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Liu Z, Lyu N, Hu Z, Zeng H, Batista VS, Sun X. Benchmarking various nonadiabatic semiclassical mapping dynamics methods with tensor-train thermo-field dynamics. J Chem Phys 2024; 161:024102. [PMID: 38980091 DOI: 10.1063/5.0208708] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2024] [Accepted: 06/20/2024] [Indexed: 07/10/2024] Open
Abstract
Accurate quantum dynamics simulations of nonadiabatic processes are important for studies of electron transfer, energy transfer, and photochemical reactions in complex systems. In this comparative study, we benchmark various approximate nonadiabatic dynamics methods with mapping variables against numerically exact calculations based on the tensor-train (TT) representation of high-dimensional arrays, including TT-KSL for zero-temperature dynamics and TT-thermofield dynamics for finite-temperature dynamics. The approximate nonadiabatic dynamics methods investigated include mixed quantum-classical Ehrenfest mean-field and fewest-switches surface hopping, linearized semiclassical mapping dynamics, symmetrized quasiclassical dynamics, the spin-mapping method, and extended classical mapping models. Different model systems were evaluated, including the spin-boson model for nonadiabatic dynamics in the condensed phase, the linear vibronic coupling model for electronic transition through conical intersections, the photoisomerization model of retinal, and Tully's one-dimensional scattering models. Our calculations show that the optimal choice of approximate dynamical method is system-specific, and the accuracy is sensitively dependent on the zero-point-energy parameter and the initial sampling strategy for the mapping variables.
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Affiliation(s)
- Zengkui Liu
- Division of Arts and Sciences, NYU Shanghai, 567 West Yangsi Road, Shanghai 200124, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
- Department of Chemistry, New York University, New York, New York 10003, USA
| | - Ningyi Lyu
- Division of Arts and Sciences, NYU Shanghai, 567 West Yangsi Road, Shanghai 200124, China
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
| | - Zhubin Hu
- Division of Arts and Sciences, NYU Shanghai, 567 West Yangsi Road, Shanghai 200124, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Hao Zeng
- Division of Arts and Sciences, NYU Shanghai, 567 West Yangsi Road, Shanghai 200124, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Victor S Batista
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
| | - Xiang Sun
- Division of Arts and Sciences, NYU Shanghai, 567 West Yangsi Road, Shanghai 200124, China
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
- Department of Chemistry, New York University, New York, New York 10003, USA
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
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Malpathak S, Church MS, Ananth N. A Semiclassical Framework for Mixed Quantum Classical Dynamics. J Phys Chem A 2022; 126:6359-6375. [PMID: 36070472 DOI: 10.1021/acs.jpca.2c03467] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Semiclassical (SC) approximations for quantum dynamic simulations in complex chemical systems range from rigorously accurate methods that are computationally expensive to methods that exhibit near-classical scaling with system size but are limited in their ability to describe quantum effects. In practical studies of high-dimensional reactions, neither extreme is the best choice: frequently a high-level quantum mechanical description is only required for a handful of modes, while the majority of environment modes that do not play a key role in the reactive event of interest are well served with a lower level of theory. In this feature, we introduce modified Filinov filtration as a powerful tool to construct mixed quantum-classical SC theories where different subsystems can be quantized to different extents without introducing ad hoc intersubsystem interaction terms. We demonstrate that these Filinov-based SC methods can systematically tune between quantum and classical limit SC behavior, offering a practical way forward to accurate and computationally efficient simulations of high-dimensional quantum processes.
