A new approach to Monte Carlo simulations in statistical physics

Landau, D. P.; Wang, F.

doi:10.1590/s0103-97332004000300004

Cited by 28 publications

(15 citation statements)

References 61 publications

(82 reference statements)

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“…Such improvements are realized only through biased sampling along . Many techniques fall under this category including the adaptive umbrella sampling, 7 metadynamics of Laio and Parrinello, [8][9][10][11][12] and flat histogram techniques used mainly, but not exclusively, in conjunction with Monte Carlo methods, such as the multicanonical method, 13 the method of Wang and Landau, [14][15][16][17][18][19] and the transition matrix method. [20][21][22] Another successful approach is the adaptive biasing force ͑ABF͒ method proposed by Darve and Pohorille.…”

Section: Introductionmentioning

confidence: 99%

Adaptive biasing force method for scalar and vector free energy calculations

Darve

Rodríguez‐Gómez

Pohorille

2008

The Journal of Chemical Physics

764

807

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In free energy calculations based on thermodynamic integration, it is necessary to compute the derivatives of the free energy as a function of one (scalar case) or several (vector case) order parameters. We derive in a compact way a general formulation for evaluating these derivatives as the average of a mean force acting on the order parameters, which involves first derivatives with respect to both Cartesian coordinates and time. This is in contrast with the previously derived formulas, which require first and second derivatives of the order parameter with respect to Cartesian coordinates. As illustrated in a concrete example, the main advantage of this new formulation is the simplicity of its use, especially for complicated order parameters. It is also straightforward to implement in a molecular dynamics code, as can be seen from the pseudocode given at the end. We further discuss how the approach based on time derivatives can be combined with the adaptive biasing force method, an enhanced sampling technique that rapidly yields uniform sampling of the order parameters, and by doing so greatly improves the efficiency of free energy calculations. Using the backbone dihedral angles Phi and Psi in N-acetylalanyl-N'-methylamide as a numerical example, we present a technique to reconstruct the free energy from its derivatives, a calculation that presents some difficulties in the vector case because of the statistical errors affecting the derivatives.

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Section: Introductionmentioning

confidence: 99%

Adaptive biasing force method for scalar and vector free energy calculations

Darve

Rodríguez‐Gómez

Pohorille

2008

The Journal of Chemical Physics

764

807

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“…Wang-Landau sampling is a Monte Carlo technique that was developed as a temperature independent, iterative method with the ability to sample rough energy landscapes [5,14]. The technique was originally implemented for discrete models [3], and in order to perform simulations of a continuous model a few issues must be addressed.…”

Section: Methodsmentioning

confidence: 99%

“…Because g(E) becomes extremely large in the actual computation, the logarithm of the density of states, ln[g(E)], is used to prevent overflow during the actual simulation. More details about Wang-Landau sampling can be found elsewhere [5,14].…”

Section: Methodsmentioning

confidence: 99%

“…However, traditional Monte Carlo methods have had trouble sampling the rough energy landscapes associated with some polymer models. The Wang-Landau method [3][4][5] has proven quite useful in overcoming these inefficiencies. Since the target of our current study is understanding the behavior of a flexible homopolymer when the temperature is lowered and multiple states begin to compete, Wang-Landau sampling is very well suited for this problem.…”

Section: Introductionmentioning

confidence: 99%

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Developments in Wang-Landau simulations of a simple continuous homopolymer

Seaton¹,

Mitchell²,

Landau³

2008

Braz. J. Phys.

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The Wang-Landau method is used to study thermodynamic properties of a three-dimensional flexible homopolymer chain with continuous monomer positions. Results describing the coil-globule and solid-liquid transitions are presented for chain lengths up to N = 100. In order to elucidate the thermodynamic behavior, finite chain length effects and the influence of the energy range over which the density of states is determined are carefully analyzed. Simulation efficiency is also studied and it is shown that setting the natural logarithm of the final modification factor equal to 10 −6 is an appropriate choice for this model.

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“…The drawback of the flat histogram method is the slow diffusion of the random walk which is the same as in the multicanonical method. Nevertheless, no method is more efficient than that recently proposed by Wang and Landau [6][7][8][9] which allows one to get around these difficulties even for large systems.…”

Section: Introductionmentioning

confidence: 99%

Wang-Landau sampling in three-dimensional polymers

Netto¹,

Silva²,

Caparica³

et al. 2006

Braz. J. Phys.

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Monte Carlo simulations using Wang-Landau sampling are performed to study three-dimensional chains of homopolymers on a lattice. We confirm the accuracy of the method by calculating the thermodynamic properties of this system. Our results are in good agreement with those obtained using Metropolis importance sampling. This algorithm enables one to accurately simulate the usually hardly accessible low-temperature regions since it determines the density of states in a single simulation.

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A new approach to Monte Carlo simulations in statistical physics

Cited by 28 publications

References 61 publications

Adaptive biasing force method for scalar and vector free energy calculations

Adaptive biasing force method for scalar and vector free energy calculations

Developments in Wang-Landau simulations of a simple continuous homopolymer

Wang-Landau sampling in three-dimensional polymers

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