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Fournier R, Wang L, Yazyev OV, Wu Q. Artificial Neural Network Approach to the Analytic Continuation Problem. PHYSICAL REVIEW LETTERS 2020; 124:056401. [PMID: 32083907 DOI: 10.1103/physrevlett.124.056401] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2018] [Revised: 07/25/2019] [Accepted: 12/20/2019] [Indexed: 05/21/2023]
Abstract
Inverse problems are encountered in many domains of physics, with analytic continuation of the imaginary Green's function into the real frequency domain being a particularly important example. However, the analytic continuation problem is ill defined and currently no analytic transformation for solving it is known. We present a general framework for building an artificial neural network (ANN) that solves this task with a supervised learning approach. Application of the ANN approach to quantum Monte Carlo calculations and simulated Green's function data demonstrates its high accuracy. By comparing with the commonly used maximum entropy approach, we show that our method can reach the same level of accuracy for low-noise input data, while performing significantly better when the noise strength increases. The computational cost of the proposed neural network approach is reduced by almost three orders of magnitude compared to the maximum entropy method.
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Affiliation(s)
- Romain Fournier
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Lei Wang
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Oleg V Yazyev
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials MARVEL, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - QuanSheng Wu
- Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
- National Centre for Computational Design and Discovery of Novel Materials MARVEL, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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2
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Grossmann F. Quantum effects in intermediate-temperature dipole-dipole correlation-functions in the presence of an environment. J Chem Phys 2014; 141:144305. [DOI: 10.1063/1.4896835] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- F. Grossmann
- Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany
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3
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Kletenik-Edelman O, Rabani E, Reichman DR. Analytic continuation average spectrum method for transport in quantum liquids. Chem Phys 2010. [DOI: 10.1016/j.chemphys.2010.01.012] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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4
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Kowalczyk P, Gauden PA, Terzyk AP, Furmaniak S. Frequency-Dependent Diffusion Constant of Quantum Fluids from Path Integral Monte Carlo and Tikhonov’s Regularizing Functional. J Chem Theory Comput 2009; 5:1990-6. [DOI: 10.1021/ct900215q] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Affiliation(s)
- Piotr Kowalczyk
- Applied Physics, Royal Melbourne Institute of Technology University, GPO Box 2476 V, Victoria 3001, Australia and Department of Chemistry, Physicochemistry of Carbon Materials Research Group, Nicolaus Copernicus University, Gagarin St. 7, 87-100 Torun, Poland
| | - Piotr A. Gauden
- Applied Physics, Royal Melbourne Institute of Technology University, GPO Box 2476 V, Victoria 3001, Australia and Department of Chemistry, Physicochemistry of Carbon Materials Research Group, Nicolaus Copernicus University, Gagarin St. 7, 87-100 Torun, Poland
| | - Artur P. Terzyk
- Applied Physics, Royal Melbourne Institute of Technology University, GPO Box 2476 V, Victoria 3001, Australia and Department of Chemistry, Physicochemistry of Carbon Materials Research Group, Nicolaus Copernicus University, Gagarin St. 7, 87-100 Torun, Poland
| | - Sylwester Furmaniak
- Applied Physics, Royal Melbourne Institute of Technology University, GPO Box 2476 V, Victoria 3001, Australia and Department of Chemistry, Physicochemistry of Carbon Materials Research Group, Nicolaus Copernicus University, Gagarin St. 7, 87-100 Torun, Poland
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5
