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Ka BJ, Thompson WH. Nonadiabatic Effects on Proton Transfer Rate Constants in a Nanoconfined Solvent. J Phys Chem B 2010; 114:7535-42. [DOI: 10.1021/jp911740c] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Being J. Ka
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045
| | - Ward H. Thompson
- Department of Chemistry, University of Kansas, Lawrence, Kansas 66045
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52
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Hanna G, Geva E. Computational study of the signature of hydrogen-bond strength on the infrared spectra of a hydrogen-bonded complex dissolved in a polar liquid. Chem Phys 2010. [DOI: 10.1016/j.chemphys.2010.01.013] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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53
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Rank JP, Kapral R. Decoherence and quantum-classical dynamics in a dissipative bath. J Chem Phys 2010; 132:074106. [DOI: 10.1063/1.3310811] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
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54
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Applications of Mixed-Quantum/Classical Trajectories to the Study of Nuclear Quantum Effects in Chemical Reactions and Vibrational Relaxation Processes. ADVANCES IN QUANTUM CHEMISTRY 2010. [DOI: 10.1016/s0065-3276(10)59008-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/08/2023]
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55
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McRobbie PL, Hanna G, Shi Q, Geva E. Signatures of nonequilibrium solvation dynamics on multidimensional spectra. Acc Chem Res 2009; 42:1299-309. [PMID: 19552404 DOI: 10.1021/ar800280s] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Abstract
Multidimensional electronic and vibrational spectroscopies have established themselves over the last decade as uniquely detailed probes of intramolecular structure and dynamics. However, these spectroscopies can also provide powerful tools for probing solute-solvent interactions and the solvation dynamics that they give rise to. To this end, it should be noted that multidimensional spectra can be expressed in terms of optical response functions that differ with respect to the chromophore's quantum state during the various time intervals separating light-matter interactions. The dynamics of the photoinactive degrees of freedom during those time intervals (that is, between pulses) is dictated by potential energy surfaces that depend on the corresponding state of the chromophore. One therefore expects the system to hop between potential surfaces in a manner dictated by the optical response functions. Thus, the corresponding spectra should reflect the system's dynamics during the resulting sequence of nonequilibrium solvation processes. However, the interpretation of multidimensional spectra is often based on the assumption that they reflect the equilibrium dynamics of the photoinactive degrees of freedom on the potential surface that corresponds to the chromophore's ground state. In this Account, we present a systematic analysis of the signature of nonequilibrium solvation dynamics on multidimensional spectra and the ability of various computational methods to capture it. The analysis is performed in the context of the following three model systems: (A) a two-state chromophore with shifted harmonic potential surfaces that differ in frequency, (B) a two-state atomic chromophore in an atomic liquid, and (C) the hydrogen stretch of a moderately strong hydrogen-bonded complex in a dipolar liquid. The following computational methods are employed and compared: (1) exact quantum dynamics (model A only), (2) the semiclassical forward-backward initial value representation (FB-IVR) method (models A and B only), (3) the linearized semiclassical (LSC) method (all three models), and (4) the standard ground-state equilibrium dynamics approach (all three models). The results demonstrate how multidimensional spectra can be used to probe nonequilibrium solvation dynamics in real time and with an unprecedented level of detail. We also show that, unlike the standard method, the LSC and FB-IVR methods can accurately capture the signature of solvation dynamics on the spectra. Our results also suggest that LSC and FB-IVR yield similar results in the presence of rapid dephasing, which is typical in complex condensed-phase systems. This observation gives credence to the use of the LSC method for modeling spectra in complex systems for which an exact or even FB-IVR-based calculation is prohibitively expensive.
