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Kananenka AA, Strong SE, Skinner JL. Dephasing and Decoherence in Vibrational and Electronic Line Shapes. J Phys Chem B 2020; 124:1531-1542. [PMID: 31990552 DOI: 10.1021/acs.jpcb.9b11655] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Absorption and emission line shapes of vibrational and electronic transitions in liquids are broadened by interactions with the "bath" (in this case, the rotational and translational degrees of freedom of all the molecules in the liquid). If these degrees of freedom are treated classically, the broadening process is often known as dephasing. If, on the other hand, the bath degrees of freedom are instead treated quantum mechanically, there is additional broadening due to what is known in the chemical-physics literature as decoherence. The question addressed in this paper is the relative importance of decoherence (bath quantum effects) and dephasing. We present general developments of this subject for absorption and emission line shapes, discover several new relationships connecting classical and quantum treatments of the bath, and also consider the Stokes shift (difference in peak frequencies in absorption and emission). We next draw some general conclusions by considering a model system whose transition-frequency time-correlation function has only one bath time scale. We then consider a realistic system of the vibrational OH stretch transition of dilute HOD in liquid D2O at room temperature. For this system, we conclude that bath quantum effects are not very important, except for the Stokes shift. More generally, we argue that this is the case for many vibrational and most electronic transitions in room-temperature liquids.
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Affiliation(s)
- Alexei A Kananenka
- Pritzker School of Molecular Engineering , The University of Chicago , Chicago , Illinois 60637 , United States.,Department of Physics and Astronomy , University of Delaware , Newark , Delaware 19716 , United States
| | - Steven E Strong
- Pritzker School of Molecular Engineering , The University of Chicago , Chicago , Illinois 60637 , United States
| | - J L Skinner
- Pritzker School of Molecular Engineering , The University of Chicago , Chicago , Illinois 60637 , United States
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de la Lande A, Řezáč J, Lévy B, Sanders BC, Salahub DR. Transmission coefficients for chemical reactions with multiple states: role of quantum decoherence. J Am Chem Soc 2011; 133:3883-94. [PMID: 21344903 DOI: 10.1021/ja107950m] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Transition-state theory (TST) is a widely accepted paradigm for rationalizing the kinetics of chemical reactions involving one potential energy surface (PES). Multiple PES reaction rate constants can also be estimated within semiclassical approaches provided the hopping probability between the quantum states is taken into account when determining the transmission coefficient. In the Marcus theory of electron transfer, this hopping probability was historically calculated with models such as Landau-Zener theory. Although the hopping probability is intimately related to the question of the transition from the fully quantum to the semiclassical description, this issue is not adequately handled in physicochemical models commonly in use. In particular, quantum nuclear effects such as decoherence or dephasing are not present in the rate constant expressions. Retaining the convenient semiclassical picture, we include these effects through the introduction of a phenomenological quantum decoherence function. A simple modification to the usual TST rate constant expression is proposed: in addition to the electronic coupling, a characteristic decoherence time τ(dec) now also appears as a key parameter of the rate constant. This new parameter captures the idea that molecular systems, although intrinsically obeying quantum mechanical laws, behave semiclassically after a finite but nonzero amount of time (τ(dec)). This new degree of freedom allows a fresh look at the underlying physics of chemical reactions involving more than one quantum state. The ability of the proposed formula to describe the main physical lines of the phenomenon is confirmed by comparison with results obtained from density functional theory molecular dynamics simulations for a triplet to singlet transition within a copper dioxygen adduct relevant to the question of dioxygen activation by copper monooxygenases.
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Affiliation(s)
- Aurélien de la Lande
- Laboratoire de Chimie Physique-CNRS UMR 8000, Université Paris-Sud 11, Bât. 349, Campus d'Orsay, 15 rue Jean Perrin, 91 405 Orsay Cedex, France.
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Mujica V, Nitzan A, Mao Y, Davis W, Kemp M, Roitberg A, Ratner MA. Electron Transfer in Molecules and Molecular Wires: Geometry Dependence, Coherent Transfer, and Control. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470141663.ch7] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/08/2023]
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Bedard-Hearn MJ, Larsen RE, Schwartz BJ. Mean-field dynamics with stochastic decoherence (MF-SD): A new algorithm for nonadiabatic mixed quantum/classical molecular-dynamics simulations with nuclear-induced decoherence. J Chem Phys 2005; 123:234106. [PMID: 16392913 DOI: 10.1063/1.2131056] [Citation(s) in RCA: 161] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The key factors that distinguish algorithms for nonadiabatic mixed quantum/classical (MQC) simulations from each other are how they incorporate quantum decoherence-the fact that classical nuclei must eventually cause a quantum superposition state to collapse into a pure state-and how they model the effects of decoherence on the quantum and classical subsystems. Most algorithms use distinct mechanisms for modeling nonadiabatic transitions between pure quantum basis states ("surface hops") and for calculating the loss of quantum-mechanical phase information (e.g., the decay of the off-diagonal elements of the density matrix). In our view, however, both processes should be unified in a single description of decoherence. In this paper, we start from the density matrix of the total system and use the frozen Gaussian approximation for the nuclear wave function to derive a nuclear-induced decoherence rate for the electronic degrees of freedom. We then use this decoherence rate as the basis for a new nonadiabatic MQC molecular-dynamics (MD) algorithm, which we call mean-field dynamics with stochastic decoherence (MF-SD). MF-SD begins by evolving the quantum subsystem according to the time-dependent Schrodinger equation, leading to mean-field dynamics. MF-SD then uses the nuclear-induced decoherence rate to determine stochastically at each time step whether the system remains in a coherent mixed state or decoheres. Once it is determined that the system should decohere, the quantum subsystem undergoes an instantaneous total wave-function collapse onto one of the adiabatic basis states and the classical velocities are adjusted to conserve energy. Thus, MF-SD combines surface hops and decoherence into a single idea: decoherence in MF-SD does not require the artificial introduction of reference states, auxiliary trajectories, or trajectory swarms, which also makes MF-SD much more computationally efficient than other nonadiabatic MQC MD algorithms. The unified definition of decoherence in MF-SD requires only a single ad hoc parameter, which is not adjustable but instead is determined by the spatial extent of the nonadiabatic coupling. We use MF-SD to solve a series of one-dimensional scattering problems and find that MF-SD is as quantitatively accurate as several existing nonadiabatic MQC MD algorithms and significantly more accurate for some problems.