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Affiliation(s)
- Shreyas Malpathak
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University Ithaca, New York 14853, United States
| | - Matthew S Church
- Department of Chemistry, Brown University, Providence, Rhode Island 02906, United States
| | - Nandini Ananth
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University Ithaca, New York 14853, United States
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3
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Liu Z, Xu W, Tuckerman ME, Sun X. Imaginary-Time Open-Chain Path-Integral Approach for Two-State Time Correlation Functions and Applications in Charge Transfer. J Chem Phys 2022; 157:114111. [DOI: 10.1063/5.0098162] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Quantum time correlation functions (TCFs) involving two states are important for describing nonadiabatic dynamical processes such as charge transfer. Based on a previous single-state method, we propose an imaginary-time open-chain path-integral (OCPI) approach for evaluating the two-state symmetrized TCFs. Expressing the forward and backward propagation on different electronic potential energy surfaces as a complex-time path integral, we then transform the path variables to average and difference variables such that the integration over the difference variables up to the second order can be performed analytically. The resulting expression for the symmetrized TCF is equivalent to sampling the open-chain configurations in an effective potential that corresponds to the average surface. Using importance sampling over the extended OCPI space via open path integral molecular dynamics, we tested the resulting path-integral approximation by calculating the Fermi's golden rule charge transfer rate constant within a widely-used spin-boson model. Comparing with the real-time linearized semiclassical method and analytical result, we show that the imaginary-time OCPI provides an accurate two-state symmetrized TCF and rate constant in the typical turnover region. It is shown that the first bead of the open chain corresponds to physical zero-time, and the endpoint bead corresponds to final time t; oscillations of the end-to-end distance perfectly match the nuclear mode frequency. The two-state OCPI scheme is seen to capture the tested model's electronic quantum coherence and nuclear quantum effects accurately.
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Affiliation(s)
- Zengkui Liu
- Division of Arts and Sciences, New York University Shanghai, China
| | - Wen Xu
- New York University Shanghai, China
| | - Mark E. Tuckerman
- Department of Chemistry and Courant Institute of Mathematical Sciences, New York University, United States of America
| | - Xiang Sun
- Division of Arts and Sciences, New York University Shanghai, China
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4
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Poulsen JA, Nyman G. A Divergence-Free Wigner Transform of the Boltzmann Operator Based on an Effective Frequency Theory. J Phys Chem A 2021; 125:9209-9225. [PMID: 34636560 PMCID: PMC8543443 DOI: 10.1021/acs.jpca.1c05860] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
Abstract
![]()
The centroid effective
frequency representation of path integrals
as developed by Feynman and Kleinert was originally aimed at calculating
partition functions and related quantities in the canonical ensemble.
In its path integral formulation, only closed paths
were relevant. This formulation has been used by the present authors
in order to calculate the many-body Wigner function of the Boltzmann
operator, which includes also open paths. This usage of the theory
outside of the original intention can lead to mathematical divergence
issues for potentials with barriers, particularly at low temperature.
In the present paper, we modify the effective frequency theory of
Feynman and Kleinert by also including open paths in its variational
equations. In this way, a divergence-free approximation to the Boltzmann
operator matrix elements is derived. This generalized version of Feynman
and Kleinert’s formulation is thus more robust and can be applied
to all types of barriers at all temperatures. This new version is
used to calculate the Wigner functions of the Boltzmann operator for
a quartic oscillator and for a double well potential and both static
and dynamic properties are studied at several temperatures. The new
theory is found to be essentially as precise as the original one.
Its advantage is that it will always deliver a well-defined, even
if approximate, Wigner function, which can, for instance, be used
for sampling initial conditions for molecular dynamics simulations.
As will be discussed, the theory can be systematically improved by
including higher-order Fourier modes into the nonquadratic part of
the trial action.
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Affiliation(s)
- Jens Aage Poulsen
- Department of Chemistry and Molecular Biology, University of Gothenburg, SE 405 30 Gothenburg, Sweden
| | - Gunnar Nyman
- Department of Chemistry and Molecular Biology, University of Gothenburg, SE 405 30 Gothenburg, Sweden
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Yamaoka S, Hyeon-Deuk K. Decelerated Liquid Dynamics Induced by Component-Dependent Supercooling in Hydrogen and Deuterium Quantum Mixtures. J Phys Chem Lett 2020; 11:4186-4192. [PMID: 32375000 DOI: 10.1021/acs.jpclett.0c00801] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Isotopic mixtures of p-H2 and o-D2 molecules have been an attractive binary system because they include two kinds of purely isotopic molecules which possess the same electronic potential but the twice different mass inducing differently pronounced nuclear quantum effects (NQEs). Accessing details of structures and dynamics in such quantum mixtures combining complex molecular dynamics with NQEs of different strengths remains a challenging problem. Taking advantage of the nonempirical molecular dynamics method which describes p-H2 and o-D2 molecules, we found that the liquid dynamics slows down at a specific mixing ratio, which can be connected to the observed anomalous slowdown of crystallization in the quantum mixtures. We attributed the decelerated dynamics to the component-dependent supercooling of p-H2 taking place in the mixtures, demonstrating that there is an optimal mixing ratio to hinder crystallization. The obtained physical insights will help in experimentally controlling and achieving unknown quantum mixtures including superfluid.
