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Fábri C, Marquardt R, Császár AG, Quack M. Controlling tunneling in ammonia isotopomers. J Chem Phys 2019; 150:014102. [DOI: 10.1063/1.5063470] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Csaba Fábri
- Laboratory of Molecular Structure and Dynamics, Institute of Chemistry, Eötvös Loránd University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
- MTA-ELTE Complex Chemical Systems Research Group, P.O. Box 32, H-1518 Budapest 112, Hungary
- Physical Chemistry, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Roberto Marquardt
- Physical Chemistry, ETH Zürich, CH-8093 Zürich, Switzerland
- Laboratoire de Chimie Quantique, Institut de Chimie UMR 7177 CNRS/Université de Strasbourg, 4, Rue Blaise Pascal CS 90032, 67081 Strasbourg Cedex, France
| | - Attila G. Császár
- Laboratory of Molecular Structure and Dynamics, Institute of Chemistry, Eötvös Loránd University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
- MTA-ELTE Complex Chemical Systems Research Group, P.O. Box 32, H-1518 Budapest 112, Hungary
| | - Martin Quack
- Physical Chemistry, ETH Zürich, CH-8093 Zürich, Switzerland
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Bredtmann T, Manz J, Zhao JM. Concerted Electronic and Nuclear Fluxes During Coherent Tunnelling in Asymmetric Double-Well Potentials. J Phys Chem A 2016; 120:3142-54. [PMID: 26799383 DOI: 10.1021/acs.jpca.5b11295] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The quantum theory of concerted electronic and nuclear fluxes (CENFs) during coherent periodic tunnelling from reactants (R) to products (P) and back to R in molecules with asymmetric double-well potentials is developed. The results are deduced from the solution of the time-dependent Schrödinger equation as a coherent superposition of two eigenstates; here, these are the two states of the lowest tunnelling doublet. This allows the periodic time evolutions of the resulting electronic and nuclear probability densities (EPDs and NPDs) as well as the CENFs to be expressed in terms of simple sinusodial functions. These analytical results reveal various phenomena during coherent tunnelling in asymmetric double-well potentials, e.g., all EPDs and NPDs as well as all CENFs are synchronous. Distortion of the symmetric reference to a system with an asymmetric double-well potential breaks the spatial symmetry of the EPDs and NPDs, but, surprisingly, the symmetry of the CENFs is conserved. Exemplary application to the Cope rearrangement of semibullvalene shows that tunnelling of the ideal symmetric system can be suppressed by asymmetries induced by rather small external electric fields. The amplitude for the half tunnelling, half nontunnelling border is as low as 0.218 × 10(-8) V/cm. At the same time, the delocalized eigenstates of the symmetric reference, which can be regarded as Schrödinger's cat-type states representing R and P with equal probabilities, get localized at one or the other minima of the asymmetric double-well potential, representing either R or P.
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Affiliation(s)
| | - Jörn Manz
- Freie Universität Berlin , Institut für Chemie und Biochemie, 14195 Berlin, Germany
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Liu C, Manz J, Yang Y. Staircase patterns of nuclear fluxes during coherent tunneling in excited doublets of symmetric double well potentials. Phys Chem Chem Phys 2016; 18:5048-55. [DOI: 10.1039/c5cp06935a] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Step-by-step flux for one-by-one transfers of the lobes of the density, from the reactant (left) to the product (right) in the excited tunneling doublet.
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Affiliation(s)
- ChunMei Liu
- State Key Laboratory of Quantum Optics and Quantum Optics Devices
- Institute of Laser Spectroscopy
- Shanxi University
- Taiyuan 030006
- China
| | - Jörn Manz
- State Key Laboratory of Quantum Optics and Quantum Optics Devices
- Institute of Laser Spectroscopy
- Shanxi University
- Taiyuan 030006
- China
| | - Yonggang Yang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices
- Institute of Laser Spectroscopy
- Shanxi University
- Taiyuan 030006
- China
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Bredtmann T, Diestler DJ, Li SD, Manz J, Pérez-Torres JF, Tian WJ, Wu YB, Yang Y, Zhai HJ. Quantum theory of concerted electronic and nuclear fluxes associated with adiabatic intramolecular processes. Phys Chem Chem Phys 2015; 17:29421-64. [DOI: 10.1039/c5cp03982g] [Citation(s) in RCA: 53] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Example of concerted electronic (right) and nuclear (left) fluxes: isomerization of B4.
