1
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Joy C, Mandal B, Bostan D, Dubernet ML, Babikov D. Mixed quantum/classical theory (MQCT) approach to the dynamics of molecule-molecule collisions in complex systems. Faraday Discuss 2024; 251:225-248. [PMID: 38770664 DOI: 10.1039/d3fd00166k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/22/2024]
Abstract
We developed a general theoretical approach and a user-ready computer code that permit study of the dynamics of collisional energy transfer and ro-vibrational energy exchange in complex molecule-molecule collisions. The method is a mixture of classical and quantum mechanics. The internal ro-vibrational motion of collision partners is treated quantum mechanically using a time-dependent Schrödinger equation that captures many quantum phenomena including state quantization and zero-point energy, propensity and selection rules for state-to-state transitions, quantum symmetry and interference phenomena. A significant numerical speed up is obtained by describing the translational motion of collision partners classically, using the Ehrenfest mean-field trajectory approach. Within this framework a family of approximate methods for collision dynamics is developed. Several benchmark studies for diatomic and triatomic molecules, such as H2O and ND3 collided with He, H2 and D2, show that the results of MQCT are in good agreement with full-quantum calculations in a broad range of energies, especially at high collision energies where they become nearly identical to the full quantum results. Numerical efficiency of the method and massive parallelism of the MQCT code permit us to embrace some of the most complicated collisional systems ever studied, such as C6H6 + He, CH3COOH + He and H2O + H2O. Application of MQCT to the collisions of chiral molecules such as CH3CHCH2O + He, and to molecule-surface collisions is also possible and will be pursued in the future.
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Affiliation(s)
- Carolin Joy
- Chemistry Department, Wehr Chemistry Building, Marquette University, Milwaukee, Wisconsin 53201-1881, USA.
| | - Bikramaditya Mandal
- Chemistry Department, Wehr Chemistry Building, Marquette University, Milwaukee, Wisconsin 53201-1881, USA.
| | - Dulat Bostan
- Chemistry Department, Wehr Chemistry Building, Marquette University, Milwaukee, Wisconsin 53201-1881, USA.
| | - Marie-Lise Dubernet
- Observatoire de Paris, PSL University, Sorbonne Universite, CNRS, SYRTE, Paris, France
| | - Dmitri Babikov
- Chemistry Department, Wehr Chemistry Building, Marquette University, Milwaukee, Wisconsin 53201-1881, USA.
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2
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Liu Y, Jambrina PG, Croft JFE, Balakrishnan N, Aoiz FJ, Guo H. New Full-Dimensional Reactive Potential Energy Surface for the H 4 System. J Chem Theory Comput 2024; 20:1829-1837. [PMID: 38354106 DOI: 10.1021/acs.jctc.3c01379] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/16/2024]
Abstract
As the most abundant molecule in the universe, collisions involving H2 have important implications in astrochemistry. Collisions between hydrogen molecules also represent a prototype for assessing various dynamic methods for understanding fundamental few-body processes. In this work, we develop a new and highly accurate full-dimensional potential energy surface (PES) covering all reactive channels of the H2 + H2 system, which extends our previously reported H2 + H2 nonreactive PES [J. Chem. Theory Comput., 2021, 17, 6747] by adding 39,538 additional ab initio points calculated at the MRCI/AV5Z level in the reactive channels. The global PES is represented with high fidelity (RMSE = 0.6 meV for a total of 79,000 points) by a permutation invariant polynomial neural network (PIP-NN) and is suitable for studying collision-induced dissociation, single-exchange, as well as four-center exchange reactions. Preliminary quasi-classical trajectory studies on the new PIP-NN PES reveal strong vibrational enhancement of all reaction channels.