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Affiliation(s)
- Shutaro Yamaoka
- Department of Chemistry, Kyoto University, Kyoto 606-8502, Japan
| | - Kim Hyeon-Deuk
- Department of Chemistry, Kyoto University, Kyoto 606-8502, Japan
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Abe K, Yamaoka S, Hyeon-Deuk K. Isotopic Effects on Intermolecular and Intramolecular Structure and Dynamics in Hydrogen, Deuterium, and Tritium Liquids: Normal Liquid and Weakly and Strongly Cooled Liquids. J Phys Chem B 2018; 122:8233-8242. [PMID: 30095260 DOI: 10.1021/acs.jpcb.8b02596] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Differences in properties such as phase-transition temperature and transport coefficients among liquids of different isotopic compositions, hydrogen, deuterium, and tritium, should originate from their differently pronounced nuclear quantum effects (NQEs) rather than from any subtle difference in the electronic interaction potentials. Accurate and efficient determination of structural and dynamical isotopic effects in the quantum liquids still remains as one of the challenging problems in condensed-phase physics. With a recently developed nonempirical real-time molecular dynamics method which describes nonspherical molecules with the NQEs, we computationally realized and investigated dynamical and quantum isotopic effects of not only traditionally studied isotopes, hydrogen, and deuterium but also a lesser known radioisotope, tritium, in broad thermodynamic conditions from normal liquid to weakly and strongly cooled liquids, which have been hindered by rapid crystallization in spite of numerous experimental attempts at supercooling. Reproducing the previously reported experimental isotope dependence on the bond length and vibrational frequencies of hydrogen, deuterium, and tritium liquids, we further demonstrate that distinctive isotope effects appear in their intermolecular and intramolecular structure and dynamics not only at lower temperature but also at higher temperature, which none has so far been able to obtain quantitative results for realistic systems. Rationalization of their physical origins and the obtained physical insights will help future experimental searching and monitoring intermolecular and intramolecular dynamics and structures of these isotopes not only in normal liquid but also in supercooled liquid.
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Affiliation(s)
- Kiharu Abe
- Department of Chemistry , Kyoto University , Kyoto 606-8502 , Japan
| | - Shutaro Yamaoka
- Department of Chemistry , Kyoto University , Kyoto 606-8502 , Japan
| | - Kim Hyeon-Deuk
- Department of Chemistry , Kyoto University , Kyoto 606-8502 , Japan.,Japan Science and Technology Agency, PRESTO , 4-1-8 Honcho , Kawaguchi , Saitama 332-0012 , Japan
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7
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Makri N. Iterative blip-summed path integral for quantum dynamics in strongly dissipative environments. J Chem Phys 2017; 146:134101. [DOI: 10.1063/1.4979197] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Nancy Makri
- Departments of Chemistry and Physics, University of Illinois, Urbana, Illinois 61801, USA
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8
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Montoya-Castillo A, Reichman DR. Path integral approach to the Wigner representation of canonical density operators for discrete systems coupled to harmonic baths. J Chem Phys 2017; 146:024107. [DOI: 10.1063/1.4973646] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - David R. Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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9
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Atomic Quantum Dynamics in Materials Research. ACTA ACUST UNITED AC 2017. [DOI: 10.1016/b978-0-12-805324-9.00007-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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10
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HYEON-DEUK K. Quantum Molecular Dynamics Simulation of Condensed Hydrogens by Nuclear and Electron Wave Packet Approach. JOURNAL OF COMPUTER CHEMISTRY-JAPAN 2016. [DOI: 10.2477/jccj.2016-0020] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Affiliation(s)
- Kim HYEON-DEUK
- Department of Chemistry, Kyoto University, Kyoto, 606-8502, Japan
- Japan Science and Technology Agency, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama, 332-0012, Japan
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11
