Computational Techniques and Strategies for Monte Carlo Thermodynamic Calculations, with Applications to Nanoclusters

Chapter 1 is a tutorial covering Monte Carlo techniques used by chemists. Introduced first are tutorials on random number generation, the Metropolis Monte Carlo method, estimation of errors and equilibration methods. The problem of non-ergodic behavior is introduced and a variety of methods useful for overcoming that problem are described. Applications and pitfalls to avoid are given. The chapter covers: 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