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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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2
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Rota R, Casulleras J, Mazzanti F, Boronat J. Quantum Monte Carlo estimation of complex-time correlations for the study of the ground-state dynamic structure function. J Chem Phys 2015; 142:114114. [DOI: 10.1063/1.4914995] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- R. Rota
- Dipartimento di Fisica and INO-CNR BEC Center, Università degli Studi di Trento, I-38123 Povo, Trento, Italy
| | - J. Casulleras
- Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4-B5, E-08034 Barcelona, Spain
| | - F. Mazzanti
- Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4-B5, E-08034 Barcelona, Spain
| | - J. Boronat
- Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4-B5, E-08034 Barcelona, Spain
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3
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Li Y, Li X, Ma W, Dong Z. Conformational Transition Pathways of Epidermal Growth Factor Receptor Kinase Domain from Multiple Molecular Dynamics Simulations and Bayesian Clustering. J Chem Theory Comput 2014; 10:3503-3511. [PMID: 25136273 PMCID: PMC4132868 DOI: 10.1021/ct500162b] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2014] [Indexed: 01/15/2023]
Abstract
![]()
The
epidermal growth factor receptor (EGFR) is aberrantly activated
in various cancer cells and an important target for cancer treatment.
Deep understanding of EGFR conformational changes between the active
and inactive states is of pharmaceutical interest. Here we present
a strategy combining multiply targeted molecular dynamics simulations,
unbiased molecular dynamics simulations, and Bayesian clustering to
investigate transition pathways during the activation/inactivation
process of EGFR kinase domain. Two distinct pathways between the active
and inactive forms are designed, explored, and compared. Based on
Bayesian clustering and rough two-dimensional free energy surfaces,
the energy-favorable pathway is recognized, though DFG-flip happens
in both pathways. In addition, another pathway with different intermediate
states appears in our simulations. Comparison of distinct pathways
also indicates that disruption of the Lys745-Glu762 interaction is
critically important in DFG-flip while movement of the A-loop significantly
facilitates the conformational change. Our simulations yield new insights
into EGFR conformational transitions. Moreover, our results verify
that this approach is valid and efficient in sampling of protein conformational
changes and comparison of distinct pathways.
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Affiliation(s)
- Yan Li
- The Hormel Institute, University of Minnesota , Austin, Minnesota 55912, United States
| | - Xiang Li
- Department of Physiology and Pathophysiology, School of Basic Medical Sciences, Zhengzhou University , 450001 Zhengzhou, Henan, China
| | - Weiya Ma
- The Hormel Institute, University of Minnesota , Austin, Minnesota 55912, United States
| | - Zigang Dong
- The Hormel Institute, University of Minnesota , Austin, Minnesota 55912, United States
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4
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Wilner EY, Levy TJ, Rabani E. Analytical continuation approaches to electronic transport: The resonant level model. J Chem Phys 2012; 137:214107. [DOI: 10.1063/1.4768674] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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5
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Monteferrante M, Bonella S, Ciccotti G. Linearized symmetrized quantum time correlation functions calculation via phase pre-averaging. Mol Phys 2011. [DOI: 10.1080/00268976.2011.619506] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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6
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7
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Steele RP, Zwickl J, Shushkov P, Tully JC. Mixed time slicing in path integral simulations. J Chem Phys 2011; 134:074112. [DOI: 10.1063/1.3518714] [Citation(s) in RCA: 14] [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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8
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Kletenik-Edelman O, Reichman DR, Rabani E. On the mode-coupling treatment of collective density fluctuations for quantum liquids: Para-hydrogen and normal liquid helium. J Chem Phys 2011; 134:044528. [DOI: 10.1063/1.3521478] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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9
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Bonella S, Monteferrante M, Pierleoni C, Ciccotti G. Path integral based calculations of symmetrized time correlation functions. II. J Chem Phys 2010; 133:164105. [DOI: 10.1063/1.3493449] [Citation(s) in RCA: 15] [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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10
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Bonella S, Monteferrante M, Pierleoni C, Ciccotti G. Path integral based calculations of symmetrized time correlation functions. I. J Chem Phys 2010; 133:164104. [DOI: 10.1063/1.3493448] [Citation(s) in RCA: 17] [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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11