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Reichman DR, Rabani E. Analytic continuation average spectrum method for quantum liquids. J Chem Phys 2009; 131:054502. [DOI: 10.1063/1.3185728] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Pereverzev YV, Pereverzev A, Shigeta Y, Prezhdo OV. Correlation functions in quantized Hamilton dynamics and quantal cumulant dynamics. J Chem Phys 2008; 129:144104. [DOI: 10.1063/1.2990005] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
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7
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Liu J, Miller WH. Linearized semiclassical initial value time correlation functions with maximum entropy analytic continuation. J Chem Phys 2008; 129:124111. [PMID: 19045010 DOI: 10.1063/1.2981065] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jian Liu
- Department of Chemistry and K. S. Pitzer Center for Theoretical Chemistry, University of California, Berkeley, California 94720-1460, USA
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8
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Habershon S, Braams BJ, Manolopoulos DE. Quantum mechanical correlation functions, maximum entropy analytic continuation, and ring polymer molecular dynamics. J Chem Phys 2007; 127:174108. [DOI: 10.1063/1.2786451] [Citation(s) in RCA: 59] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
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Navrotskaya I, Geva E. Vibrational Energy Relaxation Rates of H2 and D2 in Liquid Argon via the Linearized Semiclassical Method. J Phys Chem A 2006; 111:460-7. [PMID: 17228894 DOI: 10.1021/jp066243g] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The vibrational energy relaxation (VER) rates for H2 and D2 in liquid argon (T=152 K, rho=1.45x1022 cm-3) are calculated using the linearized semiclassical (LSC) method (J. Phys. Chem. 2003, 107, 9059, 9070). The calculation is based on Fermi's golden rule. The VER rate constant is expressed in terms of the quantum-mechanical force-force correlation function, which is then estimated using the LSC method. A local harmonic approximation (LHA) is employed in order to compute the multidimensional Wigner integrals underlying the LSC approximation. The H2-Ar and D2-Ar interactions are described by the three-body potential of Bissonette et al. (J. Phys. Chem. A 1996, 105, 2639). The LHA-LSC-based VER rate constants for both D2 and H2 are found to be about 2-3 orders of magnitude slower than those obtained experimentally. However, their ratio agrees quantitatively with the corresponding experimental result. In contrast, the classical VER rate constants are found to be 8-9 orders of magnitude slower than those obtained experimentally, and their ratio is found to be qualitatively different from the corresponding experimental result.
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Affiliation(s)
- Irina Navrotskaya
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
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10
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The influence of nonbilinear system-bath coupling on quantum-mechanical activated rate processes. Chem Phys 2006. [DOI: 10.1016/j.chemphys.2005.05.044] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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11
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Rabani E, Krilov G, Reichman DR, Berne BJ. Transport properties of normal liquid helium: Comparison of various methodologies. J Chem Phys 2005; 123:184506. [PMID: 16292913 DOI: 10.1063/1.2109927] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We revisit the problem of self-diffusion in normal liquid helium above the lambda transition. Several different methods are applied to compute the velocity autocorrelation function. Since it is still impossible to determine the exact result for the velocity autocorrelation function from simulation, we appeal to the computation of short-time moments to determine the accuracy of the different approaches at short times. The main conclusion reached from our study is that both the quantum mode-coupling theory and the numerical analytic continuation approach must be regarded as a viable and competitive methods for the computation of dynamical properties of quantum systems.
