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Real Space Triplets in Quantum Condensed Matter: Numerical Experiments Using Path Integrals, Closures, and Hard Spheres. ENTROPY 2020; 22:e22121338. [PMID: 33266522 PMCID: PMC7759805 DOI: 10.3390/e22121338] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/28/2020] [Revised: 11/20/2020] [Accepted: 11/21/2020] [Indexed: 11/17/2022]
Abstract
Path integral Monte Carlo and closure computations are utilized to study real space triplet correlations in the quantum hard-sphere system. The conditions cover from the normal fluid phase to the solid phases face-centered cubic (FCC) and cI16 (de Broglie wavelengths , densities ). The focus is on the equilateral and isosceles features of the path-integral centroid and instantaneous structures. Complementary calculations of the associated pair structures are also carried out to strengthen structural identifications and facilitate closure evaluations. The three closures employed are Kirkwood superposition, Jackson-Feenberg convolution, and their average (AV3). A large quantity of new data are reported, and conclusions are drawn regarding (i) the remarkable performance of AV3 for the centroid and instantaneous correlations, (ii) the correspondences between the fluid and FCC salient features on the coexistence line, and (iii) the most conspicuous differences between FCC and cI16 at the pair and the triplet levels at moderately high densities (. This research is expected to provide low-temperature insights useful for the future related studies of properties of real systems (e.g., helium, alkali metals, and general colloidal systems).
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Jasper AW, Harding LB, Knight C, Georgievskii Y. Anharmonic Rovibrational Partition Functions at High Temperatures: Tests of Reduced-Dimensional Models for Systems with up to Three Fluxional Modes. J Phys Chem A 2019; 123:6210-6228. [DOI: 10.1021/acs.jpca.9b03592] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Szekeres B, Pártay LB, Mátyus E. Direct Computation of the Quantum Partition Function by Path-Integral Nested Sampling. J Chem Theory Comput 2018; 14:4353-4359. [PMID: 29944376 DOI: 10.1021/acs.jctc.8b00368] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In the present work we introduce a computational approach to the absolute rovibrational quantum partition function using the path-integral formalism of quantum mechanics in combination with the nested sampling technique. The numerical applicability of path-integral nested sampling is demonstrated for small molecules of spectroscopic interest. The computational cost of the method is determined by the evaluation time of a point on the potential energy surface (PES). For efficient PES implementations, the path-integral nested sampling method can be a viable alternative to the direct-Boltzmann-summation technique of variationally computed rovibrational energies, especially for medium-sized molecules and at elevated temperatures.
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Affiliation(s)
- Béla Szekeres
- Institute of Chemistry , Eötvös Loránd University , Pázmány Péter sétány 1/A , Budapest H-1117 , Hungary.,Department of Numerical Analysis, Faculty of Informatics , Eötvös Loránd University , Pázmány Péter sétány 1/C , Budapest H-1117 , Hungary
| | - Lívia B Pártay
- Department of Chemistry , University of Reading , Whiteknights, Reading RG6 6AD , United Kingdom
| | - Edit Mátyus
- Institute of Chemistry , Eötvös Loránd University , Pázmány Péter sétány 1/A , Budapest H-1117 , Hungary
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Jasper AW, Gruey ZB, Harding LB, Georgievskii Y, Klippenstein SJ, Wagner AF. Anharmonic Rovibrational Partition Functions for Fluxional Species at High Temperatures via Monte Carlo Phase Space Integrals. J Phys Chem A 2018; 122:1727-1740. [DOI: 10.1021/acs.jpca.7b11722] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Ahren W. Jasper
- Chemical Sciences and Engineering
Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Zackery B. Gruey
- Chemical Sciences and Engineering
Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Lawrence B. Harding
- Chemical Sciences and Engineering
Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Yuri Georgievskii
- Chemical Sciences and Engineering
Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Stephen J. Klippenstein
- Chemical Sciences and Engineering
Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Albert F. Wagner
- Chemical Sciences and Engineering
Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
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Buchowiecki M, Prątnicki F. High temperature partition function – a key role of ro-vibrational coupling and inflection points. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1334132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Marcin Buchowiecki
