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Svensson P, Campbell T, Graziani F, Moldabekov Z, Lyu N, Batista VS, Richardson S, Vinko SM, Gregori G. Development of a new quantum trajectory molecular dynamics framework. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20220325. [PMID: 37393934 PMCID: PMC10315217 DOI: 10.1098/rsta.2022.0325] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Accepted: 01/19/2023] [Indexed: 07/04/2023]
Abstract
An extension to the wave packet description of quantum plasmas is presented, where the wave packet can be elongated in arbitrary directions. A generalized Ewald summation is constructed for the wave packet models accounting for long-range Coulomb interactions and fermionic effects are approximated by purpose-built Pauli potentials, self-consistent with the wave packets used. We demonstrate its numerical implementation with good parallel support and close to linear scaling in particle number, used for comparisons with the more common wave packet employing isotropic states. Ground state and thermal properties are compared between the models with differences occurring primarily in the electronic subsystem. Especially, the electrical conductivity of dense hydrogen is investigated where a 15% increase in DC conductivity can be seen in our wave packet model compared with other models. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.
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Affiliation(s)
- Pontus Svensson
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
| | - Thomas Campbell
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
| | - Frank Graziani
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
| | - Zhandos Moldabekov
- Center of Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Ningyi Lyu
- Department of Chemistry, Yale University, New Haven, CT 06520, USA
| | - Victor S Batista
- Department of Chemistry, Yale University, New Haven, CT 06520, USA
- Yale Quantum Institute, Yale University, New Haven, CT 06511, USA
| | | | - Sam M Vinko
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
- Central Laser Facility, STFC Rutherford Appleton Laboratory, Didcot OX11 0QX, UK
| | - Gianluca Gregori
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
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Schiltz C, Rappoport D, Mandelshtam VA. Implementation of the self-consistent phonons method with ab initio potentials (AI-SCP). J Chem Phys 2023; 158:2890485. [PMID: 37184023 DOI: 10.1063/5.0146682] [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: 04/24/2023] [Indexed: 05/16/2023] Open
Abstract
The self-consistent phonon (SCP) method allows one to include anharmonic effects when treating a many-body quantum system at thermal equilibrium. The system is then described by an effective temperature-dependent harmonic Hamiltonian, which can be used to estimate its various dynamic and static properties. In this paper, we combine SCP with ab initio (AI) potential energy evaluation in which case the numerical bottleneck of AI-SCP is the evaluation of Gaussian averages of the AI potential energy and its derivatives. These averages are computed efficiently by the quasi-Monte Carlo method utilizing low-discrepancy sequences leading to a fast convergence with respect to the number, S, of the AI energy evaluations. Moreover, a further substantial (an-order-of-magnitude) improvement in efficiency is achieved once a numerically cheap approximation of the AI potential is available. This is based on using a perturbation theory-like (the two-grid) approach in which it is the average of the difference between the AI and the approximate potential that is computed. The corresponding codes and scripts are provided.
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Affiliation(s)
- Colin Schiltz
- Department of Chemistry, University of California, Irvine, California 92697, USA
| | - Dmitrij Rappoport
- Department of Chemistry, University of California, Irvine, California 92697, USA
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Xu Y, Zhang X, Allahyari S, Alizadeh A, Toghraie D, Rahmani A. The effects of shape of barriers on normal distribution of fluid within different regions of microchannels using molecular dynamics simulation. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.116672] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Brown SE, Mandelshtam VA. Self-consistent phonons: An accurate and practical method to account for anharmonic effects in equilibrium properties of general classical or quantum many-body systems. Chem Phys 2016. [DOI: 10.1016/j.chemphys.2016.06.008] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Ono J, Ando K. Semiquantal molecular dynamics simulations of hydrogen-bond dynamics in liquid water using multi-dimensional Gaussian wave packets. J Chem Phys 2012; 137:174503. [DOI: 10.1063/1.4762840] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Deckman J, Mandelshtam VA. Effects of Quantum Delocalization on Structural Changes in Lennard-Jones Clusters. J Phys Chem A 2009; 113:7394-402. [DOI: 10.1021/jp900095f] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Jason Deckman
