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.

Ab-Initio Molecular Dynamics

Abstract: Computer simulation methods, such as Monte Carlo or Molecular Dynamics, are very powerful computational techniques that provide detailed and essentially exact information on classical many-body problems. With the advent of ab-initio molecular dynamics, where the forces are computed on-the-fly by accurate electronic structure calculations, the scope of either method has been greatly extended. This new approach, which unifies Newton's and Schrodinger's equations, allows for complex simulations without relying on any adjustable parameter. This review is intended to outline the basic principles as well as a survey of the field. Beginning with the derivation of Born-Oppenheimer molecular dynamics, the Car-Parrinello method and the recently devised efficient and accurate Car-Parrinello-like approach to Born-Oppenheimer molecular dynamics, which unifies best of both schemes are discussed. The predictive power of this novel second-generation Car-Parrinello approach is demonstrated by a series of applications ranging from liquid metals, to semiconductors and water. This development allows for ab-initio molecular dynamics simulations on much larger length and time scales than previously thought feasible.

Pushing the limits of Monte Carlo simulations for the three-dimensional Ising model

Abstract: While the three-dimensional Ising model has defied analytic solution, various numerical methods like Monte Carlo, Monte Carlo renormalization group, and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic, we have investigated the critical behavior of the simple cubic Ising Model, with lattice sizes ranging from ${16}^{3}$ to ${1024}^{3}$. By analyzing data with cross correlations between various thermodynamic quantities obtained from the same data pool, e.g., logarithmic derivatives of magnetization and derivatives of magnetization cumulants, we have obtained the critical inverse temperature ${K}_{c}=0.221\phantom{\rule{0.16em}{0ex}}654\phantom{\rule{0.16em}{0ex}}626(5)$ and the critical exponent of the correlation length $\ensuremath{ u}=0.629\phantom{\rule{0.16em}{0ex}}912(86)$ with precision that exceeds all previous Monte Carlo estimates.

Aggregation-volume-bias Monte Carlo simulations of vapor-liquid nucleation barriers for Lennard-Jonesium

Abstract: A combination of the aggregation-volume-bias Monte Carlo algorithm and the umbrella sampling technique is applied to investigate homogeneous vapor–liquid nucleation. This combined approach is simple, general, and robust. Its efficiency is demonstrated for nucleation of Lennard-Jonesium, for which the precise calculation of the nucleation barriers takes only a few minutes at higher supersaturations to a few hours at lower supersaturations. Comparison of the simulation results to the classical nucleation theory (CNT) shows that CNT overestimates the barrier heights by a value nearly independent of the supersaturation, but provides a reasonable description of the critical cluster sizes.

Monte Carlo simulations of spin glasses at low temperatures

Abstract: We report the results of Monte Carlo simulations on several spin-glass models at low temperatures. By using the parallel tempering (exchange Monte Carlo) technique we are able to equilibrate down to low temperatures, for moderate sizes, and hence the data should not be affected by critical fluctuations. Our results for short-range models are consistent with a picture proposed earlier that there are large-scale excitations which cost only a finite energy in the thermodynamic limit, and these excitations have a surface whose fractal dimension is less than the space dimension. For the infinite range Viana-Bray model, our results obtained for a similar number of spins, are consistent with standard replica symmetry breaking.