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Affiliation(s)
- Eran Rabani
- School of Chemistry, The Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel
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12
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Pollak E, Talkner P. Reaction rate theory: what it was, where is it today, and where is it going? CHAOS (WOODBURY, N.Y.) 2005; 15:26116. [PMID: 16035918 DOI: 10.1063/1.1858782] [Citation(s) in RCA: 157] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
A brief history is presented, outlining the development of rate theory during the past century. Starting from Arrhenius [Z. Phys. Chem. 4, 226 (1889)], we follow especially the formulation of transition state theory by Wigner [Z. Phys. Chem. Abt. B 19, 203 (1932)] and Eyring [J. Chem. Phys. 3, 107 (1935)]. Transition state theory (TST) made it possible to obtain quick estimates for reaction rates for a broad variety of processes even during the days when sophisticated computers were not available. Arrhenius' suggestion that a transition state exists which is intermediate between reactants and products was central to the development of rate theory. Although Wigner gave an abstract definition of the transition state as a surface of minimal unidirectional flux, it took almost half of a century until the transition state was precisely defined by Pechukas [Dynamics of Molecular Collisions B, edited by W. H. Miller (Plenum, New York, 1976)], but even this only in the realm of classical mechanics. Eyring, considered by many to be the father of TST, never resolved the question as to the definition of the activation energy for which Arrhenius became famous. In 1978, Chandler [J. Chem. Phys. 68, 2959 (1978)] finally showed that especially when considering condensed phases, the activation energy is a free energy, it is the barrier height in the potential of mean force felt by the reacting system. Parallel to the development of rate theory in the chemistry community, Kramers published in 1940 [Physica (Amsterdam) 7, 284 (1940)] a seminal paper on the relation between Einstein's theory of Brownian motion [Einstein, Ann. Phys. 17, 549 (1905)] and rate theory. Kramers' paper provided a solution for the effect of friction on reaction rates but left us also with some challenges. He could not derive a uniform expression for the rate, valid for all values of the friction coefficient, known as the Kramers turnover problem. He also did not establish the connection between his approach and the TST developed by the chemistry community. For many years, Kramers' theory was considered as providing a dynamic correction to the thermodynamic TST. Both of these questions were resolved in the 1980s when Pollak [J. Chem. Phys. 85, 865 (1986)] showed that Kramers' expression in the moderate to strong friction regime could be derived from TST, provided that the bath, which is the source of the friction, is handled at the same level as the system which is observed. This then led to the Mel'nikov-Pollak-Grabert-Hanggi [Mel'nikov and Meshkov, J. Chem. Phys. 85, 1018 (1986); Pollak, Grabert, and Hanggi, ibid. 91, 4073 (1989)] solution of the turnover problem posed by Kramers. Although classical rate theory reached a high level of maturity, its quantum analog leaves the theorist with serious challenges to this very day. As noted by Wigner [Trans. Faraday Soc. 34, 29 (1938)], TST is an inherently classical theory. A definite quantum TST has not been formulated to date although some very useful approximate quantum rate theories have been invented. The successes and challenges facing quantum rate theory are outlined. An open problem which is being investigated intensively is rate theory away from equilibrium. TST is no longer valid and cannot even serve as a conceptual guide for understanding the critical factors which determine rates away from equilibrium. The nonequilibrium quantum theory is even less well developed than the classical, and suffers from the fact that even today, we do not know how to solve the real time quantum dynamics for systems with "many" degrees of freedom.
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Affiliation(s)
- Eli Pollak
- Chemical Physics Department, Weizmann Institute of Science, 76100 Rehovot, Israel
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Rabani E, Reichman DR. QUANTUM MODE-COUPLING THEORY: Formulation and Applications to Normal and Supercooled Quantum Liquids. Annu Rev Phys Chem 2005; 56:157-85. [PMID: 15796699 DOI: 10.1146/annurev.physchem.56.092503.141138] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
▪ Abstract We review our recent efforts to formulate and study a mode-coupling approach to real-time dynamic fluctuations in quantum liquids. Comparison is made between the theory and recent neutron scattering experiments performed on liquid ortho-deuterium and para-hydrogen. We discuss extensions of the theory to supercooled and glassy states where quantum fluctuations compete with thermal fluctuations. Experimental scenarios for quantum glassy liquids are briefly discussed.
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Affiliation(s)
- Eran Rabani
- School of Chemistry, The Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel.
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14
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Horikoshi A, Kinugawa K. Effective potential analytic continuation approach for real time quantum correlation functions involving nonlinear operators. J Chem Phys 2005; 122:174104. [PMID: 15910020 DOI: 10.1063/1.1888576] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Abstract
We apply the effective potential analytic continuation (EPAC) method to the calculation of real time quantum correlation functions involving operators nonlinear in the position operator q. For a harmonic system the EPAC method provides the exact correlation function at all temperature ranges, while the other quantum dynamics methods, the centroid molecular dynamics and the ring polymer molecular dynamics, become worse at lower temperature. For an asymmetric anharmonic system, the EPAC correlation function is in very good agreement with the exact one at t = 0. When the time increases from zero, the EPAC method gives good coincidence with the exact result at lower temperature. Finally, we propose a simplified version of the EPAC method to reduce the computational cost required for the calculation of the standard effective potential.