- Institute of Physics, Department of Mathematics and Physics, University of Szczecin, Szczecin, Poland
| | - Filip Prątnicki
- Institute of Physics, Department of Mathematics and Physics, University of Szczecin, Szczecin, Poland
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Nikitin AV, Rey M, Tyuterev VG. First fullyab initiopotential energy surface of methane with a spectroscopic accuracy. J Chem Phys 2016. [DOI: 10.1063/1.4961973] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Sesé LM. Path-integral and Ornstein-Zernike study of quantum fluid structures on the crystallization line. J Chem Phys 2016; 144:094505. [PMID: 26957169 DOI: 10.1063/1.4943005] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Liquid neon, liquid para-hydrogen, and the quantum hard-sphere fluid are studied with path integral Monte Carlo simulations and the Ornstein-Zernike pair equation on their respective crystallization lines. The results cover the whole sets of structures in the r-space and the k-space and, for completeness, the internal energies, pressures and isothermal compressibilities. Comparison with experiment is made wherever possible, and the possibilities of establishing k-space criteria for quantum crystallization based on the path-integral centroids are discussed. In this regard, the results show that the centroid structure factor contains two significant parameters related to its main peak features (amplitude and shape) that can be useful to characterize freezing.
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Affiliation(s)
- Luis M Sesé
- Departamento de Ciencias y Técnicas Fisicoquímicas, Universidad Nacional de Educación a Distancia, Paseo Senda del Rey 9, 28040 Madrid, Spain
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Mielke SL, Truhlar DG. A whole-path importance-sampling scheme for Feynman path integral calculations of absolute partition functions and free energies. J Chem Phys 2016; 144:034110. [PMID: 26801023 DOI: 10.1063/1.4939869] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Using Feynman path integrals, a molecular partition function can be written as a double integral with the inner integral involving all closed paths centered at a given molecular configuration, and the outer integral involving all possible molecular configurations. In previous work employing Monte Carlo methods to evaluate such partition functions, we presented schemes for importance sampling and stratification in the molecular configurations that constitute the path centroids, but we relied on free-particle paths for sampling the path integrals. At low temperatures, the path sampling is expensive because the paths can travel far from the centroid configuration. We now present a scheme for importance sampling of whole Feynman paths based on harmonic information from an instantaneous normal mode calculation at the centroid configuration, which we refer to as harmonically guided whole-path importance sampling (WPIS). We obtain paths conforming to our chosen importance function by rejection sampling from a distribution of free-particle paths. Sample calculations on CH4 demonstrate that at a temperature of 200 K, about 99.9% of the free-particle paths can be rejected without integration, and at 300 K, about 98% can be rejected. We also show that it is typically possible to reduce the overhead associated with the WPIS scheme by sampling the paths using a significantly lower-order path discretization than that which is needed to converge the partition function.
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Affiliation(s)
- Steven L Mielke
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, 207 Pleasant St. S.E., Minneapolis, Minnesota 55455-0431, USA
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, 207 Pleasant St. S.E., Minneapolis, Minnesota 55455-0431, USA
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Cassam-Chenaï P, Rousseau G, Ilmane A, Bouret Y, Rey M. Application of quasi-degenerate perturbation theory to the calculation of rotational energy levels of methane vibrational polyads. J Chem Phys 2015. [DOI: 10.1063/1.4926471] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- P. Cassam-Chenaï
- University Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice, France
| | - G. Rousseau
- University Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice, France
| | - A. Ilmane
- University Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice, France
| | - Y. Bouret
- University Nice Sophia Antipolis, CNRS, LPMC, UMR 7336, 06100 Nice, France
| | - M. Rey
- Groupe de Spectrométrie Moléculaire et Atmosphérique, CNRS UMR 6089, BP 1039, F-51687 Reims Cedex 2, France
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