1
|
Mandal A, Hunt KLC. Quantum transition probabilities due to overlapping electromagnetic pulses: Persistent differences between Dirac's form and nonadiabatic perturbation theory. J Chem Phys 2021; 154:024116. [PMID: 33445917 DOI: 10.1063/5.0020169] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The probability of transition to an excited state of a quantum system in a time-dependent electromagnetic field determines the energy uptake from the field. The standard expression for the transition probability has been given by Dirac. Landau and Lifshitz suggested, instead, that the adiabatic effects of a perturbation should be excluded from the transition probability, leaving an expression in terms of the nonadiabatic response. In our previous work, we have found that these two approaches yield different results while a perturbing field is acting on the system. Here, we prove, for the first time, that differences between the two approaches may persist after the perturbing fields have been completely turned off. We have designed a pair of overlapping pulses in order to establish the possibility of lasting differences, in a case with dephasing. Our work goes beyond the analysis presented by Landau and Lifshitz, since they considered only linear response and required that a constant perturbation must remain as t → ∞. First, a "plateau" pulse populates an excited rotational state and produces coherences between the ground and excited states. Then, an infrared pulse acts while the electric field of the first pulse is constant, but after dephasing has occurred. The nonadiabatic perturbation theory permits dephasing, but dephasing of the perturbed part of the wave function cannot occur within Dirac's method. When the frequencies in both pulses are on resonance, the lasting differences in the calculated transition probabilities may exceed 35%. The predicted differences are larger for off-resonant perturbations.
Collapse
Affiliation(s)
- Anirban Mandal
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| | - Katharine L C Hunt
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| |
Collapse
|
2
|
Wong CY, Alvey RM, Turner DB, Wilk KE, Bryant DA, Curmi PMG, Silbey RJ, Scholes GD. Electronic coherence lineshapes reveal hidden excitonic correlations in photosynthetic light harvesting. Nat Chem 2012; 4:396-404. [DOI: 10.1038/nchem.1302] [Citation(s) in RCA: 97] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2011] [Accepted: 02/10/2012] [Indexed: 12/11/2022]
|
3
|
Peng J, Castonguay TC, Coker DF, Ziegler LD. Ultrafast H[sub 2] and D[sub 2] rotational Raman responses in near critical CO[sub 2]: An experimental and theoretical study of anisotropic solvation dynamics. J Chem Phys 2009; 131:054501. [DOI: 10.1063/1.3186732] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
|
4
|
Fiedler SL, Kunttu HM, Eloranta J. Application of mean-field and surface-hopping approaches for interrogation of the Xe3+ molecular ion photoexcitation dynamics. J Chem Phys 2008; 128:164309. [PMID: 18447441 DOI: 10.1063/1.2911697] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Abstract
The dissociation dynamics of the excited Xe(3) (+) molecular ion through the Pi(12)(u) and Pi(12)(g) conical intersection was interrogated by computational simulation in which no adjustable parameters were used. The electronic ground and excited state potential energy surfaces were generated by the diatomics-in-molecules method, and the Ehrenfest mean-field and Tully surface-hopping approaches treated the nonadiabatic interactions. Reproduction of the experimental spectrum of the symmetric photofragmentation as a function of excitation energy was obtained within the region of interest (2.5-3.75 eV), with the exception of a 0.25 eV width on the red side of the spectral apex. Good agreement was obtained with the experimental dissociated photofragment kinetic energy spectra. It was determined that the greatest contribution to the nonadiabatic coupling between the two states originated from the bending vibrational mode of the molecule in the Sigma(12)(u), ground electronic state before excitation.
Collapse
Affiliation(s)
- Steven L Fiedler
- Department of Mechanical Engineering, 2250 G.G. Brown, 2350 Hayward St., The University of Michigan, Ann Arbor, Michigan 48109-2125, USA
| | | | | |
Collapse
|
5
|
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
| |
Collapse
|
6
|
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.
Collapse
Affiliation(s)
- Raymond Kapral
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada.
| |
Collapse
|
7
|
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.
Collapse
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
| | | | | | | |
Collapse
|
8
|
Iuchi S, Morita A, Kato S. Electronic relaxation dynamics of Ni2+-ion aqueous solution: Molecular-dynamics simulation. J Chem Phys 2005; 123:24505. [PMID: 16050757 DOI: 10.1063/1.1949212] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Abstract
Electronic relaxation dynamics of Ni2+-ion aqueous solution is investigated using molecular-dynamics (MD) simulations with the model-effective Hamiltonian developed previously. The nonadiabatic transition rates from the first three excited states to the ground state are evaluated by the golden rule formula with the adiabatic MD simulations. The MD simulations with the fewest-switch surface-hopping method are also carried out to obtain a more detailed description of the electronic relaxation dynamics among the excited states. We found out that the transitions among the three excited states are very fast, in the order of 10 fs, while the transition between the excited and ground states is slow, about 800 ps. These findings are consistent with the time scales of energy dissipation detected by the transient lens experiment. In both simulations, we explore the effects of the quantum decoherence, where the decoherence functions are derived by the energy-gap dynamics with the displaced harmonic-oscillator model.