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Kowalczyk P, Terzyk AP, Gauden PA, Furmaniak S, Kaneko K, Miller TF. Nuclear Quantum Effects in the Layering and Diffusion of Hydrogen Isotopes in Carbon Nanotubes. J Phys Chem Lett 2015; 6:3367-3372. [PMID: 26270239 DOI: 10.1021/acs.jpclett.5b01545] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Although recent experimental studies have demonstrated that H2 and D2 molecules wet the inner surface of supergrowth carbon nanotubes at low temperatures, characterization of the structural and dynamical properties in this regime is challenging. This Letter presents a theoretical study of self-diffusion in pure and binary H2, D2, and T2 contact monolayer films formed on the inner surface of a carbon nanotube. Our results show that monolayer formation and self-diffusion both in pure hydrogen isotopes and in H2/T2 and H2/D2 isotope mixtures is impacted by nuclear quantum effects, suggesting potential applications of carbon nanotubes for the separation of hydrogen isotopes.
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Affiliation(s)
- Piotr Kowalczyk
- School of Engineering and Information Technology, Murdoch University , Perth, Western Australia 6150, Australia
| | - Artur P Terzyk
- Faculty of Chemistry, Physicochemistry of Carbon Materials Research Group, Nicolaus Copernicus University in Toruń , Gagarin Street 7, 87-100 Toruń, Poland
| | - Piotr A Gauden
- Faculty of Chemistry, Physicochemistry of Carbon Materials Research Group, Nicolaus Copernicus University in Toruń , Gagarin Street 7, 87-100 Toruń, Poland
| | - Sylwester Furmaniak
- Faculty of Chemistry, Physicochemistry of Carbon Materials Research Group, Nicolaus Copernicus University in Toruń , Gagarin Street 7, 87-100 Toruń, Poland
| | - Katsumi Kaneko
- Center for Energy and Environmental Science, Shinshu University , Nagano 380-8553, Japan
| | - Thomas F Miller
- Division of Chemistry and Chemical Engineering, California Institute of Technology , Pasadena, California 91125, United States
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12
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Smith KKG, Poulsen JA, Nyman G, Cunsolo A, Rossky PJ. Application of a new ensemble conserving quantum dynamics simulation algorithm to liquid para-hydrogen and ortho-deuterium. J Chem Phys 2015; 142:244113. [DOI: 10.1063/1.4922888] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kyle K. G. Smith
- Institute for Computational Engineering and Sciences and Department of Chemistry,University of Texas at Austin, Austin, Texas 78712, USA
| | - Jens Aage Poulsen
- Physical Chemistry, Department of Chemistry and Molecular Biology, University of Gothenburg, SE 41296 Gothenburg, Sweden
| | - Gunnar Nyman
- Physical Chemistry, Department of Chemistry and Molecular Biology, University of Gothenburg, SE 41296 Gothenburg, Sweden
| | - Alessandro Cunsolo
- Photon Sciences Directorate, Brookhaven National Laboratory, P.O. Box 5000, Upton, New York 11973, USA
| | - Peter J. Rossky
- Department of Chemistry, Rice University, Houston, Texas 77251, USA
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13
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Smith KKG, Poulsen JA, Nyman G, Rossky PJ. A new class of ensemble conserving algorithms for approximate quantum dynamics: Theoretical formulation and model problems. J Chem Phys 2015; 142:244112. [DOI: 10.1063/1.4922887] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kyle K. G. Smith
- Institute for Computational Engineering and Sciences and Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, USA
| | - Jens Aage Poulsen
- Physical Chemistry, Department of Chemistry and Molecular Biology, University of Gothenburg, SE 41296 Gothenburg, Sweden
| | - Gunnar Nyman
- Physical Chemistry, Department of Chemistry and Molecular Biology, University of Gothenburg, SE 41296 Gothenburg, Sweden
| | - Peter J. Rossky
- Department of Chemistry, Rice University, Houston, Texas 77251, USA
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14
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Makri N. Blip decomposition of the path integral: Exponential acceleration of real-time calculations on quantum dissipative systems. J Chem Phys 2014; 141:134117. [DOI: 10.1063/1.4896736] [Citation(s) in RCA: 42] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Nancy Makri
- Departments of Chemistry and Physics, University of Illinois, Urbana, Illinois 61801, USA
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15
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Hyeon-Deuk K, Ando K. Communication: Quantum molecular dynamics simulation of liquid para-hydrogen by nuclear and electron wave packet approach. J Chem Phys 2014; 140:171101. [DOI: 10.1063/1.4874635] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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16
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Smith KKG, Poulsen JA, Cunsolo A, Rossky PJ. Refinement of the experimental dynamic structure factor for liquid para-hydrogen and ortho-deuterium using semi-classical quantum simulation. J Chem Phys 2014; 140:034501. [DOI: 10.1063/1.4851997] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
