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Xiahou C, Connor JNL, De Fazio D, Sokolovski D. A single resonance Regge pole dominates the forward-angle scattering of the state-to-state F + H 2 → FH + H reaction at Etrans = 62.09 meV. Phys Chem Chem Phys 2024; 26:3647-3666. [PMID: 38224460 DOI: 10.1039/d3cp04734b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2024]
Abstract
The aim of the present paper is to bring clarity, through simplicity, to the important and long-standing problem: does a resonance contribute to the forward-angle scattering of the F + H2 reaction? We reduce the problem to its essentials and present a well-defined, yet rigorous and unambiguous, investigation of structure in the differential cross sections (DCSs) of the following three state-to-state reactions at a translational energy of 62.09 meV: F + H2(vi = 0, ji = 0, mi = 0) → FH(vf = 3, jf = 0, 1, 2, mf = 0) + H, where vi, ji, mi and vf, jf, mf are the initial and final vibrational, rotational and helicity quantum numbers respectively. Firstly, we carry out quantum-scattering calculations for the Fu-Xu-Zhang potential energy surface, obtaining accurate numerical scattering matrix elements for indistinguishable H2. The calculations use a time-independent method, with hyperspherical coordinates and an enhanced Numerov method. Secondly, the following theoretical techniques are employed to analyse structures in the DCSs: (a) full and Nearside-Farside (NF) partial wave series (PWS) and local angular momentum theory, including resummations of the full PWS up to second order. (b) The recently introduced "CoroGlo" test, which lets us distinguish between glory and corona scattering at forward angles for a Legendre PWS. (c) Six asymptotic (semiclassical) forward-angle glory theories and three asymptotic farside rainbow theories, valid for rainbows at sideward-scattering angles. (d) Complex angular momentum (CAM) theories of forward and backward scattering, with the Regge pole positions and residues computed by Thiele rational interpolation. Thirdly, our conclusions for the three PWS DCSs are: (a) the forward-angle peaks arise from glory scattering. (b) A broad (hidden) farside rainbow is present at sideward angles. (c) A single Regge pole contributes to the DCS across the whole angular range, being most prominent at forward angles. This proves that a resonance contributes to the DCSs for the three transitions. (d) The diffraction oscillations in the DCSs arise from NF interference, in particular, interference between the Regge pole and direct subamplitudes.
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Affiliation(s)
- Chengkui Xiahou
- School of Pharmacy, Qilu Medical University, Zibo Economic Zone, Zibo City 255300, Shandong, People's Republic of China
| | - J N L Connor
- Department of Chemistry, The University of Manchester, Manchester M13 9PL, UK.
| | - Dario De Fazio
- Istituto di Struttura della Materia-Consiglio Nazionale delle Ricerche, 00016 Roma, Italy
| | - Dmitri Sokolovski
- Department of Physical Chemistry, University of the Basque Country, 48940 Leioa, Bizkaia, Spain
- IKERBASQUE, Basque Foundation for Science, 48011, Bilbao, Spain
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De Fazio D, Aquilanti V, Cavalli S. Benchmark Quantum Kinetics at Low Temperatures toward Absolute Zero and Role of Entrance Channel Wells on Tunneling, Virtual States, and Resonances: The F + HD Reaction. J Phys Chem A 2020; 124:12-20. [PMID: 31829589 DOI: 10.1021/acs.jpca.9b08435] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
This paper reports a study of the quantum reaction dynamics and kinetics of the F + HD reaction at low and ultralow temperatures, focusing on the range from the Wigner limit up to 50 K. Close coupling time-independent quantum reactive scattering calculations for the production of HF and DF molecules have been carried out on two potential energy surfaces differing in the description of the reaction entrance channel. This case is computationally more demanding than the cases of F with H2 and D2 ( De Fazio et al. Frontiers in Chemistry 2019 , 7 , 328 ) but offers a wider phenomenology regarding the roles of quantum mechanical effects of tunneling, of virtual states, and of resonances. The results show that at the temperatures in the cold and ultracold regimes small changes in the entrance channel long-range interaction induce surprising near threshold features. The presence of a virtual state close to the reactive threshold gives rise to a marked anti-Arrhenius behavior of the rate constants below 100 mK. This effect enhances reaction rates by about 2 orders of magnitude, making them of the same order as those at room temperature and confining the onset of the Wigner regime in the microkelvin region.
