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London N, Bu S, Johnson B, Ananth N. Mean-Field Ring Polymer Rates Using a Population Dividing Surface. J Phys Chem A 2024; 128:5730-5739. [PMID: 38976564 DOI: 10.1021/acs.jpca.4c00005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/10/2024]
Abstract
Mean-field ring polymer molecular dynamics offers a computationally efficient method for the simulation of reaction rates in multilevel systems. Previous work has established that, to model a nonadiabatic state-to-state reaction accurately, it is necessary to ensure reactive trajectories form kinked ring polymer configurations at the dividing surface. Building on this idea, we introduce a population difference coordinate and a reactive flux expression modified to only include contributions from kinked configurations. We test the accuracy of the resulting mean-field rate theory on a series of linear vibronic coupling model systems. We demonstrate that this new kMF-RP rate approach is efficient to implement and quantitatively accurate for models over a wide range of driving forces, coupling strengths, and temperatures.
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Affiliation(s)
- Nathan London
- Department of Chemistry, Cornell University, Ithaca, New York 14853, United States
| | - Siyu Bu
- Department of Chemistry, Cornell University, Ithaca, New York 14853, United States
| | - Britta Johnson
- Department of Chemistry, Cornell University, Ithaca, New York 14853, United States
| | - Nandini Ananth
- Department of Chemistry, Cornell University, Ithaca, New York 14853, United States
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2
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Orr L, Roy PN. Operator Formulation of Feynman Path Centroid Dynamics for Rotations. J Phys Chem A 2024; 128:3419-3433. [PMID: 38651978 DOI: 10.1021/acs.jpca.3c08201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/25/2024]
Abstract
An operator formulation of centroid molecular dynamics (CMD) for rotational degrees of freedom is presented. The quasi-density operator concept was introduced by Jang and Voth [J. Chem. Phys 111, 2357 (1999)] and is used to obtain a phase-space mapping without the need for discretized path integrals. The approach allows the calculation of approximate Kubo-transformed time correlation functions. The particle on a ring is chosen as an illustrative example. Numerical results demonstrate that the proposed approach leads to accurate results when compared with exact diagonalization calculations for linear operators. At very low temperatures, it is found that rotational CMD yields results that are in exact agreement with the quantum dynamics of a spin-1 system.
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Affiliation(s)
- Lindsay Orr
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Pierre-Nicholas Roy
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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3
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Videla PE, Batista VS. Matsubara dynamics approximation for generalized multi-time correlation functions. J Chem Phys 2023; 158:2889027. [PMID: 37154285 DOI: 10.1063/5.0146654] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2023] [Accepted: 04/21/2023] [Indexed: 05/10/2023] Open
Abstract
We introduce a semi-classical approximation for calculating generalized multi-time correlation functions based on Matsubara dynamics, a classical dynamics approach that conserves the quantum Boltzmann distribution. This method is exact for the zero time and harmonic limits and reduces to classical dynamics when only one Matsubara mode is considered (i.e., the centroid). Generalized multi-time correlation functions can be expressed as canonical phase-space integrals, involving classically evolved observables coupled through Poisson brackets in a smooth Matsubara space. Numerical tests on a simple potential show that the Matsubara approximation exhibits better agreement with exact results than classical dynamics, providing a bridge between the purely quantum and classical descriptions of multi-time correlation functions. Despite the phase problem that prevents practical applications of Matsubara dynamics, the reported work provides a benchmark theory for the future development of quantum-Boltzmann-preserving semi-classical approximations for studies of chemical dynamics in condensed phase systems.
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Affiliation(s)
- Pablo E Videla
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520-8107, USA
| | - Victor S Batista
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520-8107, USA
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4
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Videla PE, Batista VS. An exact imaginary-time path-integral phase-space formulation of multi-time correlation functions. J Chem Phys 2023; 158:094101. [PMID: 36889944 DOI: 10.1063/5.0137898] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/10/2023] Open
Abstract
An exact representation of quantum mechanics using the language of phase-space variables provides a natural starting point to introduce and develop semiclassical approximations for the calculation of time correlation functions. Here, we introduce an exact path-integral formalism for calculations of multi-time quantum correlation functions as canonical averages over ring-polymer dynamics in imaginary time. The formulation provides a general formalism that exploits the symmetry of path integrals with respect to permutations in imaginary time, expressing correlations as products of imaginary-time-translation-invariant phase-space functions coupled through Poisson bracket operators. The method naturally recovers the classical limit of multi-time correlation functions and provides an interpretation of quantum dynamics in terms of "interfering trajectories" of the ring-polymer in phase space. The introduced phase-space formulation provides a rigorous framework for the future development of quantum dynamics methods that exploit the invariance of imaginary time path integrals to cyclic permutations.