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17
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Basire M, Borgis D, Vuilleumier R. Computing Wigner distributions and time correlation functions using the quantum thermal bath method: application to proton transfer spectroscopy. Phys Chem Chem Phys 2013; 15:12591-601. [DOI: 10.1039/c3cp50493j] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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18
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Ono J, Ando K. Semiquantal molecular dynamics simulations of hydrogen-bond dynamics in liquid water using multi-dimensional Gaussian wave packets. J Chem Phys 2012; 137:174503. [DOI: 10.1063/1.4762840] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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19
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Intermolecular diatomic energies of a hydrogen dimer with non-Born–Oppenheimer nuclear and electron wave packets. Chem Phys Lett 2012. [DOI: 10.1016/j.cplett.2012.02.073] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Liu J, Alder BJ, Miller WH. A semiclassical study of the thermal conductivity of low temperature liquids. J Chem Phys 2011; 135:114105. [DOI: 10.1063/1.3639107] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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22
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Liu J. Two more approaches for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics. J Chem Phys 2011; 134:194110. [DOI: 10.1063/1.3589406] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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23
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Georgescu I, Deckman J, Fredrickson LJ, Mandelshtam VA. Thermal Gaussian molecular dynamics for quantum dynamics simulations of many-body systems: Application to liquid para-hydrogen. J Chem Phys 2011; 134:174109. [PMID: 21548675 DOI: 10.1063/1.3585648] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ionut Georgescu
- Chemistry Department, University of California at Irvine, Irvine, California 92697, USA.
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24
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Liu J, Miller WH. An approach for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics. I. Theories. J Chem Phys 2011; 134:104101. [DOI: 10.1063/1.3555273] [Citation(s) in RCA: 29] [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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25
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Liu J, Miller WH. An approach for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics. II. Thermal correlation functions. J Chem Phys 2011; 134:104102. [DOI: 10.1063/1.3555274] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.0] [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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Reed SK, González-Martínez ML, Rubayo-Soneira J, Shalashilin DV. Cartesian coupled coherent states simulations: NenBr2 dissociation as a test case. J Chem Phys 2011; 134:054110. [DOI: 10.1063/1.3532407] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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27
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Kletenik-Edelman O, Reichman DR, Rabani E. On the mode-coupling treatment of collective density fluctuations for quantum liquids: Para-hydrogen and normal liquid helium. J Chem Phys 2011; 134:044528. [DOI: 10.1063/1.3521478] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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28
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Poulsen JA. A variational principle in Wigner phase-space with applications to statistical mechanics. J Chem Phys 2011; 134:034118. [DOI: 10.1063/1.3519637] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [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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Poma AB, Site LD. Adaptive resolution simulation of liquid para-hydrogen: testing the robustness of the quantum-classical adaptive coupling. Phys Chem Chem Phys 2011; 13:10510-9. [DOI: 10.1039/c0cp02865g] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
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30
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Makri N. Forward–backward semiclassical and quantum trajectory methods for time correlation functions. Phys Chem Chem Phys 2011; 13:14442-52. [DOI: 10.1039/c0cp02374d] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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31
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Deckman J, Mandelshtam VA. The ground state estimation by global optimization of an effective potential. Application to binary para-H(2)/ortho-D(2) molecular clusters. J Phys Chem A 2010; 114:9820-4. [PMID: 20540547 DOI: 10.1021/jp102898b] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
