1
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Czakó G, Gruber B, Papp D, Tajti V, Tasi DA, Yin C. First-principles mode-specific reaction dynamics. Phys Chem Chem Phys 2024; 26:15818-15830. [PMID: 38639072 DOI: 10.1039/d4cp00417e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/20/2024]
Abstract
Controlling the outcome of chemical reactions by exciting specific vibrational and/or rotational modes of the reactants is one of the major goals of modern reaction dynamics studies. In the present Perspective, we focus on first-principles vibrational and rotational mode-specific dynamics computations on reactions of neutral and anionic systems beyond six atoms such as X + C2H6 [X = F, Cl, OH], HX + C2H5 [X = Br, I], OH- + CH3I, and F- + CH3CH2Cl. The dynamics simulations utilize high-level ab initio analytical potential energy surfaces and the quasi-classical trajectory method. Besides initial state specificity and the validity of the Polanyi rules, mode-specific vibrational-state assignment for polyatomic product species using normal-mode analysis and Gaussian binning is also discussed and compared with experiment.
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Affiliation(s)
- Gábor Czakó
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group, Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science, Institute of Chemistry, University of Szeged, Rerrich Béla tér 1, Szeged H-6720, Hungary.
| | - Balázs Gruber
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group, Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science, Institute of Chemistry, University of Szeged, Rerrich Béla tér 1, Szeged H-6720, Hungary.
| | - Dóra Papp
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group, Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science, Institute of Chemistry, University of Szeged, Rerrich Béla tér 1, Szeged H-6720, Hungary.
| | - Viktor Tajti
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group, Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science, Institute of Chemistry, University of Szeged, Rerrich Béla tér 1, Szeged H-6720, Hungary.
| | - Domonkos A Tasi
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group, Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science, Institute of Chemistry, University of Szeged, Rerrich Béla tér 1, Szeged H-6720, Hungary.
| | - Cangtao Yin
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group, Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science, Institute of Chemistry, University of Szeged, Rerrich Béla tér 1, Szeged H-6720, Hungary.
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2
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Mondal S, Pan H, Liu K. Stretching-mode specificity in the Cl + CH 3D( v1-I, v1-II, and v4 = 1; | jK〉) reactions: dependency on the initial | jK〉 selectivity. Phys Chem Chem Phys 2022; 24:24050-24061. [PMID: 36168830 DOI: 10.1039/d2cp03614b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The title reactions were studied at a collisional energy of 5.4 kcal mol-1 in a crossed-beam product-imaging experiment. The dynamics attributes of the dominant ground-state CH2D(00) and the accompanied C-D bend-excited CH2D(61) products were imaged in reactions with totally 16 ro-vibrationally selected states of the CH3D(vi, |jK〉) reagents. We found that all three vibrational excitations yielded marked |jK〉-dependent rate-enhancements in forming the (00, 0/1)s product pairs. Furthermore, for a given rotational |jK〉-mode, a vibrational-mode propensity of v4 > v1-I > v1-II in rate promotion and a clear manifestation of the Fermi-phase-induced interference effect of the latter two were observed. Compared to the reactivity of the rotationless state |jK〉 = |00〉, a minute rotational-excitation of all three stretch-excited CH3D(vi = 1) reagents could yield significantly higher reaction rates for the product pair (00, 0)s, but not so for (00, 1)s. The signals in forming the (61, 0)s pair were clearly notable but smaller than that of the ground-state reaction product pair, (00, 0)g. An opposite propensity of v1-II ≈ v1-I > v4 with a milder dependency on the initial |jK〉-states was observed. The angular distributions of the (00, 0)s pairs were nearly identical for all ro-vibrationally excited reagents, displaying the typical trait for a direct abstraction of the rebound mechanism. Similar distributions were found for the (61, 0)s pairs; yet, both pairs deviated substantially from the peripheral feature of the ground-state reaction pair of (00, 0)g. Those of the (00, 1)s pairs in reactions with v4-excitation featured a prominent forward-peaking distribution-suggestive of a time-delayed, resonance-mediated pathway, again with little dependency on the initial |jK〉-states. As for the reactions with the two Fermi-dyads, v1-I and v1-II, albeit showing globally similar distributions to that for v4, a substantial variation with the initial rotational-mode excitation could be discerned in the forward-peaking features. To unravel the impact of the Fermi-phase on the |jK〉-dependent attributes, we adopted a comparative approach by contrasting the observations in reactions with the Fermi-dyad reagents (the superposition states) to those with the pure-state reagents. Remarkable distinctions are unveiled and elucidated with the unexplained results explicitly pointed out, which call for future theoretical investigations for deeper understanding.
