51
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Hone TD, Rossky PJ, Voth GA. A comparative study of imaginary time path integral based methods for quantum dynamics. J Chem Phys 2006; 124:154103. [PMID: 16674214 DOI: 10.1063/1.2186636] [Citation(s) in RCA: 117] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The recently introduced approximate many-body quantum simulation method, ring polymer molecular dynamics (RPMD), is compared to the centroid molecular dynamics method (CMD). Comparisons of simulation results for liquid para-hydrogen at two state points and liquid ortho-deuterium at one state point are presented. The calculated quantum correlation functions for the two methods are shown to be in good agreement with one another for a large portion of the time spectrum. However, as the quantum mechanical nature of the system increases, RPMD is less accurate in predicting the kinetic energy of the system than is CMD. A simplified and highly efficient algorithm is proposed which largely corrects this deficiency.
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Affiliation(s)
- Tyler D Hone
- Institute for Theoretical Chemistry, Department of Chemistry and Biochemistry, University of Texas at Austin, Austin, Texas 78712, USA
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52
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Jang S. Path-integral centroid dynamics for general initial conditions: A nonequilibrium projection operator formulation. J Chem Phys 2006; 124:64107. [PMID: 16483196 DOI: 10.1063/1.2162887] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The formulation of path-integral centroid dynamics is extended to the quantum dynamics of density operators evolving from general initial states by means of the nonequilibrium projection operator technique. It is shown that the new formulation provides a basis for applying the method of centroid dynamics to nonequilibrium situations and that it allows the derivation of new formal relations, which can be useful in improving current equilibrium centroid dynamics methods. A simple approximation of uniform relaxation for the unprojected portion of the Liouville space propagator leads to a class of practically solvable equations of motion for the centroid variables, but with an undetermined parameter of relaxation. This new class of equations encompasses the centroid molecular-dynamics (CMD) method as a limiting case, and can be applied to both equilibrium and nonequilibrium situations. Tests for the equilibrium dynamics of one-dimensional model systems demonstrate that the new equations with appropriate choice of the relaxation parameter are comparable to the CMD method.
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Affiliation(s)
- Seogjoo Jang
- Department of Chemistry and Biochemistry, Queens College, City University of New York, Flushing, 11367-1597, USA.
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53
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Molecular dynamics with quantum statistics: time correlation functions and weakly bound nano-clusters. Theor Chem Acc 2005. [DOI: 10.1007/s00214-005-0065-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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54
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Rabani E, Krilov G, Reichman DR, Berne BJ. Transport properties of normal liquid helium: Comparison of various methodologies. J Chem Phys 2005; 123:184506. [PMID: 16292913 DOI: 10.1063/1.2109927] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We revisit the problem of self-diffusion in normal liquid helium above the lambda transition. Several different methods are applied to compute the velocity autocorrelation function. Since it is still impossible to determine the exact result for the velocity autocorrelation function from simulation, we appeal to the computation of short-time moments to determine the accuracy of the different approaches at short times. The main conclusion reached from our study is that both the quantum mode-coupling theory and the numerical analytic continuation approach must be regarded as a viable and competitive methods for the computation of dynamical properties of quantum systems.
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Affiliation(s)
- Eran Rabani
- School of Chemistry, The Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel
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55
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Iftimie R, Tuckerman ME. Decomposing total IR spectra of aqueous systems into solute and solvent contributions: A computational approach using maximally localized Wannier orbitals. J Chem Phys 2005; 122:214508. [PMID: 15974755 DOI: 10.1063/1.1908950] [Citation(s) in RCA: 105] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
The theoretical principles underpinning the calculation of infrared spectra for condensed-phase systems in the context of ab initio molecular dynamics have been recently developed in literature. At present, most ab initio molecular dynamics calculations are restricted to relatively small systems and short simulation times. In this paper we devise a method that allows well-converged results for infrared spectra from ab initio molecular dynamics simulations using small systems and short trajectories characteristic of simulations typically performed in practice. We demonstrate the utility of our approach by computing the imaginary part of the dielectric constant epsilon"(omega) for H2O and D2O in solid and liquid phases and show that it compares well with experimental data. We further demonstrate that maximally localized Wannier orbitals can be used to separate the individual contributions of different molecular species to the linear spectrum of complex systems. The new spectral decomposition method is shown to be useful in present-day ab initio molecular dynamics calculations to compute the magnitude of the "continuous absorption" generated by excess protons in aqueous solutions with good accuracy even when other species present in the solutions absorb strongly in the same frequency window.
