Energy estimators for random series path-integral methods

Predescu, Cristian; Sabo, Dubravko; Doll, J. D.; Freeman, David L.

doi:10.1063/1.1619372

Cited by 27 publications

(59 citation statements)

References 26 publications

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“…20 As shown by Predescu and Doll, 14 the H-method estimator can be put into the ''force-force correlation'' form by a simple integration by parts. This form requires the first-order derivatives of the potential only.…”

Section: ͑22͒mentioning

confidence: 99%

“…Therefore, the variance of the T-method estimator is lower than that of the virial estimator because the classical part of the energy is explicitly introduced as a constant and is not obtained from the virial theorem. In a recent study of the (H 2 ) 22 cluster at the temperature of 6 K, 20 difficulties associated with the virial estimator for low-temperature systems 4,7,9 were not observed to appear for the T-method estimator introduced by Predescu and Doll. Such differences between the estimators are even more significant for the heat capacity estimators and will be revealed in the present paper by comparing the statistical errors for the Predescu and Doll-type estimators with those for the double virial estimator.…”

Section: Introductionmentioning

confidence: 99%

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Heat capacity estimators for random series path-integral methods by finite-difference schemes

Predescu

Sabo

Doll

et al. 2003

The Journal of Chemical Physics

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101

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Previous heat capacity estimators used in path integral simulations either have large variances that grow to infinity with the number of path variables or require the evaluation of first-and second-order derivatives of the potential. In the present paper, we show that the evaluation of the total energy by the T-method estimator and of the heat capacity by the TT-method estimator can be implemented by a finite difference scheme in a stable fashion. As such, the variances of the resulting estimators are finite and the evaluation of the estimators requires the potential function only. By comparison with the task of computing the partition function, the evaluation of the estimators requires kϩ1 times more calls to the potential, where k is the order of the difference scheme employed. Quantum Monte Carlo simulations for the Ne 13 cluster demonstrate that a second order central-difference scheme should suffice for most applications.

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Section: ͑22͒mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Heat capacity estimators for random series path-integral methods by finite-difference schemes

Predescu

Sabo

Doll

et al. 2003

The Journal of Chemical Physics

Self Cite

101

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“…Therefore, the thermodynamic estimators obtained from formal differentiation against the inverse temperature have finite variance in the limit of large number of path variables [13,32,33]. As for random series, Eq.…”

Section: B Sampling Efficiency For the Normal Mode Approach To Lie-tmentioning

confidence: 99%

“…(48). The estimators have been reviewed elsewhere [32,33]. In the case where all path variables are updated simultaneously, we have employed the same maximal displacements for all variables a l,j and b l,j .…”

Section: An Application Of the Lévy-ciesielski Implementationmentioning

confidence: 99%

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Lévy-Ciesielski random series as a useful platform for Monte Carlo path integral sampling

Predescu¹

2005

Phys. Rev. E

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We demonstrate that the Lévy-Ciesielski implementation of Lie-Trotter products enjoys several properties that make it extremely suitable for path-integral Monte Carlo simulations: fast computation of paths, fast Monte Carlo sampling, and the ability to use different numbers of time slices for the different degrees of freedom, commensurate with the quantum effects. It is demonstrated that a Monte Carlo simulation for which particles or small groups of variables are updated in a sequential fashion has a statistical efficiency that is always comparable to or better than that of an all-particle or all-variable update sampler. The sequential sampler results in significant computational savings if updating a variable costs only a fraction of the cost for updating all variables simultaneously or if the variables are independent. In the Lévy-Ciesielski representation, the path variables are grouped in a small number of layers, with the variables from the same layer being statistically independent. The superior performance of the fast sampling algorithm is shown to be a consequence of these observations. Both mathematical arguments and numerical simulations are employed in order to quantify the computational advantages of the sequential sampler, the Lévy-Ciesielski implementation of path integrals, and the fast sampling algorithm.

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Quantum Instanton Evaluation of the Kinetic Isotope Effects and of the Temperature Dependence of the Rate Constant

Vaníček

2011

Rate Constant Calculation for Thermal Reactions

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Energy estimators for random series path-integral methods

Cited by 27 publications

References 26 publications

Heat capacity estimators for random series path-integral methods by finite-difference schemes

Heat capacity estimators for random series path-integral methods by finite-difference schemes

Lévy-Ciesielski random series as a useful platform for Monte Carlo path integral sampling

Quantum Instanton Evaluation of the Kinetic Isotope Effects and of the Temperature Dependence of the Rate Constant

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