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Affiliation(s)
- Atsushi Horikoshi
- Japan Science and Technology Agency and Department of Chemistry, Faculty of Science, Nara Women's University.
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15
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Hone TD, Voth GA. A centroid molecular dynamics study of liquidpara-hydrogen andortho-deuterium. J Chem Phys 2004; 121:6412-22. [PMID: 15446940 DOI: 10.1063/1.1780951] [Citation(s) in RCA: 89] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Centroid molecular dynamics (CMD) is applied to the study of collective and single-particle dynamics in liquid para-hydrogen at two state points and liquid ortho-deuterium at one state point. The CMD results are compared with the results of classical molecular dynamics, quantum mode coupling theory, a maximum entropy analytic continuation approach, pair-product forward- backward semiclassical dynamics, and available experimental results. The self-diffusion constants are in excellent agreement with the experimental measurements for all systems studied. Furthermore, it is shown that the method is able to adequately describe both the single-particle and collective dynamics of quantum liquids.
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Affiliation(s)
- Tyler D Hone
- Department of Chemistry and Henry Eyring Center for Theoretical Chemistry, University of Utah, Salt Lake City, Utah 84112-0850, USA
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16
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Horikoshi A, Kinugawa K. Effective potential analytic continuation calculations of real time quantum correlation functions: asymmetric systems. J Chem Phys 2004; 121:2891-8. [PMID: 15291599 DOI: 10.1063/1.1774161] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We apply the effective potential analytic continuation (EPAC) method to one-dimensional asymmetric potential systems to obtain the real time quantum correlation functions at various temperatures. Comparing the EPAC results with the exact results, we find that for an asymmetric anharmonic oscillator the EPAC results are in very good agreement with the exact ones at low temperature, while this agreement becomes worse as the temperature increases. We also show that the EPAC calculation for a certain type of asymmetric potentials can be reduced to that for the corresponding symmetric potentials.
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Affiliation(s)
- Atsushi Horikoshi
- Japan Science and Technology Agency, Faculty of Science, Nara Women's University, 630-8506.
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17
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Shi Q, Geva E. Nonradiative Electronic Relaxation Rate Constants from Approximations Based on Linearizing the Path-Integral Forward−Backward Action. J Phys Chem A 2004. [DOI: 10.1021/jp049547g] [Citation(s) in RCA: 71] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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18
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Shi Q, Geva E. A semiclassical generalized quantum master equation for an arbitrary system-bath coupling. J Chem Phys 2004; 120:10647-58. [PMID: 15268091 DOI: 10.1063/1.1738109] [Citation(s) in RCA: 83] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
The Nakajima-Zwanzig generalized quantum master equation (GQME) provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a, possibly anharmonic, quantum bath. In this equation, a memory kernel superoperator accounts for the influence of the bath on the dynamics of the system. In a previous paper [Q. Shi and E. Geva, J. Chem. Phys. 119, 12045 (2003)] we proposed a new approach to calculating the memory kernel, in the case of arbitrary system-bath coupling. Within this approach, the memory kernel is obtained by solving a set of two integral equations, which requires a new type of two-time system-dependent bath correlation functions as input. In the present paper, we consider the application of the linearized semiclassical (LSC) approximation for calculating those correlation functions, and subsequently the memory kernel. The new approach is tested on a benchmark spin-boson model. Application of the LSC approximation for calculating the relatively short-lived memory kernel, followed by a numerically exact solution of the GQME, is found to provide an accurate description of the relaxation dynamics. The success of the proposed LSC-GQME methodology is contrasted with the failure of both the direct application of the LSC approximation and the weak coupling treatment to provide an accurate description of the dynamics, for the same model, except at very short times. The feasibility of the new methodology to anharmonic systems is also demonstrated in the case of a two level system coupled to a chain of Lennard-Jones atoms.