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Affiliation(s)
- Radu Iftimie
- Department of Chemistry, New York University, New York, New York 10003, USA.
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56
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Rabani E, Reichman DR. QUANTUM MODE-COUPLING THEORY: Formulation and Applications to Normal and Supercooled Quantum Liquids. Annu Rev Phys Chem 2005; 56:157-85. [PMID: 15796699 DOI: 10.1146/annurev.physchem.56.092503.141138] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
▪ Abstract We review our recent efforts to formulate and study a mode-coupling approach to real-time dynamic fluctuations in quantum liquids. Comparison is made between the theory and recent neutron scattering experiments performed on liquid ortho-deuterium and para-hydrogen. We discuss extensions of the theory to supercooled and glassy states where quantum fluctuations compete with thermal fluctuations. Experimental scenarios for quantum glassy liquids are briefly discussed.
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Affiliation(s)
- Eran Rabani
- School of Chemistry, The Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel.
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57
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Horikoshi A, Kinugawa K. Effective potential analytic continuation approach for real time quantum correlation functions involving nonlinear operators. J Chem Phys 2005; 122:174104. [PMID: 15910020 DOI: 10.1063/1.1888576] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Abstract
We apply the effective potential analytic continuation (EPAC) method to the calculation of real time quantum correlation functions involving operators nonlinear in the position operator q. For a harmonic system the EPAC method provides the exact correlation function at all temperature ranges, while the other quantum dynamics methods, the centroid molecular dynamics and the ring polymer molecular dynamics, become worse at lower temperature. For an asymmetric anharmonic system, the EPAC correlation function is in very good agreement with the exact one at t = 0. When the time increases from zero, the EPAC method gives good coincidence with the exact result at lower temperature. Finally, we propose a simplified version of the EPAC method to reduce the computational cost required for the calculation of the standard effective potential.
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Affiliation(s)
- Atsushi Horikoshi
- Japan Science and Technology Agency and Department of Chemistry, Faculty of Science, Nara Women's University.
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58
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Poulsen JA, Nyman G, Rossky PJ. Static and dynamic quantum effects in molecular liquids: a linearized path integral description of water. Proc Natl Acad Sci U S A 2005; 102:6709-14. [PMID: 15860585 PMCID: PMC1100757 DOI: 10.1073/pnas.0408647102] [Citation(s) in RCA: 84] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Structure, transport properties, and IR spectra including quantum effects are calculated for a flexible simple point charge model of liquid water. A recently introduced combination of a variational local harmonic description of the liquid potential surface and the classical Wigner approximation for the dynamics is used. The potential energy and interatomic radial distribution functions are in good agreement with accurate results from the literature and are significantly closer to experiment than predictions found from classical theory. The oxygen and hydrogen velocity correlation functions are also calculated, and the corresponding molecular diffusion coefficient is in good accord with existing theoretical estimates including quantum effects. Of most interest, an ab initio quantum correction factor is obtained to correct the far IR spectrum of water. When corrected, a spectrum based on a classical simulation yields results that agree well with experiment. Combined with internal tests of consistency, these observations indicate that this quite flexible approach will be effective for a variety of molecular problems involving the dynamics of light nuclei.
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Affiliation(s)
- Jens Aage Poulsen
- Department of Physical Chemistry, Gøteborg University, S-412 96 Gøteborg, Sweden
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59
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Chen X, Wu Y, Batista VS. Matching-pursuit/split-operator-Fourier-transform computations of thermal correlation functions. J Chem Phys 2005; 122:064102. [PMID: 15740362 DOI: 10.1063/1.1848513] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A rigorous and practical methodology for evaluating thermal-equilibrium density matrices, finite-temperature time-dependent expectation values, and time-correlation functions is described. The method involves an extension of the matching-pursuit/split-operator-Fourier-transform method to the solution of the Bloch equation via imaginary-time propagation of the density matrix and the evaluation of Heisenberg time-evolution operators through real-time propagation in dynamically adaptive coherent-state representations.