- Chemistry Department, University of California at Irvine, Irvine, California 92697
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Sesé LM. Feynman-Hibbs potentials and path integrals for quantum Lennard-Jones systems: Theory and Monte Carlo simulations. Mol Phys 2008. [DOI: 10.1080/00268979500101571] [Citation(s) in RCA: 81] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Time-Dependent Wavepacket Approach to Optical Spectroscopy Involving Nonadiabatically Coupled Potential Surfaces. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470141229.ch13] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register]
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Demirplak M, Rice SA. Adiabatic transfer of population in a dense fluid: The role of dephasing statistics. J Chem Phys 2006; 125:194517. [PMID: 17129133 DOI: 10.1063/1.2372498] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
We report the results of simulation studies of the statistics of vibrational dephasing of a YCl (Y=H, D, T, and I) diatom in dense fluid Ar at two temperatures, including the effect of strong field driving on the energy level modulation statistics. The distribution of energy level modulations is found to be non-Gaussian with a high energy tail. Aspects of stimulated Raman adiabatic passage (STIRAP) between the vibrational levels of HCl in dense fluid Ar have been investigated. For HCl with nearly degenerate v=0-->v=1 and v=1-->v=2 transitions, the combined effect of modulation and power broadening reduces the STIRAP efficiency for population transfer from v=0 to v=2 of the order of 30%. However, if the transitions used have very different frequencies, as in the original model studied by Demirplak and Rice [J. Chem. Phys. 116, 8028 (2002)], the STIRAP efficiency for population transfer remains high, of the order of 80%, even with non-Gaussian modulation of energy levels.
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Affiliation(s)
- Mustafa Demirplak
- Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA
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Sesé LM. Study of the Feynman-Hibbs effective potential against the path-integral formalism for Monte Carlo simulations of quantum many-body Lennard-Jones systems. Mol Phys 2006. [DOI: 10.1080/00268979400100891] [Citation(s) in RCA: 62] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Predescu C, Frantsuzov PA, Mandelshtam VA. Thermodynamics and equilibrium structure of Ne38 cluster: Quantum mechanics versus classical. J Chem Phys 2005; 122:154305. [PMID: 15945633 DOI: 10.1063/1.1860331] [Citation(s) in RCA: 61] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
The equilibrium properties of classical Lennard-Jones (LJ38) versus quantum Ne38 Lennard-Jones clusters are investigated. The quantum simulations use both the path-integral Monte Carlo (PIMC) and the recently developed variational-Gaussian wave packet Monte Carlo (VGW-MC) methods. The PIMC and the classical MC simulations are implemented in the parallel tempering framework. The classical heat capacity Cv(T) curve agrees well with that of Neirotti et al. [J. Chem. Phys. 112, 10340 (2000)], although a much larger confining sphere is used in the present work. The classical Cv(T) shows a peak at about 6 K, interpreted as a solid-liquid transition, and a shoulder at approximately 4 K, attributed to a solid-solid transition involving structures from the global octahedral (Oh) minimum and the main icosahedral (C5v) minimum. The VGW method is used to locate and characterize the low energy states of Ne38, which are then further refined by PIMC calculations. Unlike the classical case, the ground state of Ne38 is a liquidlike structure. Among the several liquidlike states with energies below the two symmetric states (Oh and C5v), the lowest two exhibit strong delocalization over basins associated with at least two classical local minima. Because the symmetric structures do not play an essential role in the thermodynamics of Ne38, the quantum heat capacity is a featureless curve indicative of the absence of any structural transformations. Good agreement between the two methods, VGW and PIMC, is obtained. The present results are also consistent with the predictions by Calvo et al. [J. Chem. Phys. 114, 7312 (2001)] based on the quantum superposition method within the harmonic approximation. However, because of its approximate nature, the latter method leads to an incorrect assignment of the Ne38 ground state as well as to a significant underestimation of the heat capacity.