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Affiliation(s)
- Sohidul Mondal
- Institute of Atomic and Molecular Sciences (IAMS), Academia Sinica, P. O. Box 23-166, Taipei, 10699, Taiwan.
| | - Huilin Pan
- Institute of Atomic and Molecular Sciences (IAMS), Academia Sinica, P. O. Box 23-166, Taipei, 10699, Taiwan. .,Department of Chemistry, Southern University of Science and Technology, Shenzhen, 518055, P. R. China
| | - Kopin Liu
- Institute of Atomic and Molecular Sciences (IAMS), Academia Sinica, P. O. Box 23-166, Taipei, 10699, Taiwan. .,Aerosol Science Research Center, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan.,State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, CAS, Dalian, 116023, P. R. China
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3
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Abstract
We perform rotational mode-specific quasi-classical trajectory simulations using a high-quality ab initio analytical potential energy surface for the Cl(2P3/2) + C2H6 → HCl + C2H5 reaction. As ethane, being a prolate-type symmetric top, can be characterized by the J and K rotational quantum numbers, the excitation of two rotational modes, the tumbling (J, K = 0) and spinning (J, K = J) rotations of the reactant is carried out with J = 10, 20, 30, and 40 at a wide range of collision energies. The impacts of rotational excitation on the reactivity, the mechanism, and the post-reaction distribution of energy are investigated: (1) exciting both rotational modes enhances the reactivity with the spinning rotation being more effective due to its coupling to the C-H stretching vibrational normal modes (C-H bond elongating effect) and larger rotational energies, (2) rotational excitation increases the dominance of direct rebound over the stripping mechanism, while collision energy favors the latter, (3) investing energy in tumbling rotation excites the translational motion of the products, while the excess spinning rotational energy readily flows into the internal degrees of freedom of the ethyl radical or, less significantly, into the HCl vibration, probably due to the pronounced rovibrational coupling in this case. We also study the relative efficiency of vibrational and rotational excitation on the reactivity of the barrierless and thus translationally hindered title reaction.
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Affiliation(s)
- Dóra Papp
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group, Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science, Institute of Chemistry, University of Szeged, Rerrich Béla tér 1, Szeged H-6720, Hungary
| | - Gábor Czakó
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group, Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science, Institute of Chemistry, University of Szeged, Rerrich Béla tér 1, Szeged H-6720, Hungary
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4
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Papp P, Czakó G. Rotational Mode Specificity in the F - + CH 3I( v = 0, JK) S N2 and Proton-Transfer Reactions. J Phys Chem A 2020; 124:8943-8948. [PMID: 33054214 PMCID: PMC7604870 DOI: 10.1021/acs.jpca.0c08043] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
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Quasiclassical
trajectory computations are performed for the F– + CH3I(v = 0, JK) →
I– + CH3F (SN2) and HF + CH2I– (proton-transfer)
reactions considering initial rotational states characterized by J = {0, 2, 4, 6, 8, 12, and 16} and K =
{0 and J} in the 1–30 kcal/mol collision energy
(Ecoll) range. Tumbling rotation (K = 0) counteracts orientation effects, thereby hindering
the SN2 reactivity by about 15% for J =
16 in the 1–15 kcal/mol Ecoll range
and has a negligible effect on proton transfer. Spinning about the
C–I bond (K = J), which is
21 times faster than tumbling, makes the reactions more direct, inhibiting
the SN2 reactivity by 25% in some cases, whereas significantly
enhancing the proton-transfer channel by a factor of 2 at Ecoll = 15 kcal/mol due to the fact that the
spinning-induced centrifugal force hinders complex formation by breaking
H-bonds and activates C–H bond cleavage, thereby promoting
proton abstraction on the expense of substitution. At higher Ecoll, as the reactions become more direct, the
rotational effects are diminishing.
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Affiliation(s)
- Paszkál Papp
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group, Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science, Institute of Chemistry, University of Szeged, Rerrich Béla tér 1, Szeged H-6720, Hungary
| | - Gábor Czakó
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group, Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science, Institute of Chemistry, University of Szeged, Rerrich Béla tér 1, Szeged H-6720, Hungary
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5
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Pan H, Wang F, Liu K. Multifaceted Stereoselectivity in Polyatomic Reactions. J Phys Chem A 2020; 124:6573-6584. [DOI: 10.1021/acs.jpca.0c04838] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Huilin Pan
- Southern University of Science and Technology, Shenzhen, P. R. China 518055
| | - Fengyan Wang
- Department of Chemistry and Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Fudan University, Shanghai, P. R. China 200433
| | - Kopin Liu
- Institute of Atomic and Molecular Sciences (IAMS), Academia Sinica, Taipei, Taiwan 10617
- State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, CAS, Dalian, P. R. China 116023
- Aerosol Science Research Center, National Sun Yat-sen University, Kaohsiung, Taiwan 80424
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6
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Czakó G, Győri T, Olasz B, Papp D, Szabó I, Tajti V, Tasi DA. Benchmark ab initio and dynamical characterization of the stationary points of reactive atom + alkane and SN2 potential energy surfaces. Phys Chem Chem Phys 2020; 22:4298-4312. [DOI: 10.1039/c9cp04944d] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We review composite ab initio and dynamical methods and their applications to characterize stationary points of atom/ion + molecule reactions.
