysis. Despite the fact that small clusters should consist of mostly surface atoms, measurement of the photon ionization threshold for Hg clusters suggest that a transition from van der Waals to metallic properties occurs in the range of 20-70 atoms per cluster [88] and near-bulk magnetic properties are expected for Ni, Pd, and Pt clusters of only 13 atoms [89] Theoretical calculations on Sin and other semiconductors predict that the stmcture reflects the bulk lattice for 1000 atoms but the bulk electronic wave functions are not obtained [90]. Bartell and co-workers [91] study beams of molecular clusters with electron dirfraction and molecular dynamics simulations and find new phases not observed in the bulk. Bulk models appear to be valid for their clusters of several thousand atoms (see Section IX-3). 

Bartell and co-workers have made significant progress by combining electron diffraction studies from beams of molecular clusters with molecular dynamics simulations [14, 51, 52]. Due to their small volumes, deep supercoolings can be attained in cluster beams however, the temperature is not easily controlled. The rapid nucleation that ensues can produce new phases not observed in the bulk [14]. Despite the concern about the appropriateness of the classic model for small clusters, its application appears to be valid in several cases [51]. 

It is possible to use the quantum states to predict the electronic properties of the melt. A typical procedure is to implement molecular dynamics simulations for the liquid, which pemiit the wavefiinctions to be detemiined at each time step of the simulation. As an example, one can use the eigenpairs for a given atomic configuration to calculate the optical conductivity. The real part of tire conductivity can be expressed as... 

Figure Al.3.30. Theoretical frequency-dependent conductivity for GaAs and CdTe liquids from ab initio molecular dynamics simulations [42].

Progress in the theoretical description of reaction rates in solution of course correlates strongly with that in other theoretical disciplines, in particular those which have profited most from the enonnous advances in computing power such as quantum chemistry and equilibrium as well as non-equilibrium statistical mechanics of liquid solutions where Monte Carlo and molecular dynamics simulations in many cases have taken on the traditional role of experunents, as they allow the detailed investigation of the influence of intra- and intemiolecular potential parameters on the microscopic dynamics not accessible to measurements in the laboratory. No attempt, however, will be made here to address these areas in more than a cursory way, and the interested reader is referred to the corresponding chapters of the encyclopedia. 

Specific solute-solvent interactions involving the first solvation shell only can be treated in detail by discrete solvent models. The various approaches like point charge models, siipennoleciilar calculations, quantum theories of reactions in solution, and their implementations in Monte Carlo methods and molecular dynamics simulations like the Car-Parrinello method are discussed elsewhere in this encyclopedia. Here only some points will be briefly mentioned that seem of relevance for later sections. 

Predicting the solvent or density dependence of rate constants by equation (A3.6.29) or equation (A3.6.31) requires the same ingredients as the calculation of TST rate constants plus an estimate of and a suitable model for the friction coefficient y and its density dependence. While in the framework of molecular dynamics simulations it may be worthwhile to numerically calculate friction coefficients from the average of the relevant time correlation fiinctions, for practical purposes in the analysis of kinetic data it is much more convenient and instructive to use experimentally detemiined macroscopic solvent parameters. 

Wang W, Nelson K A, Xiao L and Coker D F 1994 Molecular dynamics simulation studies of solvent cage effects on photodissociation in condensed phases J. Chem. Phys. 101 9663-71... 

Batista V S and Coker D F 1996 Nonadiabatic molecular dynamics simulation of photodissociation and geminate recombination of liquid xenon J. Chem. Phys. 105 4033-54... 

At any geometry g.], the gradient vector having components d EjJd Q. provides the forces (F. = -d Ej l d 2.) along each of the coordinates Q-. These forces are used in molecular dynamics simulations which solve the Newton F = ma equations and in molecular mechanics studies which are aimed at locating those geometries where the F vector vanishes (i.e. tire stable isomers and transition states discussed above). 

Wilson M R 1997 Molecular dynamics simulations of flexible liquid crystal molecules using a Gay-Berne/Lennard-Jones model J. Chem. Phys. 107 8654-63... 

Haile J M 1992 Molecular Dynamics Simulation Elementary Methods (New York Wiley)... 

Rapaport D C 1995 The Art of Molecular Dynamics Simulation (Cambridge Cambridge University Press)... 

SchlickT, Mandziuk M, Skeel R D and Srinivas K 1998 Nonlinear resonance artifacts in molecular dynamics simulations J. Comput. Phys. 140 1-29... 

Ciccotti G and Ryckaert J P 1986 Molecular dynamics simulation of rigid molecules Comput. Phys. Rep. 4 345-92... 

Procacci P, March M and Martyna G J 1998 Electrostatic calculations and multiple time scales in molecular dynamics simulation of flexible molecular systems J. Chem. Phys. 108 8799-803... 

Andersen H C 1980 Molecular dynamics simulations at constant pressure and/or temperature J. Chem. 

Tobias D J, Martyna G J and Klein M L 1993 Molecular dynamics simulations of a protein In the canonical ensemble J. Phys. Chem. 9712959-66... 

Alejandre J, Tildesley D J and Chapela G A 1995 Molecular dynamics simulation of the orthobaric densities and surface tension of water J. Chem. Phys. 102 4574-83... 

Holian B L and Lomdahl P S 1998 Plasticity induced by shockwaves in nonequilibrium molecular-dynamics simulations Soienoe 280 2085-8... 

Hilbers P A J and Esselink K 1993 Parallel computing and molecular dynamics simulations Computer Simulation In Chemloal Physios /o 397 NATO ASI Series Ced M P Allen and D J Tlldesley (Dordrecht Kluwer) pp 473-95... 

Often a degree of freedom moves very slowly for example, a heavy-atom coordinate. In that case, a plausible approach is to use a sudden approximation, i.e. fix that coordinate and do reduced dimensionality quantum-dynamics simulations on the remaining coordinates. A connnon application of this teclmique, in a three-dimensional case, is to fix the angle of approach to the target [120. 121] (see figure B3.4.14). 

Niv M Y, Krylov A I and Gerber R B 1997 Photodissociation, electronic relaxation and recombination of HCI in Ar-n(HCI) clusters—non-adiabatic molecular dynamics simulations Faraday Discuss. Chem. Soc. 108 243-54... 

Sokal A D 1995 Monte Carlo and Molecular Dynamics Simulations in Polymer Science ed K Binder (New York Oxford University Press) oh 3... 

Kremer K and Grest G S 1990 Dynamics of entangled linear polymer melts a molecular-dynamics simulation J Chem. Phys. 92 5057... 

Figure C2.3.7. Snapshot of micelle of sodium octanoate obtained during molecular dynamics simulation. The darkest shading is for sodium counter-ions, the lightest shading is for oxygens and the medium shading is for carbon atoms. Reproduced by pennission from figure 2 of [36].

Madura J D, Davis M E, Gilson, M K, Wade R C, Luty B A and McCammon J A 1994 Biological applications of electrostatic calculations and Brownian dynamics simulations Rev. Comput. Chem. 5 229-67... 

Weakliem P C and Carter E A 1993 Surface chemical reactions studied via ab /n/f/o-derived molecular dynamics simulations fluorine etching of Si(IOO) J. Chem Phys. 98 737-45... 

Barone M E and Graves D B 1995 Molecular dynamics simulations of direct reactive ion etching of silicon by fluorine and chlorine J. Appi. Phys. 78 6604-15... 

Helmer B A and Graves D B 1997 Molecular dynamics simulations of fluorosllyl Ions with silicon J. Vac. Sc/. Technol. A 15 2252-61... 

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