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Affiliation(s)
- Dario De Fazio
- Istituto di Struttura della materia-Consiglio Nazionale delle Ricerche , 00016 Roma , Italy
| | - Vincenzo Aquilanti
- Istituto di Struttura della materia-Consiglio Nazionale delle Ricerche , 00016 Roma , Italy.,Dipartimento di Chimica, Biologia e Biotecnologie , Università di Perugia , 06123 Perugia , Italy
| | - Simonetta Cavalli
- Dipartimento di Chimica, Biologia e Biotecnologie , Università di Perugia , 06123 Perugia , Italy
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Xiahou C, Shan X, Connor JNL. Application of the Partial Wave QP Decomposition to the Angular Scattering of the State-to-State F + H 2 Reaction at Etrans = 0.04088 eV. J Phys Chem A 2019; 123:10500-10513. [PMID: 31714765 DOI: 10.1021/acs.jpca.9b07959] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We analyze the physical content of structures present in the product differential cross sections (DCSs) of the benchmark F + H2(vi, ji, mi) → FH(vf, jf, mf) + H reaction, where v, j, and m are the vibrational, rotational, and helicity quantum numbers, respectively, for the initial and final states. We analyze three state-to-state transitions: 000 → 300, 000 → 310, and 000 → 320. Accurate quantum S matrix elements are employed at a translational energy of 0.04088 eV for the Fu-Xu-Zhang potential energy surface. Our analysis of the DCSs uses a new technique called the QP decomposition; it makes an exact decomposition of the scattering (S) matrix into a Q part and a P part. The P part consists of a partial wave (PW) sum of Regge poles (involving both positions and residues) together with a rapidly oscillating quadratic phase. The Q part of the decomposition is then constructed exactly by subtracting the rapidly oscillating phase and the PW Regge pole sum from the input PW S matrix. In practice, it is convenient to make a small modification, which we call the QmodPmod decomposition. All our calculations use only integer values of the total angular momentum quantum number, namely, J = 0, 1, 2,... We find that the QmodPmod decomposition is successful and physically meaningful, in that the properties of Qmod matrix are simpler than those of the input S matrix. We then carry out a QmodPmod analysis of the DCSs, which provides novel insights into interference structures present in the angular scattering. In particular, we find for all three reactions that Regge resonances contribute across the whole angular range of the DCSs, being particularly pronounced at small angles. The techniques of nearside-farside decomposition and local angular momentum analysis for resummed Legendre PW series are also employed to provide additional insights into the angular scattering.
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Affiliation(s)
- Chengkui Xiahou
- School of Pharmacy , Qilu Medical University , Zibo Economic Zone , Zibo City 255300 , Shandong , People's Republic of China
| | - Xiao Shan
- Department of Chemistry , The University of Manchester , Manchester M13 9PL , United Kingdom
| | - J N L Connor
- Department of Chemistry , The University of Manchester , Manchester M13 9PL , United Kingdom
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Sáez-Rábanos V, Verdasco JE, Herrero VJ. Orbiting resonances in the F + HD (v = 0, 1) reaction at very low collision energies. A quantum dynamical study. Phys Chem Chem Phys 2019; 21:15177-15186. [PMID: 31246200 PMCID: PMC6751073 DOI: 10.1039/c9cp02718a] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Time-independent, fully converged, quantum dynamical calculations have been performed for the F + HD (v = 0, j = 0) and F + HD (v = 1, j = 0) reactions on an accurate potential energy surface down to collision energies of 0.01 meV. The two isotopic exit channels, HF + D and DF + H, have been investigated. The calculations reproduce satisfactorily the Feshbach resonance structures for collision energies between 10 and 40 meV, previously reported in the literature for the HF + D channel. Contrary to the results of a former literature work, vibrational excitation of HD is found to enhance reactivity in all cases down to the lowest collision energy investigated. Shape-type orbiting resonances are found for collision energies lower than 2 meV. The resonances appear as peaks in the reaction cross sections that are associated to specific values of the total angular momentum, J. In contrast with the Feshbach resonances at higher energies, the orbiting resonance structure, which is caused by the van der Waals well of the entrance channel, is identical for the HF + D and DF + H exit channels. The orbiting resonance peaks for F + HD (v = 0) are very small, but those for F + HD (v = 1) could be observed, in principle, with a combination of Raman pumping and merged beams methods.
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Affiliation(s)
- V Sáez-Rábanos
- Departamento de Sistemas y Recursos Naturales, E.T.S. de Ingeniería de Montes, Forestal y del Medio Natural, Universidad Politécnica de Madrid, 28040 Madrid, Spain.
| | - J E Verdasco
- Departamento de Química Física, Facultad de Química, Universidad Complutense de Madrid (Unidad Asociada CSIC), 28040 Madrid, Spain.
| | - V J Herrero
- Instituto de Estructura de la Materia (IEM-CSIC), Serrano 123, 28006 Madrid, Spain.
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Shan X, Xiahou C, Connor JNL. Rainbows, supernumerary rainbows and interference effects in the angular scattering of chemical reactions: an investigation using Heisenberg's S matrix programme. Phys Chem Chem Phys 2018; 20:819-836. [DOI: 10.1039/c7cp06654f] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Rainbow and supernumerary rainbow in the angular scattering of a state-to-state chemical reaction.
