REVIEWS IN COMPUTATIONAL CHEMISTRY

By JOSEPH WILLIAMS

CONTENTS 1 COMPUTATIONAL TECHNIQUES AND STRATEGIES FOR MONTE CARLO THERMODYNAMIC CALCULATIONS, WITH APPLICATIONS TO NANOCLUSTERS INTRODUCTION METROPOLIS MONTE CARLO RANDOM-NUMBER GENERATION: A FEW NOTES THE GENERALIZED METROPOLIS MONTE CARLO ALGORITHM METROPOLIS MONTE CARLO: THE ‘‘CLASSIC’’ ALGORITHM THE BARKER–WATTS ALGORITHM FOR MOLECULAR ROTATIONS EQUILIBRATION: WHY WAIT? ERROR ESTIMATION QUASI-ERGODICITY: AN INSIDIOUS PROBLEM OVERCOMING QUASI-ERGODICITY MAG-WALKING SUBSPACE SAMPLING JUMP-BETWEEN-WELLS METHOD ATOM-EXCHANGE METHOD HISTOGRAM METHODS UMBRELLA SAMPLING J-WALKING, PARALLEL TEMPERING, AND RELATED METHODS J-WALKING PARALLEL TEMPERING JUMPING TO TSALLIS DISTRIBUTIONS APPLICATIONS TO MICROCANONICAL SIMULATIONS MULTICANONICAL ENSEMBLE/ENTROPY SAMPLING CONCLUSIONS ACKNOWLEDGMENTS REFERENCES 2 COMPUTING HYDROPHOBICITY SIMULATION METHODS STATISTICAL MECHANICS AND THERMODYNAMICS PARTICLE INSERTION METHODS PERTURBATION METHODS THERMODYNAMIC INTEGRATION FREE ENERGY AND STRUCTURE ENTROPY AND ENERGY HEAT CAPACITY HYDROPHOBIC HYDRATION STRUCTURE HYDRATION FREE ENERGY HYDRATION ENTROPY AND ENERGY HYDRATION HEAT CAPACITY WATER MIMICS HYDROPHOBIC INTERACTIONS FREE ENERGY OF ASSOCIATION ENTROPY AND ENERGY OF ASSOCIATION HEAT CAPACITY OF ASSOCIATION PRESSURE DEPENDENCE OF HYDROPHOBIC INTERACTIONS OUTLOOK 3 BORN–OPPENHEIMER DIRECT DYNAMICS CLASSICAL TRAJECTORY SIMULATIONS CLASSICAL TRAJECTORY SIMULATIONS TRADITIONAL APPROACH: ANALYTIC POTENTIAL ENERGY SURFACES DIRECT DYNAMICS SIMULATIONS BORN–OPPENHEIMER DIRECT DYNAMICS SEMIEMPIRICAL ELECTRONIC STRUCTURE THEORY AB INITIO ELECTRONIC STRUCTURE THEORY QMÞMM AND QM/MM METHODS INTEGRATING THE CLASSICAL EQUATIONS OF MOTION CARTESIAN COORDINATES INSTANTANEOUS NORMAL-MODE COORDINATES TRAJECTORY INITIAL CONDITIONS UNIMOLECULAR REACTIONS BIMOLECULAR REACTIONS EXCITING THE TRANSITION STATE GAS–SURFACE COLLISIONS IMPORTANCE OF QUANTUM EFFECTS INTRAMOLECULAR DYNAMICS AND UNIMOLECULAR REACTIONS SUMMARY APPLICATIONS OF BORN–OPPENHEIMER DIRECT DYNAMICS CYCLOPROPANE STEREOMUTATION CL Þ CH3CL CENTRAL-BARRIER DYNAMICS OH Þ CH3F EXIT-CHANNEL DYNAMICS PROTONATED GLYCINE SURFACE-INDUCED DISSOCIATION CONCLUDING REMARKS 4 THE POISSON–BOLTZMANN EQUATION STATE OF THE FIELD OVERVIEW OF THE CHAPTER A BRIEF HISTORY THE POISSON–BOLTZMANN EQUATION ANALYTICAL SOLUTIONS TO THE POISSON–BOLTZMANN EQUATION PLANAR GEOMETRY: THE MEMBRANE MODEL CURVED SURFACES: CYLINDERS AND SPHERES CYLINDRICAL GEOMETRY: THE POLYMER MODEL SPHERICAL GEOMETRY: THE MICELLE MODEL MIXED-GEOMETRY STUDIES NUMERICAL SOLUTIONS TO THE POISSON-BOLTZMANN EQUATION ONE-DIMENSIONAL GEOMETRIES FINITE-DIFFERENCE/FINITE-ELEMENT ALGORITHMS ALTERNATIVE GENERAL-PURPOSE METHODS LARGE-SCALE APPLICATIONS BEYOND THE POISSON–BOLTZMANN EQUATION ASSUMPTIONS OF THE POISSON–BOLTZMANN EQUATION COMMON APPROXIMATIONS TO THE POISSON–BOLTZMANN EQUATION ALTERNATIVES TO THE POISSON–BOLTZMANN EQUATION