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Affiliation(s)
- Porscha L. McRobbie
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055
| | - Gabriel Hanna
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055
| | - Qiang Shi
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences (CAS), Zhongguancun, Beijing 100190, P. R. China
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055
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56
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Hanna G, Geva E. Multidimensional Spectra via the Mixed Quantum-Classical Liouville Method: Signatures of Nonequilibrium Dynamics. J Phys Chem B 2009; 113:9278-88. [DOI: 10.1021/jp902797z] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Gabriel Hanna
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055
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57
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Hanna G, Geva E. Isotope Effects on the Vibrational Relaxation and Multidimensional Infrared Spectra of the Hydrogen Stretch in a Hydrogen-Bonded Complex Dissolved in a Polar Liquid. J Phys Chem B 2008; 112:15793-800. [DOI: 10.1021/jp8072816] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Gabriel Hanna
- Department of Chemistry and FOCUS Center, University of Michigan, Ann Arbor, Michigan 48109-1055
| | - Eitan Geva
- Department of Chemistry and FOCUS Center, University of Michigan, Ann Arbor, Michigan 48109-1055
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58
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Dunkel ER, Bonella S, Coker DF. Iterative linearized approach to nonadiabatic dynamics. J Chem Phys 2008; 129:114106. [DOI: 10.1063/1.2976441] [Citation(s) in RCA: 63] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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59
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Hanna G, Geva E. Computational Study of the One and Two Dimensional Infrared Spectra of a Vibrational Mode Strongly Coupled to Its Environment: Beyond the Cumulant and Condon Approximations. J Phys Chem B 2008; 112:12991-3004. [DOI: 10.1021/jp804120v] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Gabriel Hanna
- Department of Chemistry and FOCUS center, University of Michigan, Ann Arbor, Michigan 48109-1055
| | - Eitan Geva
- Department of Chemistry and FOCUS center, University of Michigan, Ann Arbor, Michigan 48109-1055
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60
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Kim H, Nassimi A, Kapral R. Quantum-classical Liouville dynamics in the mapping basis. J Chem Phys 2008; 129:084102. [DOI: 10.1063/1.2971041] [Citation(s) in RCA: 110] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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61
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Gelman D, Schwartz SD. Tunneling dynamics with a mixed quantum-classical method: Quantum corrected propagator combined with frozen Gaussian wave packets. J Chem Phys 2008; 129:024504. [DOI: 10.1063/1.2949818] [Citation(s) in RCA: 8] [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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62
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Hanna G, Kapral R. Quantum-classical Liouville dynamics of proton and deuteron transfer rates in a solvated hydrogen-bonded complex. J Chem Phys 2008; 128:164520. [DOI: 10.1063/1.2907847] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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63
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Grunwald R, Kim H, Kapral R. Surface-hopping dynamics and decoherence with quantum equilibrium structure. J Chem Phys 2008; 128:164110. [DOI: 10.1063/1.2906485] [Citation(s) in RCA: 14] [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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64
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Collepardo-Guevara R, Craig IR, Manolopoulos DE. Proton transfer in a polar solvent from ring polymer reaction rate theory. J Chem Phys 2008; 128:144502. [DOI: 10.1063/1.2883593] [Citation(s) in RCA: 86] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
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65
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Hanna G, Geva E. Vibrational Energy Relaxation of a Hydrogen-Bonded Complex Dissolved in a Polar Liquid via the Mixed Quantum−Classical Liouville Method. J Phys Chem B 2008; 112:4048-58. [DOI: 10.1021/jp076155b] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Gabriel Hanna
- Department of Chemistry and FOCUS center, University of Michigan, Ann Arbor, Michigan 48109-1055
| | - Eitan Geva
- Department of Chemistry and FOCUS center, University of Michigan, Ann Arbor, Michigan 48109-1055
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66
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Kim H, Kapral R. Proton and Deuteron Transfer Reactions in Molecular Nanoclusters. Chemphyschem 2008; 9:470-4. [DOI: 10.1002/cphc.200700709] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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67
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Mac Kernan D, Ciccotti G, Kapral R. Trotter-Based Simulation of Quantum-Classical Dynamics. J Phys Chem B 2007; 112:424-32. [DOI: 10.1021/jp0761416] [Citation(s) in RCA: 92] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Affiliation(s)
- Dónal Mac Kernan
- School of Physics, Trinity College Dublin, Dublin 2 and School of Physics, University College Dublin, Dublin 4, Ireland, INFM and Dipartimento di Fisica, Università “La Sapienza”, Piazzale Aldo Moro, 2, 00185 Roma, Italy, and Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, ON M5S 3H6, Canada
| | - Giovanni Ciccotti