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Affiliation(s)
- Xin Chen
- Department of Chemistry, Yale University, New Haven, Connecticut 06520-8107, USA
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60
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Hone TD, Voth GA. A centroid molecular dynamics study of liquidpara-hydrogen andortho-deuterium. J Chem Phys 2004; 121:6412-22. [PMID: 15446940 DOI: 10.1063/1.1780951] [Citation(s) in RCA: 89] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Centroid molecular dynamics (CMD) is applied to the study of collective and single-particle dynamics in liquid para-hydrogen at two state points and liquid ortho-deuterium at one state point. The CMD results are compared with the results of classical molecular dynamics, quantum mode coupling theory, a maximum entropy analytic continuation approach, pair-product forward- backward semiclassical dynamics, and available experimental results. The self-diffusion constants are in excellent agreement with the experimental measurements for all systems studied. Furthermore, it is shown that the method is able to adequately describe both the single-particle and collective dynamics of quantum liquids.
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Affiliation(s)
- Tyler D Hone
- Department of Chemistry and Henry Eyring Center for Theoretical Chemistry, University of Utah, Salt Lake City, Utah 84112-0850, USA
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61
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Horikoshi A, Kinugawa K. Effective potential analytic continuation calculations of real time quantum correlation functions: asymmetric systems. J Chem Phys 2004; 121:2891-8. [PMID: 15291599 DOI: 10.1063/1.1774161] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We apply the effective potential analytic continuation (EPAC) method to one-dimensional asymmetric potential systems to obtain the real time quantum correlation functions at various temperatures. Comparing the EPAC results with the exact results, we find that for an asymmetric anharmonic oscillator the EPAC results are in very good agreement with the exact ones at low temperature, while this agreement becomes worse as the temperature increases. We also show that the EPAC calculation for a certain type of asymmetric potentials can be reduced to that for the corresponding symmetric potentials.
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Affiliation(s)
- Atsushi Horikoshi
- Japan Science and Technology Agency, Faculty of Science, Nara Women's University, 630-8506.
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62
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Shi Q, Geva E. Nonradiative Electronic Relaxation Rate Constants from Approximations Based on Linearizing the Path-Integral Forward−Backward Action. J Phys Chem A 2004. [DOI: 10.1021/jp049547g] [Citation(s) in RCA: 71] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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63
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Shi Q, Geva E. A semiclassical generalized quantum master equation for an arbitrary system-bath coupling. J Chem Phys 2004; 120:10647-58. [PMID: 15268091 DOI: 10.1063/1.1738109] [Citation(s) in RCA: 83] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
The Nakajima-Zwanzig generalized quantum master equation (GQME) provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a, possibly anharmonic, quantum bath. In this equation, a memory kernel superoperator accounts for the influence of the bath on the dynamics of the system. In a previous paper [Q. Shi and E. Geva, J. Chem. Phys. 119, 12045 (2003)] we proposed a new approach to calculating the memory kernel, in the case of arbitrary system-bath coupling. Within this approach, the memory kernel is obtained by solving a set of two integral equations, which requires a new type of two-time system-dependent bath correlation functions as input. In the present paper, we consider the application of the linearized semiclassical (LSC) approximation for calculating those correlation functions, and subsequently the memory kernel. The new approach is tested on a benchmark spin-boson model. Application of the LSC approximation for calculating the relatively short-lived memory kernel, followed by a numerically exact solution of the GQME, is found to provide an accurate description of the relaxation dynamics. The success of the proposed LSC-GQME methodology is contrasted with the failure of both the direct application of the LSC approximation and the weak coupling treatment to provide an accurate description of the dynamics, for the same model, except at very short times. The feasibility of the new methodology to anharmonic systems is also demonstrated in the case of a two level system coupled to a chain of Lennard-Jones atoms.