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Affiliation(s)
- Pablo E Videla
- Department of Chemistry, Yale Energy Sciences Institute and Yale Quantum Institute, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA
| | - Victor S Batista
- Department of Chemistry, Yale Energy Sciences Institute and Yale Quantum Institute, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA
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5
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Jung KA, Markland TE. 2D spectroscopies from condensed phase dynamics: Accessing third-order response properties from equilibrium multi-time correlation functions. J Chem Phys 2022; 157:094111. [DOI: 10.1063/5.0107087] [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
The third-order response lies at the heart of simulating and interpreting nonlinear spectroscopies ranging from two dimensional infrared (2D-IR) to 2D electronic (2D-ES), and 2D sum frequency generation (2D-SFG). The extra time and frequency dimensions in these spectroscopies provides access to rich information on the electronic and vibrational states present, the coupling between them, and the resulting rates at which they exchange energy that are obscured in linear spectroscopy, particularly for condensed phase systems that usually contain many overlapping features. While the exact quantum expression for the third-order response is well established it is incompatible with the methods that are practical for calculating the atomistic dynamics of large condensed phase systems. These methods, which include both classical mechanics and quantum dynamics methods that retain quantum statistical properties while obeying the symmetries of classical dynamics, such as LSC-IVR, Centroid Molecular Dynamics (CMD) and Ring Polymer Molecular Dynamics (RPMD) naturally provide short-time approximations to the multi-time symmetrized Kubo transformed correlation function. Here, we show how the third-order response can be formulated in terms of equilibrium symmetrized Kubo transformed correlation functions. We demonstrate the utility and accuracy of our approach by showing how it can be used to obtain the third-order response of a series of model systems using both classical dynamics and RPMD. In particular, we show that this approach captures features such as anharmonically induced vertical splittings and peak shifts while providing a physically transparent framework for understanding multidimensional spectroscopies.
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6
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Liu X, Zhang L, Liu J. Machine learning phase space quantum dynamics approaches. J Chem Phys 2021; 154:184104. [PMID: 34241027 DOI: 10.1063/5.0046689] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
Derived from phase space expressions of the quantum Liouville theorem, equilibrium continuity dynamics is a category of trajectory-based phase space dynamics methods, which satisfies the two critical fundamental criteria: conservation of the quantum Boltzmann distribution for the thermal equilibrium system and being exact for any thermal correlation functions (even of nonlinear operators) in the classical and harmonic limits. The effective force and effective mass matrix are important elements in the equations of motion of equilibrium continuity dynamics, where only the zeroth term of an exact series expansion of the phase space propagator is involved. We introduce a machine learning approach for fitting these elements in quantum phase space, leading to a much more efficient integration of the equations of motion. Proof-of-concept applications to realistic molecules demonstrate that machine learning phase space dynamics approaches are possible as well as competent in producing reasonably accurate results with a modest computation effort.
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Affiliation(s)
- Xinzijian Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Linfeng Zhang
- Beijing Institute of Big Data Research, Beijing 100871, China
| | - Jian Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
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Jung KA, Videla PE, Batista VS. Ring-polymer, centroid, and mean-field approximations to multi-time Matsubara dynamics. J Chem Phys 2020; 153:124112. [PMID: 33003707 DOI: 10.1063/5.0021843] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Based on a recently developed generalization of Matsubara dynamics to the multi-time realm, we present a formal derivation of multi-time generalizations of ring-polymer molecular dynamics, thermostatted ring-polymer molecular dynamics (TRPMD), centroid molecular dynamics (CMD), and mean-field Matsubara dynamics. Additionally, we analyze the short-time accuracy of each methodology. We find that for multi-time correlation functions of linear operators, (T)RPMD is accurate up to order t3, while CMD is only correct up to t, indicating a degradation in the accuracy of these methodologies with respect to the single-time counterparts. The present work provides a firm justification for the use of path-integral-based approximations for the calculation of multi-time correlation functions.
