Computer Modeling of Matter Downloaded from pubs.acs.org by 185.50.250.53 on 10/27/18. For personal use only.
INDEX Brusselator 253 A "Brute force" method 87 Algorithm(s) Green's function Monte Carlo 220 "leap-frog" 2 C metropolis 159 optimization of sampling 159 Cation(s) alkali metal 210, 212 predictor-corrector 2 monatomic 206 rejection sampling 166 -water radial distribution sampling 169 function 207,208 for sampling preferentially near 66 the solute 165 Center-center distance 255 singularity-free 62 Clock, chemical Alkali halides 97 Cluster "critical" 236 Alloys 101 distributions, physical 236 Anion(s) "supercritical" 236 halide 211,212 173 monatomic 208,209 Coefficients, virial Computer storage 153 -water radial distribution field 86 function 208,209 Conductivity, high Conformation defects in polyethylene Aqueous solutions, structure of liquid chains 140 water and dilute 191 Array processor I l l Correlations, critical long-range spatial 260 floating point systems 190-L 112 "Critical" cluster 236 word length on precision, effect of 123 phenomena 231, 261 Atom-atom potential 77, 80 wave number 254 Atoms dissolved in water, mean force Crystal(s) of two noble gas 32 molecular 101 Axilrod-Teller packing in polyethylene 140 fluid 182,186,187 properties in polymer 137 force 182 quantum 219 three body 184 260 potential 174,175,183 Cycle oscillations, limit triple dipole potential 176, 177,186 D B
Banded-matrix approximation Bead chains, eightBead-and-spring model Ben-Nairn Stillinger (BNS) potential Benchmarks general Monte Carlo results of Born-Mayer-Huggins Potential Born-Mayer repulsions Bottlenecks Bound states (dimers) Bragg-Williams (meanfield)model Brownian motion
141 134 125 35 118 118 116 2 97 233 235 242 126
Density harmonic coefficient 82 -orientation profile 83 profile . 80, 82 Differential equations, "stiff" 251 Dimers (bound states) 235 Dimer, formation and destruction 237 Discrete-event simulation 233 Discs, hard 192 Distance, center-center 66 Distance, site-site 66 Distribution function anion-water radial 208, 209 for binding energy, quasicomponent 196, 201
267
COMPUTER MODELING OF MATTER
268
Distribution function (continued) cation-water radial 207, 208 methane-water radial 202 oxygen-oxygen radial 197 probability 168 quasicomponent . 197,199, 203, 210-212 radial 173,185, 186 solute-solvent radial 167,168 Distributions, physical cluster 236 Dynamic and equilibrium properties . 125 Dynamics, many-body 233 E
Energy calculations, conformational 137 configurational internal 69 free 173 function, Kistenmacher, Popkie, and Clementi (KPC) "simple" potential 40 internal 173 kinetic 23-25 minimization 138 partial molar internal 201 potential 19,148 and pressure 184 quasicomponent distribution function for binding 196, 201 surface, Hartfree-Fock 40 thermodynamic internal 196 total 4,19,20 Equilibrium data 129 Equilibrium properties 185 dynamic and 125 Ewald method 88 Ewald summation 22 F
Fletcher-Reeves method 137 Floating Point Systems 190-L Array Processor 112 Fluctuations 239 Fluid(s) Axilrod-Teller 182,186,187 Lennard-Jones 73,182,186,187 liquid-vapor surface of molecular .. 76 molecular dynamics simulations of simple 172 Monte Carlo calculations on 159 "pair theory" 172 two-dimensional Lennard-Jones .... 174 Fluoride 208 Force 148 Axilrod-Teller 182 dispersion 97 Lennard-Jones 182
Force (continued) potential, shifted 146 three body 173 Axilrod-Teller 184 of two noble gas atoms dissolved in water, mean 32 two- and three-body 182 Formalism, Hastings 161 Fourier transform method 88 Freezing of simple systems Ill Fused salt systems 88 G
Gas(es) electron molecular dynamics in dilute solids, rare Green s function Monte Carlo algorithm
219 234 97 220
H Halides, alkali Hard-sphere dynamics Hartfree-Fock energy surface Hastings formalism He-3 He-4 structure functions for Host overhead typical values for Hydronium ion, trihydrated
97 244 40 161 219 219 227 120 121 51
I Instabilities chemical 231,239 and nonequilibrium phase transitions 233 nonoscillatory 254 symmetry-breaking 253 and transitions, nonequilibrium 231 Integration schemes, predictorcorrector 155 Interactions, molecular dynamics with three-body 178 Interactions, three-body 172,174 Interference effect 103,105 Ionic interactions, molecular dynamics simulations of liquids with 1 Isomerization model, cooperative 248, 249 Isomerization reaction, cooperative 242
J Jonesfluid,two-dimensional, Lennard-
174
269
INDEX
K Kinetics, Markovian stochastic description of chemical 241 Kistenmacher Popkie Clementi potential function 40, 42 Kramers-Kronig dispersion relations . 92 Kubo type relations 87 L
Lattice-model polymer chain 125 "Leap-frog" algorithm 2 Lennard-Jones fluid 73,182,186,187 two-dimensional 174 force 182 particles 192 spheres 32 system 98 Limit cycle 255 "Link" system 88 LiOH, hydrate of 51 Liquid(s) with ionic interactions, molecular dynamics simulations of 1 molecular 144, 151 nucleation, vapor236 phase transition, vapor236 quantum 219 -vapor interface, structure of a 72 -vapor surface of molecular fluids 76 Lithium 207 cation dihydrated 47 hydrated 35 four-hydrated 47, 51, 52 trihydrated 47 with water, complexes of the 44 -water potential calibration 40 Loops, inner Monte Carlo 115 M