Collapse
Affiliation(s)
- Satoru Iuchi
- Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa, Sakyo-ku, Kyoto 606-8502, Japan
| | | | | |
Collapse
|
9
|
Sergi A, Kapral R. Quantum-classical limit of quantum correlation functions. J Chem Phys 2004; 121:7565-76. [PMID: 15485216 DOI: 10.1063/1.1797191] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Abstract
A quantum-classical limit of the canonical equilibrium time correlation function for a quantum system is derived. The quantum-classical limit for the dynamics is obtained for quantum systems comprising a subsystem of light particles in a bath of heavy quantum particles. In this limit the time evolution of operators is determined by a quantum-classical Liouville operator, but the full equilibrium canonical statistical description of the initial condition is retained. The quantum-classical correlation function expressions derived here provide a way to simulate the transport properties of quantum systems using quantum-classical surface-hopping dynamics combined with sampling schemes for the quantum equilibrium structure of both the subsystem of interest and its environment
Collapse
Affiliation(s)
- Alessandro Sergi
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada.
| | | |
Collapse
|
10
|
Moskun AC, Bradforth SE. Photodissociation of ICN in polar solvents: Evidence for long lived rotational excitation in room temperature liquids. J Chem Phys 2003. [DOI: 10.1063/1.1591726] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
|
11
|
Kapral R, Ciccotti G. A Statistical Mechanical Theory of Quantum Dynamics in Classical Environments. BRIDGING TIME SCALES: MOLECULAR SIMULATIONS FOR THE NEXT DECADE 2002. [DOI: 10.1007/3-540-45837-9_16] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
|
12
|
|
13
|
Affiliation(s)
- Raymond Kapral
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, ON M5S 3H6, Canada
| |
Collapse
|
14
|
|
15
|
Bug AL, Martyna GJ. Calculation of neutron spectra for hydrogen in zeolites: rotational motions and translational motions in the Born–Oppenheimer limit. Chem Phys 2000. [DOI: 10.1016/s0301-0104(00)00235-4] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
|
16
|
Jang J, Stratt RM. Rotational energy relaxation of individual rotational states in liquids. J Chem Phys 2000. [DOI: 10.1063/1.1290289] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
17
|
McWhirter JL. An initial value representation for semiclassical time-correlation functions. J Chem Phys 2000. [DOI: 10.1063/1.481392] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
18
|
Mavri J. Molecular Dynamics with Nonadiabatic Transitions: A Comparison of Methods. MOLECULAR SIMULATION 2000. [DOI: 10.1080/08927020008023010] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|
19
|
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
| |
Collapse
|
20
|
Anderson CR, Coker DF, Eckert J, Bug ALR. Computational study of molecular hydrogen in zeolite Na-A. I. Potential energy surfaces and thermodynamic separation factors for ortho and para hydrogen. J Chem Phys 1999. [DOI: 10.1063/1.480104] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
21
|
McWhirter JL. Analysis of the Pechukas description of mixed quantum-classical dynamics. J Chem Phys 1999. [DOI: 10.1063/1.478300] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
22
|
Faeder J, Delaney N, Maslen P, Parson R. Modeling structure and dynamics of solvated molecular ions: Photodissociation and recombination in I2−(CO2). Chem Phys 1998. [DOI: 10.1016/s0301-0104(98)00309-7] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
|
23
|
|
24
|
Egorov SA, Rabani E, Berne BJ. Vibronic spectra in condensed matter: A comparison of exact quantum mechanical and various semiclassical treatments for harmonic baths. J Chem Phys 1998. [DOI: 10.1063/1.475512] [Citation(s) in RCA: 81] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
25
|
Bittner ER, Rossky PJ. Decoherent histories and nonadiabatic quantum molecular dynamics simulations. J Chem Phys 1997. [DOI: 10.1063/1.475013] [Citation(s) in RCA: 77] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
26
|
McWhirter JL. Time correlation functions for mixed quantum-semiclassical systems. J Chem Phys 1997. [DOI: 10.1063/1.474140] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
27
|
Batista VS, Coker DF. Nonadiabatic molecular dynamics simulation of photodissociation and geminate recombination of I2liquid xenon. J Chem Phys 1996. [DOI: 10.1063/1.472277] [Citation(s) in RCA: 113] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
28
|
Mei HS, Xiao L, Coker DF. Calculation of the rotational Raman spectrum of H2 in ice. J Chem Phys 1996. [DOI: 10.1063/1.472266] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
29
|
FILINOV VS. Wigner approach to quantum statistical mechanics and quantum generalization molecular dynamics method. Part 1. Mol Phys 1996. [DOI: 10.1080/00268979609484533] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
|
30
|
|
31
|
Cao J, Voth GA. Semiclassical approximations to quantum dynamical time correlation functions. J Chem Phys 1996. [DOI: 10.1063/1.470898] [Citation(s) in RCA: 74] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
32
|
Bittner ER, Rossky PJ. Quantum decoherence in mixed quantum‐classical systems: Nonadiabatic processes. J Chem Phys 1995. [DOI: 10.1063/1.470177] [Citation(s) in RCA: 309] [Impact Index Per Article: 10.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
33
|
Xiao L, Coker DF. Nonadiabatic dynamical studies of the rotational Raman spectrum of H2 in water. J Chem Phys 1995. [DOI: 10.1063/1.469168] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
34
|
|