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Affiliation(s)
- Timm Bredtmann
- State Key Laboratory of Quantum Optics and Quantum Optics Devices
- Institute of Laser Spectroscopy
- Shanxi University
- Taiyuan 030006
- China
| | - Dennis J. Diestler
- Freie Universität Berlin
- Institut für Chemie und Biochemie
- 14195 Berlin
- Germany
- University of Nebraska-Lincoln
| | - Si-Dian Li
- Nanocluster Laboratory
- Institute of Molecular Science
- Shanxi University
- Taiyuan 030006
- China
| | - Jörn Manz
- State Key Laboratory of Quantum Optics and Quantum Optics Devices
- Institute of Laser Spectroscopy
- Shanxi University
- Taiyuan 030006
- China
| | | | - Wen-Juan Tian
- Nanocluster Laboratory
- Institute of Molecular Science
- Shanxi University
- Taiyuan 030006
- China
| | - Yan-Bo Wu
- Nanocluster Laboratory
- Institute of Molecular Science
- Shanxi University
- Taiyuan 030006
- China
| | - Yonggang Yang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices
- Institute of Laser Spectroscopy
- Shanxi University
- Taiyuan 030006
- China
| | - Hua-Jin Zhai
- Nanocluster Laboratory
- Institute of Molecular Science
- Shanxi University
- Taiyuan 030006
- China
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Manz J, Pérez-Torres JF, Yang Y. Vibrating H2+(2Σg+, JM = 00) Ion as a Pulsating Quantum Bubble in the Laboratory Frame. J Phys Chem A 2014; 118:8411-25. [DOI: 10.1021/jp5017246] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jörn Manz
- State Key Laboratory of Quantum Optics and Quantum Optics
Devices, Institute of Laser Spectroscopy, Shanxi University, 92
Wucheng Road, Taiyuan 030006, China
- Institut für Chemie and Biochemie, Freie Universitat Berlin, Takustraße 3, 14195 Berlin, Germany
| | - Jhon Fredy Pérez-Torres
- Institut für Chemie and Biochemie, Freie Universitat Berlin, Takustraße 3, 14195 Berlin, Germany
| | - Yonggang Yang
- State Key Laboratory of Quantum Optics and Quantum Optics
Devices, Institute of Laser Spectroscopy, Shanxi University, 92
Wucheng Road, Taiyuan 030006, China
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Manz J, Pérez-Torres JF, Yang Y. Nuclear fluxes in diatomic molecules deduced from pump-probe spectra with spatiotemporal resolutions down to 5 pm and 200 asec. PHYSICAL REVIEW LETTERS 2013; 111:153004. [PMID: 24160597 DOI: 10.1103/physrevlett.111.153004] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/01/2013] [Indexed: 06/02/2023]
Abstract
When molecules move, their nuclei flow. The corresponding quantum observable, i.e., the nuclear flux density, was introduced by Schrödinger in 1926, but until now, it has not been measured. Here the first experimental results are deduced from high-resolution pump-probe measurements of the time-dependent nuclear densities in a vibrating diatomic molecule or molecular ion. The nuclear densities are converted to flux densities by means of the continuity equation. The flux densities are much more sensitive to time-dependent quantum effects than the densities. Applications to the sodium molecule and the deuterium molecular ion unravel four new effects; e.g., at the turns from bond stretch to compression, the flux of the nuclei exhibits multiple changes of directions, from small to large bond lengths, a phenomenon that we call the "quantum accordion."
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Affiliation(s)
- Jörn Manz
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, 92 Wucheng Road, Taiyuan 030006, China and Institut für Chemie und Biochemie, Freie Universität Berlin, Takustraße 3, 14195 Berlin, Germany
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Affiliation(s)
- Mikhail Lemeshko
- a ITAMP, Harvard-Smithsonian Center for Astrophysics , Cambridge , MA , 02138 , USA
- b Physics Department , Harvard University , Cambridge , MA , 02138 , USA
- c Kavli Institute for Theoretical Physics , University of California , Santa Barbara , CA , 93106 , USA
| | - Roman V. Krems
- c Kavli Institute for Theoretical Physics , University of California , Santa Barbara , CA , 93106 , USA
- d Department of Chemistry , University of British Columbia , BC V6T 1Z1, Vancouver , Canada
| | - John M. Doyle
- b Physics Department , Harvard University , Cambridge , MA , 02138 , USA
| | - Sabre Kais
- e Departments of Chemistry and Physics , Purdue University , West Lafayette , IN , 47907 , USA
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