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Affiliation(s)
- Cristian Predescu
- Chemistry Department, University of California at Berkeley, Berkeley, California 94720, USA
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Frantsuzov PA, Mandelshtam VA. Quantum statistical mechanics with Gaussians: Equilibrium properties of van der Waals clusters. J Chem Phys 2004; 121:9247-56. [PMID: 15538845 DOI: 10.1063/1.1804495] [Citation(s) in RCA: 85] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The variational Gaussian wave-packet method for computation of equilibrium density matrices of quantum many-body systems is further developed. The density matrix is expressed in terms of Gaussian resolution, in which each Gaussian is propagated independently in imaginary time beta=(k(B)T)(-1) starting at the classical limit beta=0. For an N-particle system a Gaussian exp[(r-q)(T)G(r-q)+gamma] is represented by its center qinR(3N), the width matrix GinR(3Nx3N), and the scale gammainR, all treated as dynamical variables. Evaluation of observables is done by Monte Carlo sampling of the initial Gaussian positions. As demonstrated previously at not-very-low temperatures the method is surprisingly accurate for a range of model systems including the case of double-well potential. Ideally, a single Gaussian propagation requires numerical effort comparable to the propagation of a single classical trajectory for a system with 9(N(2)+N)/2 degrees of freedom. Furthermore, an approximation based on a direct product of single-particle Gaussians, rather than a fully coupled Gaussian, reduces the number of dynamical variables to 9N. The success of the methodology depends on whether various Gaussian integrals needed for calculation of, e.g., the potential matrix elements or pair correlation functions could be evaluated efficiently. We present techniques to accomplish these goals and apply the method to compute the heat capacity and radial pair correlation function of Ne(13) Lennard-Jones cluster. Our results agree very well with the available path-integral Monte Carlo calculations.
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Affiliation(s)
- Pavel A Frantsuzov
- Chemistry Department, University of California at Irvine, Irvine, California 92697, USA
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Ando K. Semiquantal time-dependent Hartree approach to condensed phase chemical dynamics: application to the system-bath model. J Chem Phys 2004; 121:7136-43. [PMID: 15473779 DOI: 10.1063/1.1793152] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
A semiquantal analysis of condensed phase chemical dynamics, outlined recently for a double-well linearly coupled to dissipative harmonic bath, is formulated in detail to clarify its general features as well as the specifics of the linear and quadratic coupling cases. The theory may be called a "semiquantal time-dependent Hartree (SQTDH)" approach, as it assumes a factorized product of the squeezed coherent state wave packets for the variational subspace of the many-dimensional time-dependent wave function. Due to this assumption, it straightforwardly satisfies the canonicity condition introduced by Marumori et al. is described by a set of Hamilton equations of motion in an extended phase space that includes auxiliary coordinates representing the wave packet widths. The potential in the extended phase space provides a pictorial understanding of the quantum effects affected due to the bath coupling, e.g., suppression of the wave packet spreading in terms of the potential wall developing along the auxiliary coordinates. The idea is illustrated by prototypical models of quartic double-well and cubic metastable potentials linearly and quadratically coupled to the bath. Further applications and extensions, where the SQTDH method will offer a practical approach for introducing quantum effects into realistic molecular dynamics simulations, are also discussed.
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Affiliation(s)
- Koji Ando
- School of Chemistry, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
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Buch V. Calculation of infrared absorption spectra using Gaussian variational wave packets. J Chem Phys 2004; 121:6961-6. [PMID: 15473756 DOI: 10.1063/1.1791152] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Formulas are developed for calculation of infrared absorption spectra with the help of Gaussian variational wave packets. The excitation is viewed as occurring to a linear combination of basis states corresponding to a Gaussian multiplied by Hermite polynomials of coordinates. Application of the formulas is examplified on HDO isolated in a D2O matrix. A simple approximation is proposed for the fundamental transitions.
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Affiliation(s)
- Victoria Buch
- Fritz Haber Institute for Molecular Dynamics, Hebrew University, Jerusalem 91904, Israel
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Heatwole E, Prezhdo OV. A canonical averaging in the second-order quantized Hamilton dynamics. J Chem Phys 2004; 121:10967-75. [PMID: 15634046 DOI: 10.1063/1.1812749] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Quantized Hamilton dynamics (QHD) is a simple and elegant extension of classical Hamilton dynamics that accurately includes zero-point energy, tunneling, dephasing, and other quantum effects. Formulated as a hierarchy of approximations to exact quantum dynamics in the Heisenberg formulation, QHD has been used to study evolution of observables subject to a single initial condition. In present, we develop a practical solution for generating canonical ensembles in the second-order QHD for position and momentum operators, which can be mapped onto classical phase space in doubled dimensionality and which in certain limits is equivalent to thawed Gaussian. We define a thermal distribution in the space of the QHD-2 variables and show that the standard beta=1/kT relationship becomes beta'=2/kT in the high temperature limit due to an overcounting of states in the extended phase space, and a more complicated function at low temperatures. The QHD thermal distribution is used to compute total energy, kinetic energy, heat capacity, and other canonical averages for a series of quartic potentials, showing good agreement with the quantum results.