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Affiliation(s)
- Qiang Shi
- Department of Chemistry and the FOCUS Center, University of Michigan, Ann Arbor, Michigan 48109-1055, USA
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64
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Yonetani Y, Kinugawa K. Centroid molecular dynamics approach to the transport properties of liquid para-hydrogen over the wide temperature range. J Chem Phys 2004; 120:10624-33. [PMID: 15268088 DOI: 10.1063/1.1735613] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Fundamental transport properties of liquid para-hydrogen (p-H(2)), i.e., diffusion coefficients, thermal conductivity, shear viscosity, and bulk viscosity, have been evaluated by means of the path integral centroid molecular dynamics (CMD) calculations. These transport properties have been obtained over the wide temperature range, 14-32 K. Calculated values of the diffusion coefficients and the shear viscosity are in good agreement with the experimental values at all the investigated temperatures. Although a relatively large deviation is found for the thermal conductivity, the calculated values are less than three times the amount of the experimental values at any temperature. On the other hand, the classical molecular dynamics has led all the transport properties to much larger deviation. For the bulk viscosity of liquid p-H(2), which was never known from experiments, the present CMD has given a clear temperature dependence. In addition, from the comparison based on the principle of corresponding states, it has been shown that the marked deviation of the transport properties of liquid p-H(2) from the feature which is expected from the molecular parameters is due to the quantum effect.
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Affiliation(s)
- Yoshiteru Yonetani
- Japan Science and Technology Corporation, Department of Chemistry, Faculty of Science, Nara Women's University, Nara 630-8506, Japan
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65
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Blinov N, Roy PN. Connection between the observable and centroid structural properties of a quantum fluid: Application to liquid para-hydrogen. J Chem Phys 2004; 120:3759-64. [PMID: 15268539 DOI: 10.1063/1.1642600] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
It is shown that the discrepancy between path integral Monte Carlo [M. Zoppi et al., Phys. Rev. B 65, 092204 (2002)] and path integral centroid molecular dynamics [F. J. Bermejo et al., Phys. Rev. Lett. 84, 5359 (2000)] calculations of the static structure factor of liquid para-hydrogen can be explained based on a deconvolution equation connecting centroid and physical radial distribution functions. An explicit expression for the kernel of the deconvolution equation has been obtained using functional derivative techniques. In the superposition approximation, this kernel is given by the functional derivative of the effective potential with respect to the pairwise classical potential. Results of path integral Monte Carlo calculations for the radial distribution function and the static structure factor of liquid para-hydrogen are presented.
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Affiliation(s)
- Nicholas Blinov
- Department of Chemistry, University of Alberta, Edmonton, Canada, T6G 2G2
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66
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Rabani E, Reichman DR. A fully self-consistent treatment of collective fluctuations in quantum liquids. J Chem Phys 2004; 120:1458-65. [PMID: 15268271 DOI: 10.1063/1.1631436] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The problem of calculating collective density fluctuations in quantum liquids is revisited. A fully quantum mechanical self-consistent treatment based on a quantum mode-coupling theory is presented. The theory is compared with the maximum entropy analytic continuation approach and with available experimental results. The quantum mode-coupling theory provides semiquantitative results for both short and long time dynamics. The proper description of long time phenomena is important in future study of problems related to the physics of glassy quantum systems, and to the study of collective fluctuations in Bose fluids.
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Affiliation(s)
- Eran Rabani
- School of Chemistry, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel.
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67
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Ohta Y, Ohta K, Kinugawa K. Ab initio centroid path integral molecular dynamics: Application to vibrational dynamics of diatomic molecular systems. J Chem Phys 2004; 120:312-20. [PMID: 15267291 DOI: 10.1063/1.1626632] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An ab initio centroid molecular dynamics (CMD) method is developed by combining the CMD method with the ab initio molecular orbital method. The ab initio CMD method is applied to vibrational dynamics of diatomic molecules, H2 and HF. For the H2 molecule, the temperature dependence of the peak frequency of the vibrational spectral density is investigated. The results are compared with those obtained by the ab initio classical molecular dynamics method and exact quantum mechanical treatment. It is shown that the vibrational frequency obtained from the ab initio CMD approaches the exact first excitation frequency as the temperature lowers. For the HF molecule, the position autocorrelation function is also analyzed in detail. The present CMD method is shown to well reproduce the exact quantum result for the information on the vibrational properties of the system.