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Affiliation(s)
- Kenneth A Jung
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
| | - Pablo E Videla
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
| | - Victor S Batista
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
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Tong Z, Videla PE, Jung KA, Batista VS, Sun X. Two-dimensional Raman spectroscopy of Lennard-Jones liquids via ring-polymer molecular dynamics. J Chem Phys 2020; 153:034117. [PMID: 32716164 DOI: 10.1063/5.0015436] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The simulation of multidimensional vibrational spectroscopy of condensed-phase systems including nuclear quantum effects is challenging since full quantum-mechanical calculations are still intractable for large systems comprising many degrees of freedom. Here, we apply the recently developed double Kubo transform (DKT) methodology in combination with ring-polymer molecular dynamics (RPMD) for evaluating multi-time correlation functions [K. A. Jung et al., J. Chem. Phys. 148, 244105 (2018)], providing a practical method for incorporating nuclear quantum effects in nonlinear spectroscopy of condensed-phase systems. We showcase the DKT approach in the simulation of the fifth-order two-dimensional (2D) Raman spectroscopy of Lennard-Jones liquids as a prototypical example, which involves nontrivial nonlinear spectroscopic observables of systems described by anharmonic potentials. Our results show that the DKT can faithfully reproduce the 2D Raman response of liquid xenon at high temperatures, where the system behaves classically. In contrast, liquid neon at low temperatures exhibits moderate but discernible nuclear quantum effects in the 2D Raman response compared to the responses obtained with classical molecular dynamics approaches. Thus, the DKT formalism in combination with RPMD simulations enables simulations of multidimensional optical spectroscopy of condensed-phase systems that partially account for nuclear quantum effects.
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Affiliation(s)
- Zhengqing Tong
- Division of Arts and Sciences, NYU Shanghai, 1555 Century Avenue, Shanghai 200122, China
| | - Pablo E Videla
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
| | - Kenneth A Jung
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
| | - 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, 1555 Century Avenue, Shanghai 200122, China
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9
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Svensson SKM, Poulsen JA, Nyman G. Classical Wigner model based on a Feynman path integral open polymer. J Chem Phys 2020; 152:094111. [DOI: 10.1063/1.5126183] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- S. Karl-Mikael Svensson
- Department of Chemistry and Molecular Biology, University of Gothenburg, SE 405 30 Gothenburg, Sweden
| | - 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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10
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Jung KA, Videla PE, Batista VS. Multi-time formulation of Matsubara dynamics. J Chem Phys 2019; 151:034108. [PMID: 31325942 DOI: 10.1063/1.5110427] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Matsubara dynamics has recently emerged as the most general form of a quantum-Boltzmann-conserving classical dynamics theory for the calculation of single-time correlation functions. Here, we present a generalization of Matsubara dynamics for the evaluation of multitime correlation functions. We first show that the Matsubara approximation can also be used to approximate the two-time symmetrized double Kubo transformed correlation function. By a straightforward extension of these ideas to the multitime realm, a multitime Matsubara dynamics approximation can be obtained for the multitime fully symmetrized Kubo transformed correlation function. Although not a practical method, due to the presence of a phase-term, this multitime formulation of Matsubara dynamics represents a benchmark theory for future development of Boltzmann preserving semiclassical approximations to general higher order multitime correlation functions. It also reveals a connection between imaginary time-ordering in the path integral and the classical dynamics of multitime correlation functions.
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Affiliation(s)
- Kenneth A Jung
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
| | - Pablo E Videla
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
| | - Victor S Batista
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
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11
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Jansen TLC, Saito S, Jeon J, Cho M. Theory of coherent two-dimensional vibrational spectroscopy. J Chem Phys 2019; 150:100901. [DOI: 10.1063/1.5083966] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Thomas la Cour Jansen
- University of Groningen, Zernike Institute for Advanced Materials, Nijenborgh 4, 9747 AG Groningen, The Netherlands
| | - Shinji Saito
- Institute for Molecular Science, Myodaiji, Okazaki, Aichi 444-8585, Japan and The Graduate University for Advanced Studies, Myodaiji, Okazaki, Aichi 444-8585, Japan
| | - Jonggu Jeon
- Center for Molecular Spectroscopy and Dynamics, Institute for Basic Science (IBS), Seoul 02841, South Korea
| | - Minhaeng Cho
- Center for Molecular Spectroscopy and Dynamics, Institute for Basic Science (IBS), Seoul 02841, South Korea
- Department of Chemistry, Korea University, Seoul 02841, South Korea
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12
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Jung KA, Videla PE, Batista VS. Inclusion of nuclear quantum effects for simulations of nonlinear spectroscopy. J Chem Phys 2018; 148:244105. [PMID: 29960352 DOI: 10.1063/1.5036768] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The computation and interpretation of nonlinear vibrational spectroscopy is of vital importance for understanding a wide range of dynamical processes in molecular systems. Here, we introduce an approach to evaluate multi-time response functions in terms of multi-time double symmetrized Kubo transformed thermal correlation functions. Furthermore, we introduce a multi-time extension of ring polymer molecular dynamics to evaluate these Kubo transforms. Benchmark calculations show that the approximations are useful for short times even for nonlinear operators, providing a consistent improvement over classical simulations of multi-time correlation functions. The introduced methodology thus provides a practical way of including nuclear quantum effects in multi-time response functions of non-linear optical spectroscopy.