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Affiliation(s)
- Yang Liu
- Department of Chemistry and Chemical Biology, Center for Computational Chemistry, University of New Mexico, Albuquerque, New Mexico 87131, United States
| | - Pablo G Jambrina
- Departamento de Quimica Fisica, Universidad de Salamanca, Salamanca 37008, Spain
| | - James F E Croft
- The Dodd-Walls Centre for Photonic and Quantum Technologies, New Zealand and Department of Physics, University of Otago, Dunedin 9054, New Zealand
| | - Naduvalath Balakrishnan
- Department of Chemistry and Biochemistry, University of Nevada, Las Vegas, Nevada 89154, United States
| | - F Javier Aoiz
- Departamento de Quimica Fisica, Universidad Complutense, Madrid 28040, Spain
| | - Hua Guo
- Department of Chemistry and Chemical Biology, Center for Computational Chemistry, University of New Mexico, Albuquerque, New Mexico 87131, United States
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3
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Song Q, Zhang X, Miao Z, Meng Q. Construction of a Mode-Combination Hamiltonian under the Grid-Based Representation for the Quantum Dynamics of OH + HO 2 → O 2 + H 2O. J Chem Theory Comput 2024; 20:597-613. [PMID: 38199964 DOI: 10.1021/acs.jctc.3c01090] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2024]
Abstract
In this work, a systematic construction framework on a mode-combination Hamiltonian operator of a typical polyatomic reaction, OH + HO2 → O2 + H2O, is developed. First, a set of Jacobi coordinates are employed to construct the kinetic energy operator (KEO) through the polyspherical approach ( Phys. Rep. 2009, 484, 169). Second, due to the multiconfigurational electronic structure of this system, a non-adiabatic potential energy surface (PES) is constructed where the first singlet and triplet states are involved with spin-orbital coupling. To improve the training database, the training set of random energy data was optimized through a popular iterative optimization approach with extensive trajectories. Here, we propose an automatic trajectory method, instead of the classical trajectory on a crude PES, where the gradients are directly computed by the present ab initio calculations. Third, on the basis of the training set, the potential function is directly constructed in the canonical polyadic decomposition (CPD) form ( J. Chem. Theory Comput. 2021, 17, 2702-2713) which is helpful in propagating the nuclear wave function under the grid-based representation. To do this, the Gaussian process regression (GPR) approach for building the CPD form, called the CPD-GPR method ( J. Phys. Chem. Lett. 2022, 13, 11128-11135) is adopted where we further revise CPD-GPR by introducing the mode-combination (mc) scheme leading to the present CPD-mc-GPR approach. Constructing the full-dimension non-adiabatic Hamiltonian operator with mode combination, as test calculations, the nuclear wave function is propagated to preliminarily compute the reactive probability of OH + HO2 → O2 + H2O where the reactants are prepared in vibrational ground states and in the first triplet electronic state.
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Affiliation(s)
- Qingfei Song
- Department of Chemistry, Northwestern Polytechnical University, West Youyi Road 127, Xi'an 710072, China
| | - Xingyu Zhang
- Department of Chemistry, Northwestern Polytechnical University, West Youyi Road 127, Xi'an 710072, China
| | - Zekai Miao
- Department of Chemistry, Northwestern Polytechnical University, West Youyi Road 127, Xi'an 710072, China
| | - Qingyong Meng
- Department of Chemistry, Northwestern Polytechnical University, West Youyi Road 127, Xi'an 710072, China
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4
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Croft JFE, Jambrina PG, Aoiz FJ, Guo H, Balakrishnan N. Cold Collisions of Ro-Vibrationally Excited D 2 Molecules. J Phys Chem A 2023; 127:1619-1627. [PMID: 36787203 DOI: 10.1021/acs.jpca.2c08855] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/15/2023]
Abstract
The H2 + H2 system has long been considered a benchmark system for ro-vibrational energy transfer in bimolecular collisions. However, most studies thus far have focused on collisions involving H2 molecules in the ground vibrational level or in the first excited vibrational state. While H2 + H2/HD collisions have received wide attention due to the important role they play in astrophysics, D2 + D2 collisions have received much less attention. Recently, Zhou et al. [ Nat. Chem. 2022, 14, 658-663, DOI: 10.1038/s41557-022-00926-z] examined stereodynamic aspects of rotational energy transfer in collisions of two aligned D2 molecules prepared in the v = 2 vibrational level and j = 2 rotational level. Here, we report quantum calculations of rotational and vibrational energy transfer in collisions of two D2 molecules prepared in vibrational levels up to v = 2 and identify key resonance features that contribute to the angular distribution in the experimental results of Zhou et al. The quantum scattering calculations were performed in full dimensionality and using the rigid-rotor approximation using a recently developed highly accurate six-dimensional potential energy surface for the H4 system that allows descriptions of collisions involving highly vibrationally excited H2 and its isotopologues.