- School of Physics, Trinity College Dublin, Dublin 2 and School of Physics, University College Dublin, Dublin 4, Ireland, INFM and Dipartimento di Fisica, Università “La Sapienza”, Piazzale Aldo Moro, 2, 00185 Roma, Italy, and Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, ON M5S 3H6, Canada
| | - Raymond Kapral
- School of Physics, Trinity College Dublin, Dublin 2 and School of Physics, University College Dublin, Dublin 4, Ireland, INFM and Dipartimento di Fisica, Università “La Sapienza”, Piazzale Aldo Moro, 2, 00185 Roma, Italy, and Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, ON M5S 3H6, Canada
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68
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Kim H, Kapral R. Quantum reaction rates and sampling of quantum equilibrium structure. J Chem Phys 2007; 127:226101. [DOI: 10.1063/1.2805071] [Citation(s) in RCA: 1] [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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69
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Takatsuka K. Generalization of classical mechanics for nuclear motions on nonadiabatically coupled potential energy surfaces in chemical reactions. J Phys Chem A 2007; 111:10196-204. [PMID: 17676718 DOI: 10.1021/jp072233j] [Citation(s) in RCA: 54] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Classical trajectory study of nuclear motion on the Born-Oppenheimer potential energy surfaces is now one of the standard methods of chemical dynamics. In particular, this approach is inevitable in the studies of large molecular systems. However, as soon as more than a single potential energy surface is involved due to nonadiabatic coupling, such a naive application of classical mechanics loses its theoretical foundation. This is a classic and fundamental issue in the foundation of chemistry. To cope with this problem, we propose a generalization of classical mechanics that provides a path even in cases where multiple potential energy surfaces are involved in a single event and the Born-Oppenheimer approximation breaks down. This generalization is made by diagonalization of the matrix representation of nuclear forces in nonadiabatic dynamics, which is derived from a mixed quantum-classical representation of the electron-nucleus entangled Hamiltonian [Takatsuka, K. J. Chem. Phys. 2006, 124, 064111]. A manifestation of quantum fluctuation on a classical subsystem that directly contacts with a quantum subsystem is discussed. We also show that the Hamiltonian thus represented gives a theoretical foundation to examine the validity of the so-called semiclassical Ehrenfest theory (or mean-field theory) for electron quantum wavepacket dynamics, and indeed, it is pointed out that the electronic Hamiltonian to be used in this theory should be slightly modified.
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Affiliation(s)
- Kazuo Takatsuka
- Department of Basic Science, The University of Tokyo, Komaba, 153-8902 Tokyo, Japan
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70
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71
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Abstract
Quantum-classical Liouville dynamics can be used to study the properties of open quantum systems that are coupled to bath or environmental degrees of freedom whose dynamics can be approximated by classical equations of motion. In contrast to many open quantum system approaches, quantum-classical dynamics provides a detailed description of the bath molecules. Such a description is especially appropriate for the study of quantum rate processes, such as proton and electron transport, where the detailed dynamics of the bath has a strong influence on the quantum rate. The quantum-classical Liouville equation can also serve as a starting point for the derivation of reduced descriptions where all or some of the bath degrees of freedom are projected out. Quantum-classical Liouville dynamics can be simulated in terms of an ensemble of surface-hopping trajectories whose character differs from that in other surface-hopping schemes. The results of studies of proton transfer in condensed phase and reactive dynamics in a dissipative environment are presented to illustrate applications of the formalism.
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Affiliation(s)
- Raymond Kapral
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada.
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72
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Grunwald R, Kapral R. Decoherence and quantum-classical master equation dynamics. J Chem Phys 2007; 126:114109. [PMID: 17381198 DOI: 10.1063/1.2567164] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Abstract
The conditions under which quantum-classical Liouville dynamics may be reduced to a master equation are investigated. Systems that can be partitioned into a quantum-classical subsystem interacting with a classical bath are considered. Starting with an exact non-Markovian equation for the diagonal elements of the density matrix, an evolution equation for the subsystem density matrix is derived. One contribution to this equation contains the bath average of a memory kernel that accounts for all coherences in the system. It is shown to be a rapidly decaying function, motivating a Markovian approximation on this term in the evolution equation. The resulting subsystem density matrix equation is still non-Markovian due to the fact that bath degrees of freedom have been projected out of the dynamics. Provided the computation of nonequilibrium average values or correlation functions is considered, the non-Markovian character of this equation can be removed by lifting the equation into the full phase space of the system. This leads to a trajectory description of the dynamics where each fictitious trajectory accounts for decoherence due to the bath degrees of freedom. The results are illustrated by computations of the rate constant of a model nonadiabatic chemical reaction.