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Affiliation(s)
- Kenneth A Jung
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
| | - Pablo E Videla
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
| | - Victor S Batista
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA
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13
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Cendagorta JR, Bačić Z, Tuckerman ME. An open-chain imaginary-time path-integral sampling approach to the calculation of approximate symmetrized quantum time correlation functions. J Chem Phys 2018; 148:102340. [PMID: 29544313 DOI: 10.1063/1.5005543] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
Abstract
We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.
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Affiliation(s)
| | - Zlatko Bačić
- Department of Chemistry, New York University, New York, New York 10003, USA
| | - Mark E Tuckerman
- Department of Chemistry, New York University, New York, New York 10003, USA
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15
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Affiliation(s)
- Xinzijian Liu
- Beijing National Laboratory For Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing, China
| | - Jian Liu
- Beijing National Laboratory For Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing, China
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16
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Orr L, Hernández de la Peña L, Roy PN. Formulation of state projected centroid molecular dynamics: Microcanonical ensemble and connection to the Wigner distribution. J Chem Phys 2017; 146:214116. [PMID: 28595402 PMCID: PMC5462618 DOI: 10.1063/1.4984229] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2017] [Accepted: 05/15/2017] [Indexed: 11/14/2022] Open
Abstract
A derivation of quantum statistical mechanics based on the concept of a Feynman path centroid is presented for the case of generalized density operators using the projected density operator formalism of Blinov and Roy [J. Chem. Phys. 115, 7822-7831 (2001)]. The resulting centroid densities, centroid symbols, and centroid correlation functions are formulated and analyzed in the context of the canonical equilibrium picture of Jang and Voth [J. Chem. Phys. 111, 2357-2370 (1999)]. The case where the density operator projects onto a particular energy eigenstate of the system is discussed, and it is shown that one can extract microcanonical dynamical information from double Kubo transformed correlation functions. It is also shown that the proposed projection operator approach can be used to formally connect the centroid and Wigner phase-space distributions in the zero reciprocal temperature β limit. A Centroid Molecular Dynamics (CMD) approximation to the state-projected exact quantum dynamics is proposed and proven to be exact in the harmonic limit. The state projected CMD method is also tested numerically for a quartic oscillator and a double-well potential and found to be more accurate than canonical CMD. In the case of a ground state projection, this method can resolve tunnelling splittings of the double well problem in the higher barrier regime where canonical CMD fails. Finally, the state-projected CMD framework is cast in a path integral form.
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Affiliation(s)
- Lindsay Orr
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | | | - Pierre-Nicholas Roy
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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Affiliation(s)
- Timothy J. H. Hele
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY, USA
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Welsch R, Song K, Shi Q, Althorpe SC, Miller TF. Non-equilibrium dynamics from RPMD and CMD. J Chem Phys 2016; 145:204118. [DOI: 10.1063/1.4967958] [Citation(s) in RCA: 42] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
Affiliation(s)
- Ralph Welsch
- Division of Chemistry and Chemical Engineering, California Institute of Technology,1200 E. California Blvd., Pasadena, California 91125, USA
| | - Kai Song
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
| | - Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China
| | - Stuart C. Althorpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Thomas F. Miller
- Division of Chemistry and Chemical Engineering, California Institute of Technology,1200 E. California Blvd., Pasadena, California 91125, USA
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19
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Ceriotti M, Fang W, Kusalik PG, McKenzie RH, Michaelides A, Morales MA, Markland TE. Nuclear Quantum Effects in Water and Aqueous Systems: Experiment, Theory, and Current Challenges. Chem Rev 2016; 116:7529-50. [DOI: 10.1021/acs.chemrev.5b00674] [Citation(s) in RCA: 339] [Impact Index Per Article: 42.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Michele Ceriotti
- Laboratory
of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Wei Fang
- Thomas
Young Centre, London Centre for Nanotechnology and Department of Physics
and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Peter G. Kusalik
- Department
of Chemistry, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
| | - Ross H. McKenzie
- School
of Mathematics and Physics, University of Queensland, Brisbane, 4072 Queensland Australia
| | - Angelos Michaelides
- Thomas
Young Centre, London Centre for Nanotechnology and Department of Physics
and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Miguel A. Morales
- Lawrence Livermore National Laboratory, Livermore, California 94550, United States
| | - Thomas E. Markland
- Department
of Chemistry, Stanford University, 333 Campus Drive, Stanford, California 94305, United States
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20
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Hele TJH. On the relation between thermostatted ring-polymer molecular dynamics and exact quantum dynamics. Mol Phys 2016. [DOI: 10.1080/00268976.2015.1136003] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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21
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Abstract
We show a new imaginary time path integral based method--path integral Liouville dynamics (PILD), which can be derived from the equilibrium Liouville dynamics [J. Liu and W. H. Miller, J. Chem. Phys. 134, 104101 (2011)] in the Wigner phase space. Numerical tests of PILD with the simple (white noise) Langevin thermostat have been made for two strongly anharmonic model problems. Since implementation of PILD does not request any specific form of the potential energy surface, the results suggest that PILD offers a potentially useful approach for general condensed phase molecular systems to have the two important properties: conserves the quantum canonical distribution and recovers exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits.