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Affiliation(s)
- James F E Croft
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Dunedin 9016, New Zealand.,Department of Physics, University of Otago, Dunedin 9016, New Zealand
| | - Pablo G Jambrina
- Departamento de Química Física, Universidad de Salamanca, Salamanca 37008, Spain
| | - F Javier Aoiz
- Departamento de Química Física, Universidad Complutense, Madrid 28040, Spain
| | - Hua Guo
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States
| | - N Balakrishnan
- Department of Chemistry and Biochemistry, University of Nevada, Las Vegas, Nevada 89154, United States
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5
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Yang D, Guo H, Xie D. Recent advances in quantum theory on ro-vibrationally inelastic scattering. Phys Chem Chem Phys 2023; 25:3577-3594. [PMID: 36602236 DOI: 10.1039/d2cp05069b] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
Molecular collisions are of fundamental importance in understanding intermolecular interaction and dynamics. Its importance is accentuated in cold and ultra-cold collisions because of the dominant quantum mechanical nature of the scattering. We review recent advances in the time-independent approach to quantum mechanical characterization of non-reactive scattering in tetratomic systems, which is ideally suited for large collisional de Broglie wavelengths characteristic in cold and ultracold conditions. We discuss quantum scattering algorithms between two diatoms and between a triatom and an atom and their implementation, as well as various approximate schemes. They not only enable the characterization of collision dynamics in realistic systems but also serve as benchmarks for developing more approximate methods.
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Affiliation(s)
- Dongzheng Yang
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, USA.
| | - Hua Guo
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, USA.
| | - Daiqian Xie
- Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, China. .,Hefei National Laboratory, Hefei 230088, China
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6
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Buren B, Chen M. Wave Packet Approach to Adiabatic and Nonadiabatic Dynamics of Cold Inelastic Scatterings. Molecules 2022; 27:2912. [PMID: 35566262 PMCID: PMC9101670 DOI: 10.3390/molecules27092912] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2022] [Revised: 04/30/2022] [Accepted: 05/02/2022] [Indexed: 11/16/2022] Open
Abstract
Due to the extremely large de Broglie wavelength of cold molecules, cold inelastic scattering is always characterized by the time-independent close-coupling (TICC) method. However, the TICC method is difficult to apply to collisions of large molecular systems. Here, we present a new strategy for characterizing cold inelastic scattering using wave packet (WP) method. In order to deal with the long de Broglie wavelength of cold molecules, the total wave function is divided into interaction, asymptotic and long-range regions (IALR). The three regions use different numbers of ro-vibrational basis functions, especially the long-range region, which uses only one function corresponding to the initial ro-vibrational state. Thus, a very large grid range can be used to characterize long de Broglie wavelengths in scattering coordinates. Due to its better numerical scaling law, the IALR-WP method has great potential in studying the inelastic scatterings of larger collision systems at cold and ultracold regimes.
