By David M. Ferguson, J. Ilja Siepmann, Donald G. Truhlar, Ilya Prigogine, Stuart A. Rice
In Monte Carlo tools in Chemical Physics: An creation to the Monte Carlo technique for Particle Simulations J. Ilja Siepmann Random quantity turbines for Parallel functions Ashok Srinivasan, David M. Ceperley and Michael Mascagni among Classical and Quantum Monte Carlo equipment: "Variational" QMC Dario Bressanini and Peter J. Reynolds Monte Carlo Eigenvalue equipment in Quantum Mechanics and Statistical Mechanics M. P. Nightingale and C.J. Umrigar Adaptive Path-Integral Monte Carlo tools for exact Computation of Molecular Thermodynamic houses Robert Q. Topper Monte Carlo Sampling for Classical Trajectory Simulations Gilles H. Peslherbe Haobin Wang and William L. Hase Monte Carlo ways to the Protein Folding challenge Jeffrey Skolnick and Andrzej Kolinski Entropy Sampling Monte Carlo for Polypeptides and Proteins Harold A. Scheraga and Minh-Hong Hao Macrostate Dissection of Thermodynamic Monte Carlo Integrals Bruce W. Church, Alex Ulitsky, and David Shalloway Simulated Annealing-Optimal Histogram tools David M. Ferguson and David G. Garrett Monte Carlo tools for Polymeric structures Juan J. de Pablo and Fernando A. Escobedo Thermodynamic-Scaling tools in Monte Carlo and Their software to part Equilibria John Valleau Semigrand Canonical Monte Carlo Simulation: Integration alongside Coexistence traces David A. Kofke Monte Carlo equipment for Simulating section Equilibria of advanced Fluids J. Ilja Siepmann Reactive Canonical Monte Carlo J. Karl Johnson New Monte Carlo Algorithms for Classical Spin platforms G. T. Barkema and M.E.J. NewmanContent:
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Additional resources for Advances in Chemical Physics: Monte Carlo Methods in Chemical Physics, Volume 105
The use of quasi-random numbers in quadrature has not been widespread because the claims of superiority of quasi-random over pseudorandom for quadrature have not been shown empirically, especially for high-dimensional integrals and never in MCMC simulations . QRNs work best in low-dimensional spaces where the spacing between the points can be made small with respect to the curvature of the integrand. QRNs work well for very smooth integrands. The Boltzmann distribution exp( - V(R)/k,T ) is highly peaked for R, a many-dimensional point.
An extension of this argument to the electron-electron cusp is also readily done. In this case, as electron i approaches electron j , one has a two-body problem essentially equivalent to the hydrogenic atom. Therefore, in analogy to the preceding electron-nucleus case, one obtains the cusp conditions 1 1 unlike spin like spin For like spins, the vanishing of the Slater determinant at rij = 0 contributes partially to satisfying the cusp condition. ) From these equations we see the need for explicit two-body terms in the wavefunction, for with a sufficiently flexible form of Y, we can then satisfy the cusp conditions, thereby matching the Coulomb singularity for any particle pair with terms from the kinetic energy.
3) where z is the step size of the time integration and x is a Gaussian random variable with zero mean and unit width. Numerically one can use the Langevin equation to generate the path of a configuration, or random walker (more generally, an ensemble of such walkers), through position space. As with Metropolis, this path is also a Markov chain. One can see that the function F(R) acts as a drift, pushing the walkers toward regions of configuration space where the trial wavefunction is large. This increases the efficiency of the simulation, in contrast to the standard Metropolis move where the walker has the same probability of moving in every direction.