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Affiliation(s)
- Michael J Bedard-Hearn
- Department of Chemistry and Biochemistry, University of California, 607 Charles E. Young Drive East, Los Angeles, California 90095-1569, USA
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Coalson RD, Evans DG. Condensed phase vibrational relaxation: calibration of approximate relaxation theories with analytical and numerically exact results. Chem Phys 2004. [DOI: 10.1016/j.chemphys.2003.08.028] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Lockwood DM, Ratner MA, Kosloff R. Effects of anharmonicity and electronic coupling on photoinduced electron transfer in mixed valence compounds. J Chem Phys 2002. [DOI: 10.1063/1.1519258] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
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Wong KF, Rossky PJ. Dissipative mixed quantum-classical simulation of the aqueous solvated electron system. J Chem Phys 2002. [DOI: 10.1063/1.1468886] [Citation(s) in RCA: 72] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Jen CF, Warshel A. Microscopic Based Density Matrix Treatments of Electron-Transfer Reactions in Condensed Phases. J Phys Chem A 1999. [DOI: 10.1021/jp991304e] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Chienyu F. Jen
- Department of Chemistry, University of Southern California, Los Angeles, California 90089
| | - Arieh Warshel
- Department of Chemistry, University of Southern California, Los Angeles, California 90089
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Egorov SA, Rabani E, Berne BJ. On the Adequacy of Mixed Quantum-Classical Dynamics in Condensed Phase Systems. J Phys Chem B 1999. [DOI: 10.1021/jp9921349] [Citation(s) in RCA: 66] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- S. A. Egorov
- Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706
| | - Eran Rabani
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027
| | - B. J. Berne
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027
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Cárdenas AE, Coalson RD. Calculation of reduced partial cross sections of molecules photodesorbing from a cold crystal surface with internal vibrations: Inclusion of curve-crossing effects. J Chem Phys 1999. [DOI: 10.1063/1.479096] [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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Egorov SA, Rabani E, Berne BJ. Nonradiative relaxation processes in condensed phases: Quantum versus classical baths. J Chem Phys 1999. [DOI: 10.1063/1.478420] [Citation(s) in RCA: 60] [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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Yoshimori A. Comparisons of semiclassical approximations by expansion in Planck’s constant. J Chem Phys 1998. [DOI: 10.1063/1.477549] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Mosyak AA, Prezhdo OV, Rossky PJ. Solvation dynamics of an excess electron in methanol and water. J Chem Phys 1998. [DOI: 10.1063/1.477282] [Citation(s) in RCA: 44] [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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Yokoyama K, Silva C, Son DH, Walhout PK, Barbara PF. Detailed Investigation of the Femtosecond Pump−Probe Spectroscopy of the Hydrated Electron. J Phys Chem A 1998. [DOI: 10.1021/jp981809p] [Citation(s) in RCA: 129] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Kazushige Yokoyama
- Department of Chemistry, University of Minnesota, 207 Pleasant St. S. E., Minneapolis, Minnesota 55455
| | - Carlos Silva
- Department of Chemistry, University of Minnesota, 207 Pleasant St. S. E., Minneapolis, Minnesota 55455
| | - Dong Hee Son
- Department of Chemistry, University of Minnesota, 207 Pleasant St. S. E., Minneapolis, Minnesota 55455
| | - Peter K. Walhout
- Department of Chemistry, University of Minnesota, 207 Pleasant St. S. E., Minneapolis, Minnesota 55455
| | - Paul F. Barbara
- Department of Chemistry, University of Minnesota, 207 Pleasant St. S. E., Minneapolis, Minnesota 55455
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Prezhdo OV, Rossky PJ. Evaluation of quantum transition rates from quantum-classical molecular dynamics simulations. J Chem Phys 1997. [DOI: 10.1063/1.474312] [Citation(s) in RCA: 254] [Impact Index Per Article: 9.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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A wavepacket — path integral method for curve-crossing problems: application to resonance Raman spectra and photodissociation cross sections. Chem Phys Lett 1997. [DOI: 10.1016/s0009-2614(96)01406-6] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Barbara PF, Meyer TJ, Ratner MA. Contemporary Issues in Electron Transfer Research. ACTA ACUST UNITED AC 1996. [DOI: 10.1021/jp9605663] [Citation(s) in RCA: 1285] [Impact Index Per Article: 45.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Paul F. Barbara
- Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455
| | - Thomas J. Meyer
- Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599
| | - Mark A. Ratner
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208
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Schwartz BJ, Bittner ER, Prezhdo OV, Rossky PJ. Quantum decoherence and the isotope effect in condensed phase nonadiabatic molecular dynamics simulations. J Chem Phys 1996. [DOI: 10.1063/1.471326] [Citation(s) in RCA: 292] [Impact Index Per Article: 10.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Stock G. Nonperturbative generalized master equation for the spin-boson problem. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 51:3038-3044. [PMID: 9962982 DOI: 10.1103/physreve.51.3038] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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