It is demonstrated how the problem of ground state estimation of an n-body system can be recast as the less demanding problem of finding the global minimum of an effective potential in the 3n-dimensional coordinate space. The latter emerges when the solution of the imaginary-time Schrödinger equation is approximated by a variational Gaussian wavepacket (VGW). The VGW becomes stationary in the infinite-imaginary-time limit. Such a stationary solution is not only exact for a harmonic potential, but it also provides a good approximation for a quantum state that is still localized in one of the basins of attraction, when, for example, the harmonic approximation may fail. The landscape of the effective potential is favorable for its global optimization, and is particularly suitable for optimization by GMIN, an open source program designed for global optimization using the basin-hopping algorithm. Consequently, the methodology is applied within GMIN to estimate the ground state structures of several binary para-H(2)/ortho-D(2) molecular clusters. The results are generally consistent with the previous observations for homogeneous para-H(2) and ortho-D(2) clusters, as well as for smaller binary clusters.
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Affiliation(s)
- Jason Deckman
- Chemistry Department, University of California at Irvine, Irvine, California 92697, USA
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32
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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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33
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Habershon S, Manolopoulos DE. Zero point energy leakage in condensed phase dynamics: An assessment of quantum simulation methods for liquid water. J Chem Phys 2009; 131:244518. [DOI: 10.1063/1.3276109] [Citation(s) in RCA: 108] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Liu J, Miller WH, Paesani F, Zhang W, Case DA. Quantum dynamical effects in liquid water: A semiclassical study on the diffusion and the infrared absorption spectrum. J Chem Phys 2009; 131:164509. [PMID: 19894958 DOI: 10.1063/1.3254372] [Citation(s) in RCA: 71] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [MESH Headings] [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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35
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Liu J, Miller WH. A simple model for the treatment of imaginary frequencies in chemical reaction rates and molecular liquids. J Chem Phys 2009; 131:074113. [DOI: 10.1063/1.3202438] [Citation(s) in RCA: 64] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
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36
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Lee TB, Jung DH, Kim D, Kim J, Choi K, Choi SH. Molecular dynamics simulation study on the hydrogen adsorption and diffusion in non-interpenetrating and interpenetrating IRMOFs. Catal Today 2009. [DOI: 10.1016/j.cattod.2008.12.011] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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37
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Poulsen JA, Li H, Nyman G. Classical Wigner method with an effective quantum force: Application to reaction rates. J Chem Phys 2009; 131:024117. [PMID: 19603980 DOI: 10.1063/1.3167299] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Affiliation(s)
- Jens Aage Poulsen
- Department of Chemistry, Physical Chemistry, University of Gothenburg, SE-412 96 Gothenburg, Sweden.
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38
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Paesani F, Voth GA. The properties of water: insights from quantum simulations. J Phys Chem B 2009; 113:5702-19. [PMID: 19385690 DOI: 10.1021/jp810590c] [Citation(s) in RCA: 189] [Impact Index Per Article: 12.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The properties of water play a central role in many phenomena of relevance to different areas of science, including physics, chemistry, biology, geology, and climate research. Although well studied for decades, the behavior of water under different conditions and in different environments still remains mysterious and often surprising. In this article, various efforts aimed at providing a comprehensive representation of the water properties at a molecular level through computer modeling and simulation will be described. In particular, the unique role played by the hydrogen-bond network will be examined, first in liquid water, then in the solvation of model biological compounds, and finally in ice, especially highlighting the important effects related to the quantization of the nuclear motion.