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Affiliation(s)
- Jian Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
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22
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Jang S, Sinitskiy AV, Voth GA. Can the ring polymer molecular dynamics method be interpreted as real time quantum dynamics? J Chem Phys 2014. [DOI: 10.1063/1.4870717] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Zeng T, Roy PN. Microscopic molecular superfluid response: theory and simulations. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2014; 77:046601. [PMID: 24647079 DOI: 10.1088/0034-4885/77/4/046601] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Since its discovery in 1938, superfluidity has been the subject of much investigation because it provides a unique example of a macroscopic manifestation of quantum mechanics. About 60 years later, scientists successfully observed this phenomenon in the microscopic world though the spectroscopic Andronikashvili experiment in helium nano-droplets. This reduction of scale suggests that not only helium but also para-H2 (pH2) can be a candidate for superfluidity. This expectation is based on the fact that the smaller number of neighbours and surface effects of a finite-size cluster may hinder solidification and promote a liquid-like phase. The first prediction of superfluidity in pH2 clusters was reported in 1991 based on quantum Monte Carlo simulations. The possible superfluidity of pH2 was later indirectly observed in a spectroscopic Andronikashvili experiment in 2000. Since then, a growing number of studies have appeared, and theoretical simulations have been playing a special role because they help guide and interpret experiments. In this review, we go over the theoretical studies of pH2 superfluid clusters since the experiment of 2000. We provide a historical perspective and introduce the basic theoretical formalism along with key experimental advances. We then present illustrative results of the theoretical studies and comment on the possible future developments in the field. We include sufficient theoretical details such that the review can serve as a guide for newcomers to the field.
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Affiliation(s)
- Tao Zeng
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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24
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Richardson JO, Thoss M. Communication: Nonadiabatic ring-polymer molecular dynamics. J Chem Phys 2013; 139:031102. [DOI: 10.1063/1.4816124] [Citation(s) in RCA: 99] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
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25
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Hernández de la Peña L. On the zero temperature limit of the Kubo-transformed quantum time correlation function. Mol Phys 2013. [DOI: 10.1080/00268976.2013.812755] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Pérez A, Tuckerman ME. Improving the convergence of closed and open path integral molecular dynamics via higher order Trotter factorization schemes. J Chem Phys 2011; 135:064104. [PMID: 21842923 DOI: 10.1063/1.3609120] [Citation(s) in RCA: 51] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Alejandro Pérez
- Department of Chemistry, New York University, New York, New York 10003, USA.