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Liu P, Shi Q, Daumé H, Voth GA. A Bayesian statistics approach to multiscale coarse graining. J Chem Phys 2009; 129:214114. [PMID: 19063551 DOI: 10.1063/1.3033218] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Coarse-grained (CG) modeling provides a promising way to investigate many important physical and biological phenomena over large spatial and temporal scales. The multiscale coarse-graining (MS-CG) method has been proven to be a thermodynamically consistent way to systematically derive a CG model from atomistic force information, as shown in a variety of systems, ranging from simple liquids to proteins embedded in lipid bilayers. In the present work, Bayes' theorem, an advanced statistical tool widely used in signal processing and pattern recognition, is adopted to further improve the MS-CG force field obtained from the CG modeling. This approach can regularize the linear equation resulting from the underlying force-matching methodology, therefore substantially improving the quality of the MS-CG force field, especially for the regions with limited sampling. Moreover, this Bayesian approach can naturally provide an error estimation for each force field parameter, from which one can know the extent the results can be trusted. The robustness and accuracy of the Bayesian MS-CG algorithm is demonstrated for three different systems, including simple liquid methanol, polyalanine peptide solvated in explicit water, and a much more complicated peptide assembly with 32 NNQQNY hexapeptides.
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Affiliation(s)
- Pu Liu
- Center for Biophysical Modeling and Simulation and Department of Chemistry, University of Utah, 315 S. 1400 E. Rm. 2020, Salt Lake City, Utah 84112-0850, USA
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12
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Reichman DR, Rabani E. Analytic continuation average spectrum method for quantum liquids. J Chem Phys 2009; 131:054502. [DOI: 10.1063/1.3185728] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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13
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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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Habershon S, Braams BJ, Manolopoulos DE. Quantum mechanical correlation functions, maximum entropy analytic continuation, and ring polymer molecular dynamics. J Chem Phys 2007; 127:174108. [DOI: 10.1063/1.2786451] [Citation(s) in RCA: 59] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
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15
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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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16
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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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17
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Kim SY, Hammes-Schiffer S. Hybrid quantum/classical molecular dynamics for a proton transfer reaction coupled to a dissipative bath. J Chem Phys 2006; 124:244102. [PMID: 16821968 DOI: 10.1063/1.2206175] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A hybrid quantum/classical molecular dynamics approach is applied to a proton transfer reaction represented by a symmetric double well system coupled to a dissipative bath. In this approach, the proton is treated quantum mechanically and all bath modes are treated classically. The transition state theory rate constant is obtained from the potential of mean force, which is generated along a collective reaction coordinate with umbrella sampling techniques. The transmission coefficient, which accounts for dynamical recrossings of the dividing surface, is calculated with a reactive flux approach combined with the molecular dynamics with quantum transitions surface hopping method. The hybrid quantum/classical results agree well with numerically exact results in the spatial-diffusion-controlled regime, which is most relevant for proton transfer in proteins. This hybrid quantum/classical approach has already been shown to be computationally practical for studying proton transfer in large biological systems. These results have important implications for future applications to hydrogen transfer reactions in solution and proteins.
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Affiliation(s)
- Soo Young Kim
- Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania 16802, USA
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18
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Fujisaki H, Zhang Y, Straub JE. Time-dependent perturbation theory for vibrational energy relaxation and dephasing in peptides and proteins. J Chem Phys 2006; 124:144910. [PMID: 16626248 DOI: 10.1063/1.2191038] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Without invoking the Markov approximation, we derive formulas for vibrational energy relaxation (VER) and dephasing for an anharmonic system oscillator using a time-dependent perturbation theory. The system-bath Hamiltonian contains more than the third order coupling terms since we take a normal mode picture as a zeroth order approximation. When we invoke the Markov approximation, our theory reduces to the Maradudin-Fein formula which is used to describe the VER properties of glass and proteins. When the system anharmonicity and the renormalization effect due to the environment vanishes, our formulas reduce to those derived by and Mikami and Okazaki [J. Chem. Phys. 121, 10052 (2004)] invoking the path-integral influence functional method with the second order cumulant expansion. We apply our formulas to VER of the amide I mode of a small amino-acid like molecule, N-methylacetamide, in heavy water.