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Affiliation(s)
- Eric Heatwole
- Department of Chemistry, University of Washington, Seattle, WA 98195-1700, USA
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Buch V. Exploration of multidimensional variational Gaussian wave packets as a simulation tool. J Chem Phys 2002. [DOI: 10.1063/1.1497968] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Martínez TJ, Ben-Nun M, Levine RD. Molecular Collision Dynamics on Several Electronic States. J Phys Chem A 1997. [DOI: 10.1021/jp970842t] [Citation(s) in RCA: 107] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Affiliation(s)
- T. J. Martínez
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801
| | - M. Ben-Nun
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093-0339
| | - R. D. Levine
- The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University, Jerusalem 91904, Israel
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Messina M, Wilson KR, Krause JL. Quantum control of multidimensional systems: Implementation within the time‐dependent Hartree approximation. J Chem Phys 1996. [DOI: 10.1063/1.470887] [Citation(s) in RCA: 28] [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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Li Z, Gerber RB. Treatment of zero‐point motions in cluster dynamics: Semiclassical time‐dependent self‐consistent‐field simulation of (Ne)N. J Chem Phys 1993. [DOI: 10.1063/1.465587] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Nieminen J. Computer simulation of quantum features of very weakly quantum-mechanical systems. Chem Phys Lett 1992. [DOI: 10.1016/0009-2614(92)85413-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Coalson RD, Karplus M. Multidimensional variational Gaussian wave packet dynamics with application to photodissociation spectroscopy. J Chem Phys 1990. [DOI: 10.1063/1.458778] [Citation(s) in RCA: 92] [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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van Gunsteren WF, Berendsen HJC. Moleküldynamik-Computersimulationen; Methodik, Anwendungen und Perspektiven in der Chemie. Angew Chem Int Ed Engl 1990. [DOI: 10.1002/ange.19901020907] [Citation(s) in RCA: 90] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Miller BN, Fan Y. Localization in fluids: A comparison of competing theories and their application to positron annihilation. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 42:2228-2234. [PMID: 9904272 DOI: 10.1103/physreva.42.2228] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Neumann M, Zoppi M. Asymptotic expansions and effective potentials for almost classical N-body systems. PHYSICAL REVIEW. A, GENERAL PHYSICS 1989; 40:4572-4584. [PMID: 9902701 DOI: 10.1103/physreva.40.4572] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Heller EJ, Reimers JR, Drolshagen G. Classical and semiclassical approximations for incoherent neutron scattering. PHYSICAL REVIEW. A, GENERAL PHYSICS 1987; 36:2613-2627. [PMID: 9899167 DOI: 10.1103/physreva.36.2613] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Barocchi F, Neumann M, Zoppi M. Wigner-Kirkwood expansion: Calculation of "almost classical" static properties of a Lennard-Jones many-body system. PHYSICAL REVIEW. A, GENERAL PHYSICS 1987; 36:2440-2454. [PMID: 9899139 DOI: 10.1103/physreva.36.2440] [Citation(s) in RCA: 26] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Coalson RD, Freeman DL, Doll JD. Partial averaging approach to Fourier coefficient path integration. J Chem Phys 1986. [DOI: 10.1063/1.451778] [Citation(s) in RCA: 115] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Thirumalai D, Bruskin EJ, Berne BJ. On the use of semiclassical dynamics in determining electronic spectra of Br2in an Ar matrix. J Chem Phys 1985. [DOI: 10.1063/1.449813] [Citation(s) in RCA: 67] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Behrman EC, Jongeward GA, Wolynes PG. A Monte Carlo approach for the real time dynamics of tunneling systems in condensed phases. J Chem Phys 1983. [DOI: 10.1063/1.445732] [Citation(s) in RCA: 79] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Reimers JR, Wilson KR, Heller EJ. Complex time dependent wave packet technique for thermal equilibrium systems: Electronic spectra. J Chem Phys 1983. [DOI: 10.1063/1.445618] [Citation(s) in RCA: 61] [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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