Marginal stability 243 Matrix o, optimization of step acceptance . 162 approximation, banded 141 Q, optimization of transition 162 Matter, neutron 219 Matter, nuclear 219 Melting of simple systems Ill Metals 101 Metastable 243 Methane 203 dilute aqueous solution of 200 molecular dynamics simulation of 62 stereographic view of 204, 205 -water radial distribution 202 Metropolis algorithm 159
Models studied, root mean squared deviations for 67 Molecular crystals 101 dynamics 231 (CMD), conventional 178 in dilute gases 234 (MD) method 94 program 155 reactive 241, 243 simulations 144 of liquids with ionic interactions 1 of methane 62 of simple fluids 172 with three-body interactions 178 liquids 144,151 site-site potentials for 145 mechanics method 137 Molecules, spherical 147 Momentum, total 8,9 Monte Carlo algorithm, Greens function 220 benchmarks 118 calculations on fluids 159 computer simulation 202 loops, inner 115 methods 111,219 program, N-particle 119 simulation(s) 50, 56, 57, 72 of water 29 studies 191 techniques 125 Motion, Brownian 126 Multiple time scales 232,233 Multiple time step (MTS) method 144,147,179 linear 183 N Nernst-Einstein equation 87 Newton-Raphson method 137,139,142 Nonadditivity, previous work on 173 Nucleation chemical 244,249 homogeneous 234 RMD simulation of chemical 249 vapor-liquid 236 Nucleus 243 "supercritical" 243 O
Orientation profile, density83 Oscillations, chemical 239 Oscillations, limit cycle 260 Oxygen-oxygen radial distribution .... 196 function 197
COMPUTER
270 P
"Pair theory" of fluids 172 Parameter sets studied, potential 66 Particle trajectories 188 Pechhold kink 140, 142 Peskun's results 164 Phonons 94, 106, 107 Polarization, effect of 102 Polarization Model 35, 39 Polyethylene chains, conformation defects in 140 Polymer chain, lattice-model 125 chain, single linear 126 system, multichain 125 Potassium 208 Potential function(s) 42 Kistenmacher Popkie Clementi 42 Precision, effect of AP word length on 123 Predictor-corrector algorithm 2 Predictor-corrector integration schemes 155 Pressure 69 internal energy and 184 Program development 114 Proton, quadrihydrated 51 Q Quantum crystals Quantum liquids
219 219 R
Radial distribution, oxygen-oxygen 196 Reaction, trimolecular 253 Reactive molecular dynamics (RMD) 240 Rejection sampling algorithm 166 Relaxation method 137, 142 hybrid Newton Raphson 139 Relaxation times for vector end-to-end length 133 Reneker twist 140 RMD simulation^) 248 of chemical nucleation 249 Root mean squared deviations for models studied 67 Rouse model 126 S
Salts, molten Shifted force potential Simulations averages obtained during chemical hierarchy of of liquids with ionic interactions, molecular dynamics
1 146 84 260 261 1
MODELING O F M A T T E R
Simulations (continued) methods, discrete microscopic chemical stochastic 241, Singularity-free algorithm Site-site distance Site-site potentials) for molecular liquids Smooth twist Sodium Solids, collective modes in Solute, algorithm for sampling preferentially near the Solute-solvent radial distribution function Solutions, aqueous Speed, computing Spheres Spring model, bead-andST2 potential Stability, marginal Steepest descent method Step methods, multiple time "Stiffness," numerical Stochastic description of chemical kinetics, Markovian Stochastic simulation Storage, computer Storage requirements, computing time and Structure dissipative factor, dynamical spatial dissipative "Supercritical" cluster Symmetry-breaking instabilities
260 249 241 252, 260 62 66 77 145 140 207 94 165 167,168 14 154 192 125 35 243 137 144, 147 241 241 241 153 153 239,255 95 255, 260 236 253
T Teller force, three-body Axilrod184 Teller potential, Axilrod 174-177,183,186 Thermodynamic branch 239 Time, computing 153 Time and storage requirements, computing 153 Transition (s) chemical instabilities 233 equilibrium phase 261 first-order chemical phase 242 nonequilibrium instabilities and 231 nonequilibrium phase 231, 233, 239, 261 phase 231 reactive 244 state theory 233 vapor-liquid phase 236 Trimolecular reaction 253 Truncated potentials 145
271
INDEX
v Van Hove function 95 Vapor interface, structure of a liquid72 -liquid nucleation 236 -liquid phase transition 236 surface of molecular fluids, liquid76 Vector end-to-end length, relaxation times for 133 Velocity autocorrelation functions 10, 13, 18 Verlet algorithm 88
Water (continued) liquid Monte Carlo simulation of potential calibration, lithium cationradial distribution function, anion208, function, cation207, methanestatistical state of liquid 199, Wave number, "critical" Waves, chemical Williams (mean field) model, Bragg-
195 29 40 209 208 202 202 254 239 242
W Water complexes of the lithium cation with and dilute aqueous solutions, structure of liquid
X
44 191
Xenon atoms
32