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Affiliation(s)
- Gábor Czakó
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group
- Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science
- Institute of Chemistry
- University of Szeged
- Szeged H-6720
| | - Tibor Győri
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group
- Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science
- Institute of Chemistry
- University of Szeged
- Szeged H-6720
| | - Balázs Olasz
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group
- Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science
- Institute of Chemistry
- University of Szeged
- Szeged H-6720
| | - Dóra Papp
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group
- Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science
- Institute of Chemistry
- University of Szeged
- Szeged H-6720
| | - István Szabó
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group
- Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science
- Institute of Chemistry
- University of Szeged
- Szeged H-6720
| | - Viktor Tajti
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group
- Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science
- Institute of Chemistry
- University of Szeged
- Szeged H-6720
| | - Domonkos A. Tasi
- MTA-SZTE Lendület Computational Reaction Dynamics Research Group
- Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science
- Institute of Chemistry
- University of Szeged
- Szeged H-6720
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7
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Liu R, Song HW, Yang MH. Understanding rotational mode specificity in the O(3P)+CHD3→ OH+CD3 reaction by simple reactant alignment pictures. CHINESE J CHEM PHYS 2019. [DOI: 10.1063/1674-0068/cjcp1810238] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Affiliation(s)
- Rui Liu
- Key Laboratory of Magnetic Resonance in Biological Systems, National Center for Magnetic Resonance in Wuhan, State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
| | - Hong-wei Song
- Key Laboratory of Magnetic Resonance in Biological Systems, National Center for Magnetic Resonance in Wuhan, State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
| | - Ming-hui Yang
- Key Laboratory of Magnetic Resonance in Biological Systems, National Center for Magnetic Resonance in Wuhan, State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
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8
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Liu K. Vibrational Control of Bimolecular Reactions with Methane by Mode, Bond, and Stereo Selectivity. Annu Rev Phys Chem 2016; 67:91-111. [DOI: 10.1146/annurev-physchem-040215-112522] [Citation(s) in RCA: 76] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Kopin Liu
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan;
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9
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Pan H, Cheng Y, Liu K. Rotational Mode Specificity in Cl + CH4(v3=1,|jNl⟩): Role of Reactant’s Vibrational Angular Momentum. J Phys Chem A 2016; 120:4799-804. [DOI: 10.1021/acs.jpca.5b12156] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Huilin Pan
- Institute of Atomic and Molecular
Sciences (IAMS), Academia Sinica, P.O. Box 23-166, Taipei, Taiwan 10617
| | - Yuan Cheng
- Institute of Atomic and Molecular
Sciences (IAMS), Academia Sinica, P.O. Box 23-166, Taipei, Taiwan 10617
| | - Kopin Liu
- Institute of Atomic and Molecular
Sciences (IAMS), Academia Sinica, P.O. Box 23-166, Taipei, Taiwan 10617
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10
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Füchsel G, Thomas PS, den Uyl J, Öztürk Y, Nattino F, Meyer HD, Kroes GJ. Rotational effects on the dissociation dynamics of CHD3 on Pt(111). Phys Chem Chem Phys 2016; 18:8174-85. [DOI: 10.1039/c5cp07898a] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
MCTDH calculations suggest that experiments on the effect of alignment on dissociation of CH4 on metal surfaces are affected by steering.