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Affiliation(s)
- Francesco Paesani
- Center for Biophysical Modeling and Simulation and Department of Chemistry, University of Utah, 315 South 1400 East Room 2020, Salt Lake City, Utah 84112-0850, USA
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39
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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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40
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Direct Monte Carlo evaluation of real-time quantum correlation functions using single-step propagators. Chem Phys Lett 2009. [DOI: 10.1016/j.cplett.2008.11.057] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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41
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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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42
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Liu J, Miller WH. Test of the consistency of various linearized semiclassical initial value time correlation functions in application to inelastic neutron scattering from liquid para-hydrogen. J Chem Phys 2008; 128:144511. [DOI: 10.1063/1.2889945] [Citation(s) in RCA: 52] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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43
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Marković N, Poulsen JA. A Linearized Path Integral Description of the Collision Process between a Water Molecule and a Graphite Surface. J Phys Chem A 2008; 112:1701-11. [DOI: 10.1021/jp074875c] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Nikola Marković
- Physical Chemistry, Department of Chemical and Biological Engineering, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
| | - Jens A. Poulsen
- Physical Chemistry, Department of Chemistry, Göteborg University, SE-412 96 Göteborg, Sweden
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44
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Hone TD, Poulsen JA, Rossky PJ, Manolopoulos DE. Comparison of Approximate Quantum Simulation Methods Applied to Normal Liquid Helium at 4 K. J Phys Chem B 2007; 112:294-300. [DOI: 10.1021/jp075022n] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Affiliation(s)
- Tyler D. Hone
- Center for Computational Molecular Science, Institute for Computational Engineering and Sciences and Department of Chemistry and Biochemistry, University of Texas at Austin, Austin, Texas 78712
| | - Jens A. Poulsen
- Physical Chemistry, Göteborg University, S-412-96, Göteborg, Sweden
| | - Peter J. Rossky
- Center for Computational Molecular Science, Institute for Computational Engineering and Sciences and Department of Chemistry and Biochemistry, University of Texas at Austin, Austin, Texas 78712
| | - David E. Manolopoulos
- Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QZ, United Kingdom
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45
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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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46
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Liu J, Miller WH. Linearized semiclassical initial value time correlation functions using the thermal Gaussian approximation: Applications to condensed phase systems. J Chem Phys 2007; 127:114506. [PMID: 17887856 DOI: 10.1063/1.2774990] [Citation(s) in RCA: 81] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The linearized approximation to the semiclassical initial value representation (LSC-IVR) has been used together with the thermal Gaussian approximation (TGA) (TGA/LSC-IVR) [J. Liu and W. H. Miller, J. Chem. Phys. 125, 224104 (2006)] to simulate quantum dynamical effects in realistic models of two condensed phase systems. This represents the first study of dynamical properties of the Ne(13) Lennard-Jones cluster in its liquid-solid phase transition region (temperature from 4 to 14 K). Calculation of the force autocorrelation function shows considerable differences from that given by classical mechanics, namely that the cluster is much more mobile (liquidlike) than in the classical case. Liquid para-hydrogen at two thermodynamic state points (25 and 14 K under nearly zero external pressure) has also been studied. The momentum autocorrelation function obtained from the TGA/LSC-IVR approach shows very good agreement with recent accurate path integral Monte Carlo results at 25 K [A. Nakayama and N. Makri, J. Chem. Phys. 125, 024503 (2006)]. The self-diffusion constants calculated by the TGA/LSC-IVR are in reasonable agreement with those from experiment and from other theoretical calculations. These applications demonstrate the TGA/LSC-IVR to be a practical and versatile method for quantum dynamics simulations of condensed phase systems.