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Affiliation(s)
- Robbie Grunwald
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
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73
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Abstract
An approach to the quantum-classical mechanics of phase space dependent operators, which has been proposed recently, is remodeled as a formalism for wave fields. Such wave fields obey a system of coupled nonlinear equations that can be written by means of a suitable non-Hamiltonian bracket. As an example, the theory is applied to the relaxation dynamics of the spin-boson model. In the adiabatic limit, a good agreement with calculations performed by the operator approach is obtained. Moreover, the theory proposed in this paper can take nonadiabatic effects into account without resorting to surface-hopping approximations. Hence, the results obtained follow qualitatively those of previous surface-hopping calculations and increase by a factor of (at least) 2, the time length over which nonadiabatic dynamics can be propagated with small statistical errors. Moreover, it is worth to note that the dynamics of quantum-classical wave fields proposed here is a straightforward non-Hamiltonian generalization of the formalism for nonlinear quantum mechanics that Weinberg introduced recently.
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Affiliation(s)
- Alessandro Sergi
- Dipartimento di Fisica, Universitá degli Studi di Messina, Contrada Papardo 98166 Messina, Italy.
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74
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Fernandez-Ramos A, Miller JA, Klippenstein SJ, Truhlar DG. Modeling the kinetics of bimolecular reactions. Chem Rev 2007; 106:4518-84. [PMID: 17091928 DOI: 10.1021/cr050205w] [Citation(s) in RCA: 393] [Impact Index Per Article: 23.1] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Antonio Fernandez-Ramos
- Departamento de Quimica Fisica, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
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75
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Quantum–Classical Reaction Rate Theory. ACTA ACUST UNITED AC 2007. [DOI: 10.1007/978-3-540-34460-5_13] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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76
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Kim H, Kapral R. Solvation and proton transfer in polar molecule nanoclusters. J Chem Phys 2006; 125:234309. [PMID: 17190560 DOI: 10.1063/1.2404956] [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
Proton transfer in a phenol-amine complex dissolved in polar molecule nanoclusters is investigated. The proton transfer rates and mechanisms, as well as the solvation of the complex in the cluster, are studied using both adiabatic and nonadiabatic dynamics. The phenol-amine complex exists in ionic and covalent forms and as the size of the cluster increases the ionic form gains stability at the expense of the covalent form. Both the adiabatic and nonadiabatic transfer reaction rates increase with cluster size. Given a fixed cluster size, the stability of the covalent state increases with increasing temperature. The proton transfer rates do not change monotonously with an increase in temperature. A strong correlation between the solvent polarization reaction coordinate and the location of the phenol-amine complex in the cluster is found. The ionic form of the complex strongly prefers the interior of the cluster while the covalent form prefers to lie on the cluster surface.
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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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77
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Toutounji M. Mixed quantum-classical description of spectroscopy of dissipative systems. J Chem Phys 2006; 125:194520. [PMID: 17129136 DOI: 10.1063/1.2382916] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Mixed quantum-classical statistical mechanics is employed to calculate dipole moment correlation function and linear absorption spectra. A quantum two-level subsystem interacting with quantum vibrations (primary oscillators) which in turn are coupled to a classical bath composed of infinite set of harmonic oscillators is used as a dissipative system. Starting with mixed quantum-classical Liouville equation for the evaluation of the mixed quantum-classical dipole moment correlation function and using coherent states and the inverse of Baker-Campbell-Hausdorf formula to evaluate the trace over the primary oscillators, whereby, a closed analytical expression for the electronic dipole moment correlation function is obtained. Illustrations of several absorption spectra at different temperatures are provided. An approximate optical four-point correlation is obtained in the high temperature limit. A strategy for deriving an exact optical four-point correlation is suggested.
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Affiliation(s)
- Mohamad Toutounji
- College of Science, Department of Chemistry, P.O. Box 17551, United Arab Emirates University, Al-Ain, United Arab Emirates.
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78
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Kim H, Hanna G, Kapral R. Analysis of kinetic isotope effects for nonadiabatic reactions. J Chem Phys 2006; 125:084509. [PMID: 16965031 DOI: 10.1063/1.2336778] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Factors influencing the rates of quantum mechanical particle transfer reactions in many-body systems are discussed. The investigations are carried out on a simple model for a proton transfer reaction that captures generic features seen in more realistic models of condensed phase systems. The model involves a bistable quantum oscillator coupled to a one-dimensional double-well reaction coordinate, which is in turn coupled to a bath of harmonic oscillators. Reactive-flux correlation functions that involve quantum-classical Liouville dynamics for chemical species operators and quantum equilibrium sampling are used to estimate the reaction rates. Approximate analytical expressions for the quantum equilibrium structure are derived. Reaction rates are shown to be influenced significantly by both the quantum equilibrium structure and nonadiabatic dynamics. Nonadiabatic dynamical effects are found to play the major role in determining the magnitude of the kinetic isotope effect for the model transfer reaction.
