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Prada A, Pós ES, Althorpe SC. Comparison of Matsubara dynamics with exact quantum dynamics for an oscillator coupled to a dissipative bath. J Chem Phys 2023; 158:114106. [PMID: 36948794 DOI: 10.1063/5.0138250] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/17/2023] Open
Abstract
We report the first numerical calculations in which converged Matsubara dynamics is compared directly with exact quantum dynamics with no artificial damping of the time-correlation functions (TCFs). The system treated is a Morse oscillator coupled to a harmonic bath. We show that, when the system-bath coupling is sufficiently strong, the Matsubara calculations can be converged by explicitly including up to M = 200 Matsubara modes, with the remaining modes included as a harmonic "tail" correction. The resulting Matsubara TCFs are in near-perfect agreement with the exact quantum TCFs, for non-linear as well as linear operators, at a temperature at which the TCFs are dominated by quantum thermal fluctuations. These results provide compelling evidence that incoherent classical dynamics can arise in the condensed phase at temperatures at which the statistics are dominated by quantum (Boltzmann) effects, as a result of smoothing of imaginary-time Feynman paths. The techniques developed here may also lead to efficient methods for benchmarking system-bath dynamics in the overdamped regime.
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Affiliation(s)
- Adam Prada
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Eszter S Pós
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Stuart C Althorpe
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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Constable S, Schmidt M, Ing C, Zeng T, Roy PN. Langevin Equation Path Integral Ground State. J Phys Chem A 2013; 117:7461-7. [DOI: 10.1021/jp4015178] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Steve Constable
- Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
| | - Matthew Schmidt
- Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
| | - Christopher Ing
- Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
| | - Tao Zeng
- Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
| | - Pierre-Nicholas Roy
- Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
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Glaesemann KR, Fried LE. Quantitative molecular thermochemistry based on path integrals. J Chem Phys 2007; 123:34103. [PMID: 16080726 DOI: 10.1063/1.1954771] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The calculation of thermochemical data requires accurate molecular energies and heat capacities. Traditional methods rely upon the standard harmonic normal-mode analysis to calculate the vibrational and rotational contributions. We utilize path-integral Monte Carlo for going beyond the harmonic analysis and to calculate the vibrational and rotational contributions to ab initio energies. This is an application and an extension of a method previously developed in our group [J. Chem. Phys. 118, 1596 (2003)].
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Affiliation(s)
- Kurt R Glaesemann
- Chemistry and Materials Science Directorate, Lawrence Livermore National Laboratory, University of California, 94551, USA.
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Yamamoto TM. Path-integral virial estimator based on the scaling of fluctuation coordinates: Application to quantum clusters with fourth-order propagators. J Chem Phys 2005; 123:104101. [PMID: 16178583 DOI: 10.1063/1.2013257] [Citation(s) in RCA: 48] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Abstract
We first show that a simple scaling of fluctuation coordinates defined in terms of a given reference point gives the conventional virial estimator in discretized path integral, where different choices of the reference point lead to different forms of the estimator (e.g., centroid virial). The merit of this procedure is that it allows a finite-difference evaluation of the virial estimator with respect to temperature, which totally avoids the need of higher-order potential derivatives. We apply this procedure to energy and heat-capacity calculations of the (H(2))(22) and Ne(13) clusters at low temperature using the fourth-order Takahashi-Imada [J. Phys. Soc. Jpn. 53, 3765 (1984)] and Suzuki [Phys. Lett. A 201, 425 (1995)] propagators. This type of calculation requires up to third-order potential derivatives if analytical virial estimators are used, but in practice only first-order derivatives suffice by virtue of the finite-difference scheme above. From the application to quantum clusters, we find that the fourth-order propagators do improve upon the primitive approximation, and that the choice of the reference point plays a vital role in reducing the variance of the virial estimator.
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Affiliation(s)
- Takeshi M Yamamoto
- Department of Chemistry, Graduate School of Science, Kyoto University, Japan.
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Predescu C, Sabo D, Doll JD, Freeman DL. Heat capacity estimators for random series path-integral methods by finite-difference schemes. J Chem Phys 2003. [DOI: 10.1063/1.1625366] [Citation(s) in RCA: 56] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Predescu C, Sabo D, Doll JD, Freeman DL. Energy estimators for random series path-integral methods. J Chem Phys 2003. [DOI: 10.1063/1.1619372] [Citation(s) in RCA: 22] [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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Ivanov SD, Lyubartsev AP, Laaksonen A. Bead-Fourier path integral molecular dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:066710. [PMID: 16241383 DOI: 10.1103/physreve.67.066710] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2002] [Indexed: 05/04/2023]
Abstract
Molecular dynamics formulation of Bead-Fourier path integral method for simulation of quantum systems at finite temperatures is presented. Within this scheme, both the bead coordinates and Fourier coefficients, defining the path representing the quantum particle, are treated as generalized coordinates with corresponding generalized momenta and masses. Introduction of the Fourier harmonics together with the center-of-mass thermostating scheme is shown to remove the ergodicity problem, known to pose serious difficulties in standard path integral molecular dynamics simulations. The method is tested for quantum harmonic oscillator and hydrogen atom (Coulombic potential). The simulation results are compared with the exact analytical solutions available for both these systems. Convergence of the results with respect to the number of beads and Fourier harmonics is analyzed. It was shown that addition of a few Fourier harmonics already improves the simulation results substantially, even for a relatively small number of beads. The proposed Bead-Fourier path integral molecular dynamics is a reliable and efficient alternative to simulations of quantum systems.
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Affiliation(s)
- Sergei D Ivanov
- Division of Physical Chemistry, Arrhenius Laboratory, Stockholm University, S-10691 Stockholm, Sweden.
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Glaesemann KR, Fried LE. Improved heat capacity estimator for path integral simulations. J Chem Phys 2002. [DOI: 10.1063/1.1493184] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Glaesemann KR, Fried LE. An improved thermodynamic energy estimator for path integral simulations. J Chem Phys 2002. [DOI: 10.1063/1.1460861] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Sabo D, Doll JD, Freeman DL. Stationary tempering and the complex quadrature problem. J Chem Phys 2002. [DOI: 10.1063/1.1446431] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Mielke SL, Truhlar DG. A new Fourier path integral method, a more general scheme for extrapolation, and comparison of eight path integral methods for the quantum mechanical calculation of free energies. J Chem Phys 2001. [DOI: 10.1063/1.1290476] [Citation(s) in RCA: 43] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Ceperley DM, Manousakis E. Path integral Monte Carlo applications to quantum fluids in confined geometries. J Chem Phys 2001. [DOI: 10.1063/1.1418443] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Krumrine JR, Jang S, Alexander MH, Voth GA. Quantum molecular dynamics and spectral simulation of a boron impurity in solid para-hydrogen. J Chem Phys 2000. [DOI: 10.1063/1.1318225] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Sabo D, Doll JD, Freeman DL. Self-adaptive quadrature and numerical path integration. J Chem Phys 2000. [DOI: 10.1063/1.1305743] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Chakravarty C, Gordillo MC, Ceperley DM. Response to “Comment on ‘A comparison of the efficiency of Fourier- and discrete time-path integral Monte Carlo’ ” [J. Chem. Phys.111, 7685 (1999)]. J Chem Phys 1999. [DOI: 10.1063/1.480273] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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