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Paesani F. Temperature-Dependent Infrared Spectroscopy of Water from a First-Principles Approach. J Phys Chem A 2011; 115:6861-71. [DOI: 10.1021/jp111426r] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Francesco Paesani
- Department of Chemistry and Biochemistry, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093, United States
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29
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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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30
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Paesani F, Xantheas SS, Voth GA. Infrared Spectroscopy and Hydrogen-Bond Dynamics of Liquid Water from Centroid Molecular Dynamics with an Ab Initio-Based Force Field. J Phys Chem B 2009; 113:13118-30. [DOI: 10.1021/jp907648y] [Citation(s) in RCA: 114] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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, and Chemical and Materials Sciences Division, Pacific Northwest National Laboratory, 902 Battelle Boulevard, P.O. Box 999, MS K1-83, Richland, Washington 99352
| | - Sotiris S. Xantheas
- 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, and Chemical and Materials Sciences Division, Pacific Northwest National Laboratory, 902 Battelle Boulevard, P.O. Box 999, MS K1-83, Richland, Washington 99352
| | - Gregory A. Voth
- 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, and Chemical and Materials Sciences Division, Pacific Northwest National Laboratory, 902 Battelle Boulevard, P.O. Box 999, MS K1-83, Richland, Washington 99352
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31
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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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32
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Thomas V, Iftimie R. Toward Understanding the Dissociation of Weak Acids in Water: 1. Using IR Spectroscopy to Identify Proton-Shared Hydrogen-Bonded Ion-Pair Intermediates. J Phys Chem B 2008; 113:4152-60. [DOI: 10.1021/jp807378x] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Affiliation(s)
- Vibin Thomas
- Département de Chimie, Université de Montréal, CP 6128, succursale Centre-Ville, Montréal, H3C3J7, Canada
| | - Radu Iftimie
- Département de Chimie, Université de Montréal, CP 6128, succursale Centre-Ville, Montréal, H3C3J7, Canada
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33
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Paesani F, Voth GA. Nonlinear quantum time correlation functions from centroid molecular dynamics and the maximum entropy method. J Chem Phys 2008; 129:194113. [DOI: 10.1063/1.3013365] [Citation(s) in RCA: 15] [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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34
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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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35
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Yoshimori A. New conditions for validity of the centroid molecular dynamics and ring polymer molecular dynamics. J Chem Phys 2008; 128:234105. [DOI: 10.1063/1.2939480] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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36
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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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37
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Iftimie R, Thomas V, Plessis S, Marchand P, Ayotte P. Spectral Signatures and Molecular Origin of Acid Dissociation Intermediates. J Am Chem Soc 2008; 130:5901-7. [DOI: 10.1021/ja077846o] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Radu Iftimie
- Départment de Chimie, Université de Montréal, CP 6128, succursale Centre-Ville, Montréal H3C3J7, Canada, and Département de Chimie, Université de Sherbrooke, 2500 Boulevard Université, Sherbrooke J1K2R1, Canada
| | - Vibin Thomas
- Départment de Chimie, Université de Montréal, CP 6128, succursale Centre-Ville, Montréal H3C3J7, Canada, and Département de Chimie, Université de Sherbrooke, 2500 Boulevard Université, Sherbrooke J1K2R1, Canada
| | - Sylvain Plessis
- Départment de Chimie, Université de Montréal, CP 6128, succursale Centre-Ville, Montréal H3C3J7, Canada, and Département de Chimie, Université de Sherbrooke, 2500 Boulevard Université, Sherbrooke J1K2R1, Canada
| | - Patrick Marchand
- Départment de Chimie, Université de Montréal, CP 6128, succursale Centre-Ville, Montréal H3C3J7, Canada, and Département de Chimie, Université de Sherbrooke, 2500 Boulevard Université, Sherbrooke J1K2R1, Canada
| | - Patrick Ayotte
- Départment de Chimie, Université de Montréal, CP 6128, succursale Centre-Ville, Montréal H3C3J7, Canada, and Département de Chimie, Université de Sherbrooke, 2500 Boulevard Université, Sherbrooke J1K2R1, Canada
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38
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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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39
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Paesani F, Iuchi S, Voth GA. Quantum effects in liquid water from an ab initio-based polarizable force field. J Chem Phys 2007; 127:074506. [PMID: 17718619 DOI: 10.1063/1.2759484] [Citation(s) in RCA: 131] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The importance of quantum effects as well as the accuracy of the ab initio-based polarizable TTM2.1-F force field in describing liquid water are quantitatively assessed by a detailed analysis of the temperature dependence of several thermodynamic and dynamical properties computed using the path-integral molecular dynamics and centroid molecular dynamics methods. The results show that quantum effects are not negligible even at relatively high temperatures, and their inclusion in simulations with the TTM2.1-F water model is necessary to achieve a more accurate description of the liquid properties. Comparison with the results reported in the literature for empirical, nonpolarizable force fields demonstrates that the effects of the nuclear quantization on the dielectric constant are dependent in part on how the electronic polarization is described in the underlying water model, while comparison with other ab initio-based force fields shows that the TTM2.1-F model provides an overall accurate description of liquid water. Analysis of the isotope effect on the dynamical properties does not display significant temperature dependence. This suggests that the contribution of quantum tunneling, which has been proposed as a possible cause for the different orientational dynamics observed for the HDO:H(2)O and HDO:D(2)O systems, appears to be small.