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Affiliation(s)
- Gernot Füchsel
- Leiden Institute of Chemistry
- Gorlaeus Laboratories
- Leiden University
- 2300 RA Leiden
- The Netherlands
| | | | - Jurriaan den Uyl
- Leiden Institute of Chemistry
- Gorlaeus Laboratories
- Leiden University
- 2300 RA Leiden
- The Netherlands
| | - Yesim Öztürk
- Leiden Institute of Chemistry
- Gorlaeus Laboratories
- Leiden University
- 2300 RA Leiden
- The Netherlands
| | - Francesco Nattino
- Leiden Institute of Chemistry
- Gorlaeus Laboratories
- Leiden University
- 2300 RA Leiden
- The Netherlands
| | - Hans-Dieter Meyer
- Theoretische Chemie
- Physikalisch-Chemisches Institut
- Universität Heidelberg
- D-69120 Heidelberg
- Germany
| | - Geert-Jan Kroes
- Leiden Institute of Chemistry
- Gorlaeus Laboratories
- Leiden University
- 2300 RA Leiden
- The Netherlands
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11
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Espinosa-Garcia J. Quasiclassical Trajectory Study on the Role of CH-Stretching Vibrational Excitation in the F(2P) + CHD3(v1=0,1) Reactions. J Phys Chem A 2015; 120:5-13. [DOI: 10.1021/acs.jpca.5b10399] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- J. Espinosa-Garcia
- Departamento de Quimica Fisica, Universidad de Extremadura, 06071 Badajoz, Spain
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12
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Szabó I, Czakó G. Rotational Mode Specificity in the F– + CH3Y [Y = F and Cl] SN2 Reactions. J Phys Chem A 2015; 119:12231-7. [DOI: 10.1021/acs.jpca.5b06212] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- István Szabó
- Laboratory of Molecular Structure
and Dynamics, Institute of Chemistry, Eötvös University, P.O. Box
32, H-1518 Budapest 112, Hungary
| | - Gábor Czakó
- Laboratory of Molecular Structure
and Dynamics, Institute of Chemistry, Eötvös University, P.O. Box
32, H-1518 Budapest 112, Hungary
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13
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Wang F, Pan H, Liu K. Imaging the Effect of Reactant Rotations on the Dynamics of the Cl + CHD3(v1 = 1, |J,K⟩) Reaction. J Phys Chem A 2015; 119:11983-8. [DOI: 10.1021/acs.jpca.5b03524] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Fengyan Wang
- Institute
of Atomic and Molecular Sciences (IAMS), Academia Sinica, P.O. Box 23-166, Taipei, Taiwan 10617
- Department
of Chemistry, Fudan University, Shanghai 200433, People’s Republic of China
| | - Huilin Pan
- Institute
of Atomic and Molecular Sciences (IAMS), Academia Sinica, P.O. Box 23-166, Taipei, Taiwan 10617
| | - Kopin Liu
- Institute
of Atomic and Molecular Sciences (IAMS), Academia Sinica, P.O. Box 23-166, Taipei, Taiwan 10617
- Department
of Physics, National Taiwan University, Taipei, Taiwan 10617
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14
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Song H, Guo H. Vibrational and Rotational Mode Specificity in The Cl + H2O → HCl + OH Reaction: A Quantum Dynamical Study. J Phys Chem A 2015; 119:6188-94. [DOI: 10.1021/acs.jpca.5b03740] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Hongwei Song
- Department of Chemistry
and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States
| | - Hua Guo
- Department of Chemistry
and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States
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15
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Yan P, Wang Y, Li Y, Wang D. A seven-degree-of-freedom, time-dependent quantum dynamics study on the energy efficiency in surmounting the central energy barrier of the OH + CH3 → O + CH4 reaction. J Chem Phys 2015; 142:164303. [DOI: 10.1063/1.4918981] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Pengxiu Yan
- College of Physics and Electronics, Shandong Normal University, Jinan 250014, China
| | - Yuping Wang
- College of Physics and Electronics, Shandong Normal University, Jinan 250014, China
| | - Yida Li
- College of Physics and Electronics, Shandong Normal University, Jinan 250014, China
| | - Dunyou Wang
- College of Physics and Electronics, Shandong Normal University, Jinan 250014, China
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16
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Liu K. Perspective: Vibrational-induced steric effects in bimolecular reactions. J Chem Phys 2015; 142:080901. [DOI: 10.1063/1.4913323] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Kopin Liu
- Institute of Atomic and Molecular Sciences (IAMS), Academia Sinica, P.O. Box 23-166, Taipei 10617, Taiwan
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17
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Yan P, Meng F, Wang Y, Wang D. Energy efficiency in surmounting the central energy barrier: a quantum dynamics study of the OH + CH3 → O + CH4 reaction. Phys Chem Chem Phys 2015; 17:5187-93. [DOI: 10.1039/c4cp05488a] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A quantum dynamics study of the OH + CH3 with a slightly early barrier shows that vibrational energy is more effective in promoting the reactivity than translational energy, which is just opposite to the Polanyi rules.
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Affiliation(s)
- Pengxiu Yan
- College of Physics and Electronics
- Shandong Normal University
- Jinan
- China
| | - Fanbin Meng
- College of Physics and Electronics
- Shandong Normal University
- Jinan
- China
| | - Yuping Wang
- College of Physics and Electronics
- Shandong Normal University
- Jinan
- China
| | - Dunyou Wang
- College of Physics and Electronics
- Shandong Normal University
- Jinan
- China
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