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Affiliation(s)
- Yasuhito Ohta
- Japan Science and Technology Corporation, Osaka 563-8577, Japan
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68
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Poulsen JA, Nyman G, Rossky PJ. Practical evaluation of condensed phase quantum correlation functions: A Feynman–Kleinert variational linearized path integral method. J Chem Phys 2003. [DOI: 10.1063/1.1626631] [Citation(s) in RCA: 203] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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69
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Shi Q, Geva E. A new approach to calculating the memory kernel of the generalized quantum master equation for an arbitrary system–bath coupling. J Chem Phys 2003. [DOI: 10.1063/1.1624830] [Citation(s) in RCA: 91] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
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70
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Yonetani Y, Kinugawa K. Transport properties of liquid para-hydrogen: The path integral centroid molecular dynamics approach. J Chem Phys 2003. [DOI: 10.1063/1.1616912] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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71
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Shi Q, Geva E. On the calculation of vibrational energy relaxation rate constants from centroid molecular dynamics simulations. J Chem Phys 2003. [DOI: 10.1063/1.1613636] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
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72
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Shi Q, Geva E. Semiclassical Theory of Vibrational Energy Relaxation in the Condensed Phase. J Phys Chem A 2003. [DOI: 10.1021/jp030497+] [Citation(s) in RCA: 143] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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73
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Affiliation(s)
- Shenmin Li
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045-7582
| | - Ward H. Thompson
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045-7582
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74
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Horikoshi A, Kinugawa K. Quantum dynamical correlations: Effective potential analytic continuation approach. J Chem Phys 2003. [DOI: 10.1063/1.1595638] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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75
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Saito H, Nagao H, Nishikawa K, Kinugawa K. Molecular collective dynamics in solid para-hydrogen and ortho-deuterium: The Parrinello–Rahman-type path integral centroid molecular dynamics approach. J Chem Phys 2003. [DOI: 10.1063/1.1578474] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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76
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Shi Q, Geva E. A relationship between semiclassical and centroid correlation functions. J Chem Phys 2003. [DOI: 10.1063/1.1564814] [Citation(s) in RCA: 122] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
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77
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78
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Poulsen JA, Nyman G, Rossky PJ. A second-order Kubo response theory-centroid approach to vibrational energy relaxation for single-mode excitations. J Chem Phys 2002. [DOI: 10.1063/1.1522376] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
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79
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80
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Navrotskaya I, Shi Q, Geva E. Quantum-mechanical reaction rate constants from centroid molecular dynamics simulations: Barrier crossing in an asymmetrical double-well. Isr J Chem 2002. [DOI: 10.1560/46pr-4lgf-ehny-ndhl] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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81
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Rabani E, Reichman DR. A self-consistent mode-coupling theory for dynamical correlations in quantum liquids: Rigorous formulation. J Chem Phys 2002. [DOI: 10.1063/1.1458545] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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82
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Brumer Y, Golosov AA, Chen ZD, Reichman DR. Calculating approximate quantum mechanical rates without an a priori reaction coordinate. J Chem Phys 2002. [DOI: 10.1063/1.1467334] [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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83
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Geva E, Shi Q, Voth GA. Quantum-mechanical reaction rate constants from centroid molecular dynamics simulations. J Chem Phys 2001. [DOI: 10.1063/1.1412870] [Citation(s) in RCA: 82] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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84
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Blinov N, Roy PN. Operator formulation of centroid dynamics for Bose–Einstein and Fermi–Dirac statistics. J Chem Phys 2001. [DOI: 10.1063/1.1407291] [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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85
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Poulsen JA, Rossky PJ. Path integral centroid molecular-dynamics evaluation of vibrational energy relaxation in condensed phase. J Chem Phys 2001. [DOI: 10.1063/1.1408618] [Citation(s) in RCA: 27] [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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86
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Poulsen JA, Rossky PJ. An ansatz-based variational path integral centroid approach to vibrational energy relaxation in simple liquids. J Chem Phys 2001. [DOI: 10.1063/1.1408617] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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87
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Blinov NV, Roy PN, Voth GA. Path integral formulation of centroid dynamics for systems obeying Bose–Einstein statistics. J Chem Phys 2001. [DOI: 10.1063/1.1392355] [Citation(s) in RCA: 30] [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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88
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Poulsen J, Keiding SR, Rossky PJ. Extracting rates of vibrational energy relaxation from centroid molecular dynamics. Chem Phys Lett 2001. [DOI: 10.1016/s0009-2614(01)00136-1] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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89
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Kinugawa K, Nagao H, Ohta K. A semiclassical approach to the dynamics of many-body Bose/Fermi systems by the path integral centroid molecular dynamics. J Chem Phys 2001. [DOI: 10.1063/1.1334661] [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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