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Affiliation(s)
- Qiang Shi
- Department of Chemistry and the FOCUS Center, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
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19
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Yonetani Y, Kinugawa K. Centroid molecular dynamics approach to the transport properties of liquid para-hydrogen over the wide temperature range. J Chem Phys 2004; 120:10624-33. [PMID: 15268088 DOI: 10.1063/1.1735613] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Fundamental transport properties of liquid para-hydrogen (p-H(2)), i.e., diffusion coefficients, thermal conductivity, shear viscosity, and bulk viscosity, have been evaluated by means of the path integral centroid molecular dynamics (CMD) calculations. These transport properties have been obtained over the wide temperature range, 14-32 K. Calculated values of the diffusion coefficients and the shear viscosity are in good agreement with the experimental values at all the investigated temperatures. Although a relatively large deviation is found for the thermal conductivity, the calculated values are less than three times the amount of the experimental values at any temperature. On the other hand, the classical molecular dynamics has led all the transport properties to much larger deviation. For the bulk viscosity of liquid p-H(2), which was never known from experiments, the present CMD has given a clear temperature dependence. In addition, from the comparison based on the principle of corresponding states, it has been shown that the marked deviation of the transport properties of liquid p-H(2) from the feature which is expected from the molecular parameters is due to the quantum effect.
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Affiliation(s)
- Yoshiteru Yonetani
- Japan Science and Technology Corporation, Department of Chemistry, Faculty of Science, Nara Women's University, Nara 630-8506, Japan
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20
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Blinov N, Song X, Roy PN. Path integral Monte Carlo approach for weakly bound van der Waals complexes with rotations: Algorithm and benchmark calculations. J Chem Phys 2004; 120:5916-31. [PMID: 15267473 DOI: 10.1063/1.1650301] [Citation(s) in RCA: 65] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Abstract
A path integral Monte Carlo technique suitable for the treatment of doped helium clusters with inclusion of the rotational degrees of freedom of the dopant is introduced. The extrapolation of the results to the limit of infinite Trotter number is discussed in detail. Benchmark calculations for small weakly bound (4)He(N)--OCS clusters are presented. The Monte Carlo results are compared with those of basis set calculations for the He--OCS dimer. A technique to analyze the orientational imaginary time correlation function is suggested. It allows one to obtain information regarding the effective rotational constant for a doped helium cluster based on a model for the rotational Hamiltonian. The renormalization of the effective rotational constant for (4)He(N)--OCS clusters derived from the orientational imaginary time correlation function is in good agreement with experimental results.
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Affiliation(s)
- Nicholas Blinov
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
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Rabani E, Reichman DR. A fully self-consistent treatment of collective fluctuations in quantum liquids. J Chem Phys 2004; 120:1458-65. [PMID: 15268271 DOI: 10.1063/1.1631436] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The problem of calculating collective density fluctuations in quantum liquids is revisited. A fully quantum mechanical self-consistent treatment based on a quantum mode-coupling theory is presented. The theory is compared with the maximum entropy analytic continuation approach and with available experimental results. The quantum mode-coupling theory provides semiquantitative results for both short and long time dynamics. The proper description of long time phenomena is important in future study of problems related to the physics of glassy quantum systems, and to the study of collective fluctuations in Bose fluids.
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Affiliation(s)
- Eran Rabani
- School of Chemistry, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel.