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Affiliation(s)
- Xiao Shan
- School of Chemistry
- The University of Manchester
- Manchester M13 9PL
- UK
| | - Chengkui Xiahou
- School of Pharmacy
- Qilu Medical University
- Zibo 255213
- People's Republic of China
| | - J. N. L. Connor
- School of Chemistry
- The University of Manchester
- Manchester M13 9PL
- UK
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Wang T, Yang T, Xiao C, Sun Z, Zhang D, Yang X, Weichman ML, Neumark DM. Dynamical resonances in chemical reactions. Chem Soc Rev 2018; 47:6744-6763. [DOI: 10.1039/c8cs00041g] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The transition state is a key concept in the field of chemistry and is important in the study of chemical kinetics and reaction dynamics.
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Affiliation(s)
- Tao Wang
- State Key Laboratory of Molecular Reaction Dynamics
- Dalian Institute of Chemical Physics
- Chinese Academy of Sciences
- Dalian
- China
| | - Tiangang Yang
- State Key Laboratory of Molecular Reaction Dynamics
- Dalian Institute of Chemical Physics
- Chinese Academy of Sciences
- Dalian
- China
| | - Chunlei Xiao
- State Key Laboratory of Molecular Reaction Dynamics
- Dalian Institute of Chemical Physics
- Chinese Academy of Sciences
- Dalian
- China
| | - Zhigang Sun
- State Key Laboratory of Molecular Reaction Dynamics
- Dalian Institute of Chemical Physics
- Chinese Academy of Sciences
- Dalian
- China
| | - Donghui Zhang
- State Key Laboratory of Molecular Reaction Dynamics
- Dalian Institute of Chemical Physics
- Chinese Academy of Sciences
- Dalian
- China
| | - Xueming Yang
- State Key Laboratory of Molecular Reaction Dynamics
- Dalian Institute of Chemical Physics
- Chinese Academy of Sciences
- Dalian
- China
| | | | - Daniel M. Neumark
- Department of Chemistry
- University of California at Berkeley
- Berkeley
- USA
- Chemical Sciences Division
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De Fazio D, Cavalli S, Aquilanti V. Benchmark Quantum Mechanical Calculations of Vibrationally Resolved Cross Sections and Rate Constants on ab Initio Potential Energy Surfaces for the F + HD Reaction: Comparisons with Experiments. J Phys Chem A 2016; 120:5288-99. [PMID: 27186680 DOI: 10.1021/acs.jpca.6b01471] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Dario De Fazio
- Istituto di Struttura della
Materia, Consiglio Nazionale delle Ricerche, 00016 Roma, Italy
| | - Simonetta Cavalli
- Dipartimento di Chimica,
Biologia e Biotecnologie, Università di Perugia, 06123 Perugia, Italy
| | - Vincenzo Aquilanti
- Dipartimento di Chimica,
Biologia e Biotecnologie, Università di Perugia, 06123 Perugia, Italy
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Esposito F, Coppola CM, De Fazio D. Complementarity between Quantum and Classical Mechanics in Chemical Modeling. The H + HeH+ → H2 + + He Reaction: A Rigourous Test for Reaction Dynamics Methods. J Phys Chem A 2015; 119:12615-26. [PMID: 26583384 DOI: 10.1021/acs.jpca.5b09660] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
In this work we present a dynamical study of the H + HeH+ → H2+ + He reaction in a collision energy range from 0.1 meV to 10 eV, suitable to be used in applicative models. The paper extends and complements a recent work [ Phys. Chem. Chem. Phys. 2014, 16, 11662] devoted to the characterization of the reactivity from the ultracold regime up to the three-body dissociation breakup. In particular, the accuracy of the quasi-classical trajectory method below the three-body dissociation threshold has been assessed by a detailed comparison with previous calculations performed with different reaction dynamics methods, whereas the reliability of the results in the high energy range has been checked by a direct comparison with the available experimental data. Integral cross sections for several HeH+ roto-vibrational states have been analyzed and used to understand the extent of quantum effects in the reaction dynamics. By using the quasi-classical trajectory method and quantum mechanical close coupling data, respectively, in the high and low collision energy ranges, we obtain highly accurate thermal rate costants until 15 000 K including all (178) the roto-vibrational bound and quasi-bound states of HeH+. The role of the collision-induced dissociation is also discussed and explicitly calculated for the ground roto-vibrational state of HeH+.
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Affiliation(s)
- Fabrizio Esposito
- Consiglio Nazionale delle Ricerche, Istituto di Nanotecnologia, via Amendola 122/d, 70126 Bari, Italy
| | - Carla Maria Coppola
- Consiglio Nazionale delle Ricerche, Istituto di Nanotecnologia, via Amendola 122/d, 70126 Bari, Italy.,INAF-Osservatorio Astrofisico di Arcetri , 50125 Firenze, Italy
| | - Dario De Fazio
- Consiglio Nazionale delle Ricerche, Istituto di Struttura della Materia, Area della Ricerca di Roma 1, 00016 Roma, Italy
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