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Affiliation(s)
- Francesco Paesani
- The Center for Biophysical Modeling and Simulation, Department of Chemistry, University of Utah, 315 S. 1400 E., Room 2020, Salt Lake City, Utah 84112-0850, USA
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40
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Paesani F, Zhang W, Case DA, Cheatham TE, Voth GA. An accurate and simple quantum model for liquid water. J Chem Phys 2007; 125:184507. [PMID: 17115765 DOI: 10.1063/1.2386157] [Citation(s) in RCA: 164] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Abstract
The path-integral molecular dynamics and centroid molecular dynamics methods have been applied to investigate the behavior of liquid water at ambient conditions starting from a recently developed simple point charge/flexible (SPC/Fw) model. Several quantum structural, thermodynamic, and dynamical properties have been computed and compared to the corresponding classical values, as well as to the available experimental data. The path-integral molecular dynamics simulations show that the inclusion of quantum effects results in a less structured liquid with a reduced amount of hydrogen bonding in comparison to its classical analog. The nuclear quantization also leads to a smaller dielectric constant and a larger diffusion coefficient relative to the corresponding classical values. Collective and single molecule time correlation functions show a faster decay than their classical counterparts. Good agreement with the experimental measurements in the low-frequency region is obtained for the quantum infrared spectrum, which also shows a higher intensity and a redshift relative to its classical analog. A modification of the original parametrization of the SPC/Fw model is suggested and tested in order to construct an accurate quantum model, called q-SPC/Fw, for liquid water. The quantum results for several thermodynamic and dynamical properties computed with the new model are shown to be in a significantly better agreement with the experimental data. Finally, a force-matching approach was applied to the q-SPC/Fw model to derive an effective quantum force field for liquid water in which the effects due to the nuclear quantization are explicitly distinguished from those due to the underlying molecular interactions. Thermodynamic and dynamical properties computed using standard classical simulations with this effective quantum potential are found in excellent agreement with those obtained from significantly more computationally demanding full centroid molecular dynamics simulations. The present results suggest that the inclusion of nuclear quantum effects into an empirical model for water enhances the ability of such model to faithfully represent experimental data, presumably through an increased ability of the model itself to capture realistic physical effects.
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Affiliation(s)
- Francesco Paesani
- Center for Biophysical Modeling and Simulation, University of Utah, Salt Lake City, Utah 84112, USA
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41
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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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42
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43
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Craig IR, Manolopoulos DE. A refined ring polymer molecular dynamics theory of chemical reaction rates. J Chem Phys 2007; 123:34102. [PMID: 16080725 DOI: 10.1063/1.1954769] [Citation(s) in RCA: 232] [Impact Index Per Article: 13.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We further develop the ring polymer molecular dynamics (RPMD) method for calculating chemical reaction rates [I. R. Craig and D. E. Manolopoulos, J. Chem. Phys. 122, 084106 (2005)]. We begin by showing how the rate coefficient we obtained before can be calculated in a more efficient way by considering the side functions of the ring-polymer centroids, rather than averaging over the side functions of the individual ring-polymer beads. This has two distinct advantages. First, the statistics of the phase-space average over the ring-polymer coordinates and momenta are greatly improved. Second, the resulting flux-side correlation function converges to its long-time limit much more rapidly. Indeed the short-time limit of this flux-side correlation function already provides a "quantum transition state theory" approximation to the final rate coefficient. In cases where transition state recrossing effects are negligible, and the transition state dividing surface is put in the right place, the RPMD rate is therefore obtained almost instantly. We then go on to show that the long-time limit of the new flux-side correlation function, and hence the fully converged RPMD reaction rate, is rigorously independent of the choice of the transition state dividing surface. This is especially significant because the optimum dividing surface can often be very difficult to determine for reactions in complex chemical systems.
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Affiliation(s)
- Ian R Craig
- Physical and Theoretical Chemistry Laboratory, Oxford University, UK
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44
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45
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Huh Y, Roy PN. Inclusion of inversion symmetry in centroid molecular dynamics: a possible avenue to recover quantum coherence. J Chem Phys 2006; 125:164103. [PMID: 17092059 DOI: 10.1063/1.2358989] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
Inversion symmetry is included in the operator formulation of the centroid molecular dynamics (CMD). This work involves the development of a symmetry-adapted CMD (SA-CMD), here particularly for symmetrization and antisymmetrization projections. A symmetry-adapted quasidensity operator, as defined by Blinov and Roy [J. Chem. Phys. 115, 7822 (2001)], is employed to obtain the centroid representation of quantum mechanical operators. Numerical examples are given for a single particle confined to one-dimensional symmetric quartic and symmetric double-well potentials. Two SA-CMD simulations are performed separately for both projections, and centroid position autocorrelation functions are obtained. For each projection, the quality of the approximation as well as the accuracy are similar to those of regular CMD. It is shown that individual trajectories from two separate SA-CMD simulations can be properly combined to recover trajectories for Boltzmann statistics. Position autocorrelation functions are compared to the exact quantum mechanical ones. This explicit account of inversion symmetry provides a qualitative improvement on the conventional CMD approach and allows the recovery of some quantum coherence.