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22
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Shi Q, Geva E. A new approach to calculating the memory kernel of the generalized quantum master equation for an arbitrary system–bath coupling. J Chem Phys 2003. [DOI: 10.1063/1.1624830] [Citation(s) in RCA: 91] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
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23
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Shi Q, Geva E. On the calculation of vibrational energy relaxation rate constants from centroid molecular dynamics simulations. J Chem Phys 2003. [DOI: 10.1063/1.1613636] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
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24
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Shi Q, Geva E. Semiclassical Theory of Vibrational Energy Relaxation in the Condensed Phase. J Phys Chem A 2003. [DOI: 10.1021/jp030497+] [Citation(s) in RCA: 143] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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25
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Horikoshi A, Kinugawa K. Quantum dynamical correlations: Effective potential analytic continuation approach. J Chem Phys 2003. [DOI: 10.1063/1.1595638] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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26
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Shi Q, Geva E. A relationship between semiclassical and centroid correlation functions. J Chem Phys 2003. [DOI: 10.1063/1.1564814] [Citation(s) in RCA: 122] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
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27
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Navrotskaya I, Shi Q, Geva E. Quantum-mechanical reaction rate constants from centroid molecular dynamics simulations: Barrier crossing in an asymmetrical double-well. Isr J Chem 2002. [DOI: 10.1560/46pr-4lgf-ehny-ndhl] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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28
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Liao JL, Voth GA. Numerical approaches for computing nonadiabatic electron transfer rate constants. J Chem Phys 2002. [DOI: 10.1063/1.1474584] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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29
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Rabani E, Reichman DR. A self-consistent mode-coupling theory for dynamical correlations in quantum liquids: Rigorous formulation. J Chem Phys 2002. [DOI: 10.1063/1.1458545] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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30
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Shi Q, Geva E. Centroid-based methods for calculating quantum reaction rate constants: Centroid sampling versus centroid dynamics. J Chem Phys 2002. [DOI: 10.1063/1.1445120] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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31
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Rabani E, Reichman DR, Krilov G, Berne BJ. The calculation of transport properties in quantum liquids using the maximum entropy numerical analytic continuation method: application to liquid para-hydrogen. Proc Natl Acad Sci U S A 2002; 99:1129-33. [PMID: 11830656 PMCID: PMC122155 DOI: 10.1073/pnas.261540698] [Citation(s) in RCA: 86] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We present a method based on augmenting an exact relation between a frequency-dependent diffusion constant and the imaginary time velocity autocorrelation function, combined with the maximum entropy numerical analytic continuation approach to study transport properties in quantum liquids. The method is applied to the case of liquid para-hydrogen at two thermodynamic state points: a liquid near the triple point and a high-temperature liquid. Good agreement for the self-diffusion constant and for the real-time velocity autocorrelation function is obtained in comparison to experimental measurements and other theoretical predictions. Improvement of the methodology and future applications are discussed.
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Affiliation(s)
- Eran Rabani
- School of Chemistry, The Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel
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32
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Geva E, Shi Q, Voth GA. Quantum-mechanical reaction rate constants from centroid molecular dynamics simulations. J Chem Phys 2001. [DOI: 10.1063/1.1412870] [Citation(s) in RCA: 82] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Krilov G, Sim E, Berne B. On the Bayesian approach to calculating time correlation functions in quantum systems; reaction dynamics and spectroscopy. Chem Phys 2001. [DOI: 10.1016/s0301-0104(01)00287-7] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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Sim E, Krilov G, Berne BJ. Quantum Rate Constants from Short-Time Dynamics: An Analytic Continuation Approach. J Phys Chem A 2001. [DOI: 10.1021/jp004307w] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Eunji Sim
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027
| | - Goran Krilov
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027
| | - B. J. Berne
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027
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Krilov G, Sim E, Berne BJ. Quantum time correlation functions from complex time Monte Carlo simulations: A maximum entropy approach. J Chem Phys 2001. [DOI: 10.1063/1.1331613] [Citation(s) in RCA: 44] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Rabani E, Krilov G, Berne BJ. Quantum mechanical canonical rate theory: A new approach based on the reactive flux and numerical analytic continuation methods. J Chem Phys 2000. [DOI: 10.1063/1.480834] [Citation(s) in RCA: 68] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Krilov G, Berne BJ. Real time quantum correlation functions. II. Maximum entropy numerical analytic continuation of path integral Monte Carlo and centroid molecular dynamics data. J Chem Phys 1999. [DOI: 10.1063/1.480028] [Citation(s) in RCA: 44] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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