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Affiliation(s)
- Hiroshi Fujisaki
- Department of Chemistry, Boston University, Boston, Massachusetts 02215, USA.
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19
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Zhao Y, Li X, Zheng Z, Liang W. Semiclassical calculation of nonadiabatic thermal rate constants: Application to condensed phase reactions. J Chem Phys 2006; 124:114508. [PMID: 16555902 DOI: 10.1063/1.2178323] [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 nonadiabatic transition state theory proposed recently by Zhao et al. [J. Chem. Phys. 121, 8854 (2004)] is extended to calculate rate constants of complex systems by using the Monte Carlo and umbrella sampling methods. Surface hopping molecular dynamics technique is incorporated to take into account the dynamic recrossing effect. A nontrivial benchmark model of the nonadiabatic reaction in the condensed phase is used for the numerical test. It is found that our semiclassical results agree well with those produced by the rigorous quantum mechanical method. Comparing with available analytical approaches, we find that the simple statistical theory proposed by Straub and Berne [J. Chem. Phys. 87, 6111 (1987)] is applicable for a wide friction region although their formula is obtained using Landau-Zener [Phys. Z. Sowjetunion 2, 46 (1932); Proc. R. Soc. London, Ser. A 137, 696 (1932)] nonadiabatic transition probability along a one-dimensional diffusive coordinate. We also investigate how the nuclear tunneling events affect the dependence of the rate constant on the friction.
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Affiliation(s)
- Yi Zhao
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
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20
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Ravitz O. On the computation of imaginary-time correlation functions beyond the ℏβ limit. Chem Phys 2006. [DOI: 10.1016/j.chemphys.2005.08.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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21
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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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22
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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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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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Rabani E, Miyazaki K, Reichman DR. Quantum mode-coupling theory for binary mixtures. J Chem Phys 2005; 122:34502. [PMID: 15740204 DOI: 10.1063/1.1832593] [Citation(s) in RCA: 4] [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 extend the quantum mode-coupling theory of neat liquids to the case of binary mixtures, in order to study supercooled liquids where quantum fluctuations may compete with thermal fluctuations. We apply the theory to a generic model of a binary mixture of Lennard-Jones particles. Our treatment may be used to study quantum aging and exotic glass melting scenarios in structural supercooled quantum liquids.
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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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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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Cheney BG, Andersen HC. Dynamical corrections to quantum transition state theory. J Chem Phys 2003. [DOI: 10.1063/1.1570404] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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28
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Golosov AA, Reichman DR, Rabani E. Analytic continuation for quantum nonadiabatic rate constants. J Chem Phys 2003. [DOI: 10.1063/1.1535214] [Citation(s) in RCA: 27] [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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Rabani E, Reichman DR, Krilov G, Berne BJ. The calculation of transport properties in quantum liquids using the maximum entropy numerical analytic continuation method: application to liquid para-hydrogen. Proc Natl Acad Sci U S A 2002; 99:1129-33. [PMID: 11830656 PMCID: PMC122155 DOI: 10.1073/pnas.261540698] [Citation(s) in RCA: 86] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We present a method based on augmenting an exact relation between a frequency-dependent diffusion constant and the imaginary time velocity autocorrelation function, combined with the maximum entropy numerical analytic continuation approach to study transport properties in quantum liquids. The method is applied to the case of liquid para-hydrogen at two thermodynamic state points: a liquid near the triple point and a high-temperature liquid. Good agreement for the self-diffusion constant and for the real-time velocity autocorrelation function is obtained in comparison to experimental measurements and other theoretical predictions. Improvement of the methodology and future applications are 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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