Comment on “Path-integral virial estimator based on the scaling of fluctuation coordinates: Application to quantum clusters with fourth-order propagators” [J. Chem. Phys. <b>123</b>, 104101 (2005)]

Predescu, Cristian

doi:10.1063/1.2132281

The Journal of Chemical Physics

2005

DOI: 10.1063/1.2132281

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Comment on “Path-integral virial estimator based on the scaling of fluctuation coordinates: Application to quantum clusters with fourth-order propagators” [J. Chem. Phys. 123, 104101 (2005)]

Cristian Predescu

Abstract: The comment attempts to clarify what constitutes a safe use of the Feynman-Kac formula for the purpose of deriving estimators through formal differentiation of the density matrix.

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Cited by 2 publications

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Quantum mechanical single molecule partition function from path integral Monte Carlo simulations

Chempath

Predescu

Bell

2006

The Journal of Chemical Physics

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An algorithm for calculating the partition function of a molecule with the path integral MonteCarlo method is presented. Staged thermodynamic perturbation with respect to a reference harmonic potential is utilized to evaluate the ratio of partition functions. Parallel tempering and a new Monte Carlo estimator for the ratio of partition functions are implemented here to achieve well converged simulations that give an accuracy of 0.04 kcal/mol in the reported free energies. The method is applied to various test systems, including a catalytic system composed of 18 atoms. Absolute free energies calculated by this method lead to corrections as large as 2.6 kcal/mol at 300 K for some of the examples presented.

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Quantum mechanical single molecule partition function from path integral Monte Carlo simulations

Chempath

Predescu

Bell

2006

The Journal of Chemical Physics

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Calculation of thermodynamic properties of helium using path integral Monte Carlo simulations in the NpT ensemble and ab initio potentials

Marienhagen,

Meier

2024

The Journal of Chemical Physics

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We apply the methodology of Lustig, with which rigorous expressions for all thermodynamic properties can be derived in any statistical ensemble, to derive expressions for the calculation of thermodynamic properties in the path integral formulation of the quantum-mechanical isobaric–isothermal (NpT) ensemble. With the derived expressions, thermodynamic properties such as the density, speed of sound, or Joule–Thomson coefficient can be calculated in path integral Monte Carlo simulations, fully incorporating quantum effects without uncontrolled approximations within the well-known isomorphism between the quantum-mechanical partition function and a classical system of ring polymers. The derived expressions are verified by simulations of supercritical helium above the vapor–liquid critical point at selected state points using recent highly accurate ab initio potentials for pairwise and nonadditive three-body interactions. We observe excellent agreement of our results with the most accurate experimental data for the density and speed of sound and a reference virial equation of state for helium in the region where the virial equation of state is converged. Moreover, our results agree closer with the experimental data and virial equation of state than the results of semiclassical simulations using the Feynman–Hibbs correction for quantum effects, which demonstrates the necessity to fully include quantum effects by path integral simulations. Our results also show that nonadditive three-body interactions must be accounted for when accurately predicting thermodynamic properties of helium by solely theoretical means.

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Comment on “Path-integral virial estimator based on the scaling of fluctuation coordinates: Application to quantum clusters with fourth-order propagators” [J. Chem. Phys. 123, 104101 (2005)]

Abstract: The comment attempts to clarify what constitutes a safe use of the Feynman-Kac formula for the purpose of deriving estimators through formal differentiation of the density matrix.

Cited by 2 publications

References 12 publications

Quantum mechanical single molecule partition function from path integral Monte Carlo simulations

Quantum mechanical single molecule partition function from path integral Monte Carlo simulations

Calculation of thermodynamic properties of helium using path integral Monte Carlo simulations in the NpT ensemble and ab initio potentials

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