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Affiliation(s)
| | - Maodu Chen
- Key Laboratory of Materials Modification by Laser, Electron, and Ion Beams (Ministry of Education), School of Physics, Dalian University of Technology, Dalian 116024, China;
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7
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Zhao B, Manthe U. Direct product-type grid representations for angular coordinates in extended space and their application in the MCTDH approach. J Chem Phys 2021; 154:104115. [PMID: 33722051 DOI: 10.1063/5.0045054] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Multi-configurational time-dependent Hartree (MCTDH) calculations using time-dependent grid representations can be used to accurately simulate high-dimensional quantum dynamics on general ab initio potential energy surfaces. Employing the correlation discrete variable representation, sets of direct product type grids are employed in the calculation of the required potential energy matrix elements. This direct product structure can be a problem if the coordinate system includes polar and azimuthal angles that result in singularities in the kinetic energy operator. In the present work, a new direct product-type discrete variable representation (DVR) for arbitrary sets of polar and azimuthal angles is introduced. It employs an extended coordinate space where the range of the polar angles is taken to be [-π, π]. The resulting extended space DVR resolves problems caused by the singularities in the kinetic energy operator without generating a very large spectral width. MCTDH calculations studying the F·CH4 complex are used to investigate important properties of the new scheme. The scheme is found to allow for more efficient integration of the equations of motion compared to the previously employed cot-DVR approach [G. Schiffel and U. Manthe, Chem. Phys. 374, 118 (2010)] and decreases the required central processing unit times by about an order of magnitude.
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Affiliation(s)
- Bin Zhao
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany
| | - Uwe Manthe
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany
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8
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Chen J, Li J, Bowman JM, Guo H. Energy transfer between vibrationally excited carbon monoxide based on a highly accurate six-dimensional potential energy surface. J Chem Phys 2020; 153:054310. [DOI: 10.1063/5.0015101] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jun Chen
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Jun Li
- School of Chemistry and Chemical Engineering, Chongqing University, Chongqing 401331, China
| | - Joel M. Bowman
- Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Hua Guo
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, USA
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9
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Sur S, Ndengué SA, Quintas-Sánchez E, Bop C, Lique F, Dawes R. Rotationally inelastic scattering of O3–Ar: state-to-state rates with the multiconfigurational time dependent Hartree method. Phys Chem Chem Phys 2020; 22:1869-1880. [DOI: 10.1039/c9cp06501f] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The rates of state-changing collisions are compared for different isotopologues of ozone from quantum scattering calculations with the MCTDH method.
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Affiliation(s)
- Sangeeta Sur
- Department of Chemistry
- Missouri University of Science & Technology
- Rolla
- USA
| | - Steve A. Ndengué
- Department of Chemistry
- Missouri University of Science & Technology
- Rolla
- USA
- ICTP-East African Institute for Fundamental Research
| | | | - Cheikh Bop
- LOMC – UMR 6294
- CNRS-Université du Havre
- F-76063 Le Havre
- France
| | - François Lique
- LOMC – UMR 6294
- CNRS-Université du Havre
- F-76063 Le Havre
- France
| | - Richard Dawes
- Department of Chemistry
- Missouri University of Science & Technology
- Rolla
- USA
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10
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Ndengué S, Scribano Y, Gatti F, Dawes R. State-to-state inelastic rotational cross sections in five-atom systems with the multiconfiguration time dependent Hartree method. J Chem Phys 2019; 151:134301. [PMID: 31594314 DOI: 10.1063/1.5119381] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a MultiConfiguration Time Dependent Hartree (MCTDH) method as an attractive alternative approach to the usual quantum close-coupling method that approaches some computational limits in the calculation of rotational excitation (and de-excitation) between polyatomic molecules (here collisions between triatomic and diatomic rigid molecules). We have performed a computational investigation of the rotational (de-)excitation of the benchmark rigid rotor H2O-H2 system on a recently developed Potential Energy Surface of the complex using the MCTDH method. We focus here on excitations and de-excitations from the 000, 111, and 110 states of H2O with H2 in its ground rotational state, looking at all the potential transitions in the energy range 1-200 cm-1. This work follows a recently completed study on the H2O-H2 cluster where we characterized its spectroscopy and more generally serves a broader goal to describe inelastic collision processes of high dimensional systems using the MCTDH method. We find that the cross sections obtained from the MCTDH calculations are in excellent agreement with time independent calculations from previous studies but does become challenging for the lower kinetic energy range of the de-excitation process: that is, below approximately 20 cm-1 of collision energy, calculations with a relative modest basis become unreliable. The MCTDH method therefore appears to be a useful complement to standard approaches to study inelastic collision for various collision partners, even at low energy, though performing better for rotational excitation than for de-excitation.
