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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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Nandi A, Sucher A, Kozuch S. Ping-Pong Tunneling Reactions: Can Fluoride Jump at Absolute Zero? Chemistry 2018; 24:16348-16355. [PMID: 30044526 DOI: 10.1002/chem.201802782] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2018] [Indexed: 12/12/2022]
Abstract
In a recent study, Scheiner designed a double-germanium-based fluoride receptor that binds the halogen by means of strong tetrel bonds (Chem. Eur. J. 2016, 22, 18850). In this system the F- binds to the germanium atoms in an asymmetric fashion, thereby producing a double-well potential in which the fluoride can jump from one germanium to the other as in a ping-pong game. Herein we prove through the use of computational tools that at cryogenic temperatures this rearrangement occurs by heavy-atom quantum mechanical tunneling. The inductive strength of the substituents and the polarity of the solvent can modify the barrier and the tunneling rate. But the strongest effect is observed upon modification of the geometry of the molecule by specific substitutions that affect the barrier width, the most critical factor in a tunneling mechanism. We postulate two experimental tests, one by microwave spectroscopy and one by cryogenic NMR spectroscopy, that can prove the predicted fluoride tunneling.
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Affiliation(s)
- Ashim Nandi
- Department of Chemistry, Ben-Gurion University of the Negev, Beer-Sheva, 841051, Israel
| | - Adam Sucher
- Department of Chemistry, Ben-Gurion University of the Negev, Beer-Sheva, 841051, Israel
| | - Sebastian Kozuch
- Department of Chemistry, Ben-Gurion University of the Negev, Beer-Sheva, 841051, Israel
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Petersen J, Pollak E. Instantaneous Tunneling Flight Time for Wavepacket Transmission through Asymmetric Barriers. J Phys Chem A 2018; 122:3563-3571. [PMID: 29558141 DOI: 10.1021/acs.jpca.8b01772] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The time it takes a particle to tunnel through the asymmetric Eckart barrier potential is investigated using Gaussian wavepackets, where the barrier serves as a model for the potential along a chemical reaction coordinate. We have previously shown that the, in principle experimentally measurable, tunneling flight time, which determines the time taken by the transmitted particle to traverse the barrier, vanishes for symmetric potentials like the Eckart and square barrier [ Petersen , J. ; Pollak , E. J. Phys. Chem. Lett. 2017 , 9 , 4017 ]. Here we show that the same result is obtained for the asymmetric Eckart barrier potential, and therefore, the zero tunneling flight time seems to be a general result for one-dimensional time-independent potentials. The wavepacket dynamics is simulated using both an exact quantum mechanical method and a classical Wigner prescription. The excellent agreement between the two methods shows that quantum coherences are not important in pure one-dimensional tunneling and reinforces the conclusion that the tunneling flight time vanishes.
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Affiliation(s)
- Jakob Petersen
- Chemical and Biological Physics Department , Weizmann Institute of Science , 76100 Rehovot , Israel
| | - Eli Pollak
- Chemical and Biological Physics Department , Weizmann Institute of Science , 76100 Rehovot , Israel
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Abstract
Attosecond ionization experiments have not resolved the question "What is the tunneling time?". Different definitions of tunneling time lead to different results. Second, a zero tunneling time for a material particle suggests that the nonrelativistic theory includes speeds greater than the speed of light. Chemical reactions, occurring via tunneling, should then not be considered in terms of a nonrelativistic quantum theory calling into question quantum dynamics computations on tunneling reactions. To answer these questions, we define a new experimentally measurable paradigm, the tunneling flight time, and show that it vanishes for scattering through an Eckart or a square barrier, irrespective of barrier length or height, generalizing the Hartman effect. We explain why this result does not lead to experimental measurement of speeds greater than the speed of light. We show that this tunneling is an incoherent process by comparing a classical Wigner theory with exact quantum mechanical computations.
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Affiliation(s)
- Jakob Petersen
- Chemical Physics Department, Weizmann Institute of Science , 76100 Rehovoth, Israel
| | - Eli Pollak
- Chemical Physics Department, Weizmann Institute of Science , 76100 Rehovoth, Israel
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Schild A, Agostini F, Gross EKU. Electronic Flux Density beyond the Born–Oppenheimer Approximation. J Phys Chem A 2016; 120:3316-25. [DOI: 10.1021/acs.jpca.5b12657] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Axel Schild
- Max-Planck Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
| | - Federica Agostini
- Max-Planck Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
| | - E. K. U. Gross
- Max-Planck Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
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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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Borden WT. Reactions that involve tunneling by carbon and the role that calculations have played in their study. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2015. [DOI: 10.1002/wcms.1235] [Citation(s) in RCA: 67] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Weston Thatcher Borden
- Department of Chemistry and the Center for Advanced Scientific Computing and Modeling University of North Texas Denton TX USA
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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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