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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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79
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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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80
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81
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Takatsuka K. Non-Born-Oppenheimer path in anti-Hermitian dynamics for nonadiabatic transitions. J Chem Phys 2006; 124:64111. [PMID: 16483200 DOI: 10.1063/1.2167648] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
A serious difficulty in the semiclassical Ehrenfest theory for nonadiabatic transitions is that a path passing across the avoided crossing is forced to run on a potential averaged over comprising adiabatic potential surfaces that commit the avoided crossing. Therefore once a path passes through the crossing region, it immediately becomes incompatible with the standard view of "classical trajectory" running on an adiabatic surface. This casts a fundamental question to the theoretical structure of chemical dynamics. In this paper, we propose a non-Born-Oppenheimer path that is generated by an anti-Hermitian Hamiltonian, whose complex-valued eigenenergies can cross in their real parts and avoid crossing in the imaginary parts in the vicinity of the nonadiabatic transition region. We discuss the properties of this non-Born-Oppenheimer path and thereby show its compatibility with the Born-Oppenheimer classical trajectories. This theory not only allows the geometrical branching of the paths but gives the nonadiabatic transition amplitudes and quantum phases along the generated paths.
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Affiliation(s)
- Kazuo Takatsuka
- Department of Basic Science, The University of Tokyo, Komaba, Japan.
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82
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Sergi A. Statistical mechanics of quantum-classical systems with holonomic constraints. J Chem Phys 2006; 124:024110. [PMID: 16422574 DOI: 10.1063/1.2159477] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The statistical mechanics of quantum-classical systems with holonomic constraints is formulated rigorously by unifying the classical Dirac bracket and the quantum-classical bracket in matrix form. The resulting Dirac quantum-classical theory, which conserves the holonomic constraints exactly, is then used to formulate time evolution and statistical mechanics. The correct momentum-jump approximation for constrained systems arises naturally from this formalism. Finally, in analogy with what was found in the classical case, it is shown that the rigorous linear-response function of constrained quantum-classical systems contains nontrivial additional terms which are absent in the response of unconstrained systems.
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Affiliation(s)
- Alessandro Sergi
- Dipartimento di Fisica, Universitá degli Studi di Messina, Contrada Papardo, 98166 Messina, Italy.
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83
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Calculation of the transition state theory rate constant for a general reaction coordinate: Application to hydride transfer in an enzyme. Chem Phys Lett 2006. [DOI: 10.1016/j.cplett.2005.10.129] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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84
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Abstract
The study of quantum rate processes occurring in condensed phase environments is difficult because of the large number of degrees of freedom involved. Since a full quantum mechanical treatment is not computationally feasible, one is motivated to use mixed quantum-classical dynamical methods. This type of dynamics is applicable when one can single out a few degrees of freedom to be quantum in nature while treating the remainder classically. We describe a method that is based on the quantum-classical Liouville equation, which clearly prescribes the details of the coupling between the quantum and classical degrees of freedom. With the aid of this machinery, we show how to compute rate constants of reactions involving quantum particles immersed in a classical bath. We illustrate the use of this method on a model for proton transfer in a molecular complex dissolved in a polar solvent.
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Affiliation(s)
- Gabriel Hanna
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada.
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85
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Kim H, Kapral R. Nonadiabatic quantum-classical reaction rates with quantum equilibrium structure. J Chem Phys 2005; 123:194108. [PMID: 16321077 DOI: 10.1063/1.2110140] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Time correlation function expressions for quantum reaction-rate coefficients are computed in a quantum-classical limit. This form for the correlation function retains the full quantum equilibrium structure of the system in the spectral density function but approximates the time evolution of the operator by quantum-classical Liouville dynamics. Approximate analytical expressions for the spectral density function, which incorporate quantum effects in the many-body environment and reaction coordinate, are derived. The results of numerical simulations of the reaction rate are presented for a reaction model in which a two-level system is coupled to a bistable oscillator which is, in turn, coupled to a bath of harmonic oscillators. The nonadiabatic quantum-classical dynamics is simulated in terms of an ensemble of surface-hopping trajectories and the effects of the quantum equilibrium structure on the reaction rate are discussed.
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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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