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Affiliation(s)
- Yoonjung Huh
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
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46
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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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47
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Kim H, Rossky PJ. Evaluation of quantum correlation functions from classical data: Anharmonic models. J Chem Phys 2006; 125:074107. [PMID: 16942322 DOI: 10.1063/1.2274412] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The previously introduced method of evaluating quantum mechanical time correlation functions using as input only classical simulation data is generalized and applied to two anharmonic model systems, as a further test. The quantum correction approach utilizes the relation between a general quantum correlation function and its classical analog. For the tested models, we obtain numerical results of nonlinear correlation functions with comparable accuracy to that of the centroid molecular dynamics method, although the present method is much simpler to implement and not limited to real valued quantum correlation functions.
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Affiliation(s)
- Hyojoon Kim
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada.
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48
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Hernández de la Peña L, Kusalik PG. Quantum effects in liquid water and ice: Model dependence. J Chem Phys 2006; 125:054512. [PMID: 16942231 DOI: 10.1063/1.2238861] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This paper explores the influence of choice of potential model on the quantum effects observed in liquid water and ice. This study utilizes standard rigid models and a more formal context for the rigid-body centroid molecular dynamics methodology used to perform the quantum simulations is provided. Quantum and classical molecular dynamics simulations are carried out for liquid water and ice Ih at 298 and 220 K, respectively, with the simple point charge/extended and TIP4P-Ew water models. The results obtained for equilibrium and dynamical properties are compared with those recently reported on TIP4P [L. Hernandez de la Pena and P. G. Kusalik, J. Chem. Phys. 121, 5992 (2004); L. Hernandez de la Pena et al., J. Chem. Phys 123, 144506 (2005)]. For the liquid, an energy shift of about 8% and an average molecular uncertainty of about 11 degrees were found independently of the water model. The self-diffusion coefficient consistently increases by more than 50% when going from the classical to the quantum system and quantum dynamics are found to reproduce the experimental isotopic shifts with the models examined. The ice results compare remarkably well with those previously reported for the TIP4P water model; they confirm that quantum effects are considerable and that the quantum mechanical uncertainty and the energy shifts due to quantization are smaller in ice than in liquid water. The relevance of these findings in the context of the construction of water models is briefly discussed.
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49
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Krishna V, Voth GA. Evaluation of Nonlinear Quantum Time Correlation Functions within the Centroid Dynamics Formulation. J Phys Chem B 2006; 110:18953-7. [PMID: 16986889 DOI: 10.1021/jp060073q] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A method to evaluate nonlinear centroid correlation functions is presented that is amenable to simple numerical computation. It can be implemented with the centroid molecular dynamics method for approximate quantum dynamics with no additional assumptions. Two nonlinear correlation functions are evaluated for a model potential using this scheme and compared with results from exact quantum calculations.
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Affiliation(s)
- Vinod Krishna
- Center for Biophysical Modeling and Simulation and Department of Chemistry, University of Utah, 315 S, 1400 E, Room 2020, Salt Lake City, Utah 84112-0850, USA
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50
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Craig IR, Manolopoulos DE. Chemical reaction rates from ring polymer molecular dynamics. J Chem Phys 2006; 122:84106. [PMID: 15836019 DOI: 10.1063/1.1850093] [Citation(s) in RCA: 293] [Impact Index Per Article: 16.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We show how the ring-polymer molecular dynamics method can be adapted to calculate approximate Kubo-transformed flux-side correlation functions, and hence rate coefficients for condensed phase reactions. An application of the method to the standard model for a chemical reaction in solution--a quartic double-well potential linearly coupled to a bath of harmonic oscillators--is found to give results of comparable accuracy to those of the classical Wigner model and the centroid molecular dynamics method. However, since the present method does not require that one evaluate the Wigner transform of a thermal flux operator or that one perform a separate path integral calculation for each molecular dynamics time step, we believe it will prove easier to apply to more general problems than either of these alternative techniques. We also present a (logarithmic) discretization scheme for the Ohmic bath in the system-bath model that gives converged results with just nine bath modes--a surprisingly small number for a model of a condensed phase reaction. Finally, we present some calculations of the transmission through an Eckart barrier which show that the present method provides a satisfactory (although not perfect) description of the deep quantum tunneling regime. Part of the reason for the success of the method is that it gives the exact quantum-mechanical rate constant for the transmission through a parabolic barrier, as we demonstrate analytically in the Appendix.
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Affiliation(s)
- Ian R Craig
- Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QZ, United Kingdom
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