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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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47
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Liu J, Miller WH. Real time correlation function in a single phase space integral beyond the linearized semiclassical initial value representation. J Chem Phys 2007; 126:234110. [PMID: 17600407 DOI: 10.1063/1.2743023] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
It is shown how quantum mechanical time correlation functions [defined, e.g., in Eq. (1.1)] can be expressed, without approximation, in the same form as the linearized approximation of the semiclassical initial value representation (LSC-IVR), or classical Wigner model, for the correlation function [cf. Eq. (2.1)], i.e., as a phase space average (over initial conditions for trajectories) of the Wigner functions corresponding to the two operators. The difference is that the trajectories involved in the LSC-IVR evolve classically, i.e., according to the classical equations of motion, while in the exact theory they evolve according to generalized equations of motion that are derived here. Approximations to the exact equations of motion are then introduced to achieve practical methods that are applicable to complex (i.e., large) molecular systems. Four such methods are proposed in the paper--the full Wigner dynamics (full WD) and the second order WD based on "Wigner trajectories" [H. W. Lee and M. D. Scully, J. Chem. Phys. 77, 4604 (1982)] and the full Donoso-Martens dynamics (full DMD) and the second order DMD based on "Donoso-Martens trajectories" [A. Donoso and C. C. Martens, Phys. Rev. Lett. 8722, 223202 (2001)]--all of which can be viewed as generalizations of the original LSC-IVR method. Numerical tests of the four versions of this new approach are made for two anharmonic model problems, and for each the momentum autocorrelation function (i.e., operators linear in coordinate or momentum operators) and the force autocorrelation function (nonlinear operators) have been calculated. These four new approximate treatments are indeed seen to be significant improvements to the original LSC-IVR approximation.
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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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48
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Quantum Contributions to Free Energy Changes in Fluids. ACTA ACUST UNITED AC 2007. [DOI: 10.1007/978-3-540-38448-9_11] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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49
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Liu J, Miller WH. Using the thermal Gaussian approximation for the Boltzmann operator in semiclassical initial value time correlation functions. J Chem Phys 2006; 125:224104. [PMID: 17176131 DOI: 10.1063/1.2395941] [Citation(s) in RCA: 80] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The thermal Gaussian approximation (TGA) recently developed by Frantsuzov et al. [Chem. Phys. Lett. 381, 117 (2003)] has been demonstrated to be a practical way for approximating the Boltzmann operator exp(-betaH) for multidimensional systems. In this paper the TGA is combined with semiclassical (SC) initial value representations (IVRs) for thermal time correlation functions. Specifically, it is used with the linearized SC-IVR (LSC-IVR, equivalent to the classical Wigner model), and the "forward-backward semiclassical dynamics" approximation developed by Shao and Makri [J. Phys. Chem. A 103, 7753 (1999); 103, 9749 (1999)]. Use of the TGA with both of these approximate SC-IVRs allows the oscillatory part of the IVR to be integrated out explicitly, providing an extremely simple result that is readily applicable to large molecular systems. Calculation of the force-force autocorrelation for a strongly anharmonic oscillator demonstrates its accuracy, and calculation of the velocity autocorrelation function (and thus the diffusion coefficient) of liquid neon demonstrates its applicability.
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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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50
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Braams BJ, Manolopoulos DE. On the short-time limit of ring polymer molecular dynamics. J Chem Phys 2006; 125:124105. [PMID: 17014164 DOI: 10.1063/1.2357599] [Citation(s) in RCA: 123] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We examine the short-time accuracy of a class of approximate quantum dynamical techniques that includes the centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD) methods. Both of these methods are based on the path integral molecular dynamics (PIMD) technique for calculating the exact static equilibrium properties of quantum mechanical systems. For Kubo-transformed real-time correlation functions involving operators that are linear functions of positions or momenta, the RPMD and (adiabatic) CMD approximations differ only in the choice of the artificial mass matrix of the system of ring polymer beads that is employed in PIMD. The obvious ansatz for a general method of this type is therefore to regard the elements of the PIMD (or Parrinello-Rahman) mass matrix as an adjustable set of parameters that can be chosen to improve the accuracy of the resulting approximation. We show here that this ansatz leads uniquely to the RPMD approximation when the criterion that is used to select the mass matrix is the short-time accuracy of the Kubo-transformed correlation function. In particular, we show that the leading error in the RPMD position autocorrelation function is O(t(8)) and the error in the velocity autocorrelation function is O(t(6)), for a general anharmonic potential. The corresponding errors in the CMD approximation are O(t(6)) and O(t(4)), respectively.
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Affiliation(s)
- Bastiaan J Braams
- Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30332, USA
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