Monte Carlo molecular modeling

About: Monte Carlo molecular modeling is a research topic. Over the lifetime, 11307 publications have been published within this topic receiving 409122 citations.

Monte Carlo simulations: Hidden errors from "good" random number generators.

Abstract: The Wolff algorithm is now accepted as the best cluster-flipping Monte Carlo algorithm for beating ``critical slowing down.'' We show how this method can yield incorrect answers due to subtle correlations in ``high quality'' random number generators.

Monte Carlo evaluation of transport coefficients

Abstract: A method is developed for evaluating transport coefficients in asymmetric geometries using the Monte Carlo method. The method is applied to the stellarator.

Computational investigations of low-discrepancy sequences

Abstract: The Halton, Sobol, and Faure sequences and the Braaten-Weller construction of the generalized Halton sequence are studied in order to assess their applicability for the quasi Monte Carlo integration with large number of variates. A modification of the Halton sequence (the Halton sequence leaped) and a new construction of the generalized Halton sequence are suggested for unrestricted number of dimensions and are shown to improve considerably on the original Halton sequence. Problems associated with estimation of the error in quasi Monte Carlo integration and with the selection of test functions are identified. Then an estimate of the maximum error of the quasi Monte Carlo integration of nine test functions is computed for up to 400 dimensions and is used to evaluate the known generators mentioned above and the two new generators. An empirical formula for the error of the quasi Monte Carlo integration is suggested.

Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

Abstract: Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.

Generalized-ensemble algorithms: enhanced sampling techniques for Monte Carlo and molecular dynamics simulations.

Abstract: In complex systems with many degrees of freedom such as spin glass and biomolecular systems, conventional simulations in canonical ensemble suffer from the quasi-ergodicity problem. A simulation in generalized ensemble performs a random walk in potential energy space and overcomes this difficulty. From only one simulation run, one can obtain canonical ensemble averages of physical quantities as functions of temperature by the single-histogram and/or multiple-histogram reweighting techniques. In this article we review the generalized ensemble algorithms. Three well-known methods, namely, multicanonical algorithm (MUCA), simulated tempering (ST), and replica-exchange method (REM), are described first. Both Monte Carlo (MC) and molecular dynamics (MD) versions of the algorithms are given. We then present five new generalized-ensemble algorithms which are extensions of the above methods.