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Affiliation(s)
- Steve Ndengué
- ICTP-East African Institute for Fundamental Research, University of Rwanda, Kigali, Rwanda
| | - Yohann Scribano
- Laboratoire Univers et Particule de Montpellier, Université de Montpellier, UMR-CNRS 5299, 34095 Montpellier Cedex, France
| | - Fabien Gatti
- Institut de Sciences Moléculaires d'Orsay, UMR 8214, Université Paris-Sud - Université Paris-Saclay, 91405 Orsay, France
| | - Richard Dawes
- Department of Chemistry, Missouri University of Science and Technology, Rolla, Missouri 65409, USA
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11
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Croft JFE, Balakrishnan N. Controlling rotational quenching rates in cold molecular collisions. J Chem Phys 2019; 150:164302. [PMID: 31042924 DOI: 10.1063/1.5091576] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The relative orientation and alignment of colliding molecules plays a key role in determining the rates of chemical processes. Here, we examine in detail a prototypical example: rotational quenching of HD in cold collisions with H2. We show that the rotational quenching rate from j = 2 → 0, in the v = 1 vibrational level, can be maximized by aligning the HD along the collision axis and can be minimized by aligning the HD at the so called magic angle. This follows from quite general helicity considerations and suggests that quenching rates for other similar systems can also be controlled in this manner.
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Affiliation(s)
- J F E Croft
- The Dodd Walls Centre for Photonic and Quantum Technologies, Dunedin, New Zealand
| | - N Balakrishnan
- Department of Chemistry and Biochemistry, University of Nevada, Las Vegas, Nevada 89154, USA
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12
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Croft JFE, Balakrishnan N, Huang M, Guo H. Unraveling the Stereodynamics of Cold Controlled HD-H_{2} Collisions. PHYSICAL REVIEW LETTERS 2018; 121:113401. [PMID: 30265091 DOI: 10.1103/physrevlett.121.113401] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2018] [Indexed: 06/08/2023]
Abstract
Measuring inelastic rates with partial-wave resolution requires temperatures close to a Kelvin or below, even for the lightest molecule. In a recent experiment, Perreault, Mukherjee, and Zare [Nat. Chem. 10, 561 (2018).NCAHBB1755-433010.1038/s41557-018-0028-5] studied collisional relaxation of excited HD molecules in the v=1, j=2 state by para- and ortho-H_{2} at a temperature of about 1 K, extracting the angular distribution of scattered HD in the v=1, j=0 state. By state preparation of the HD molecules, control of the angular distribution of scattered HD was demonstrated. Here, we report a first-principles simulation of that experiment which enables us to attribute the main features of the observed angular distribution to a single L=2 partial-wave shape resonance. Our results demonstrate important stereodynamical insights that can be gained when numerically exact quantum scattering calculations are combined with experimental results in the few-partial-wave regime.
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Affiliation(s)
- James F E Croft
- Department of Chemistry and Biochemistry, University of Nevada, Las Vegas, Nevada 89154, USA
| | - Naduvalath Balakrishnan
- Department of Chemistry and Biochemistry, University of Nevada, Las Vegas, Nevada 89154, USA
| | - Meng Huang
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Hua Guo
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, USA
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13
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Ndengué S, Dawes R, Gatti F, Guo H. Influence of Renner–Teller Coupling between Electronic States on H + CO Inelastic Scattering. J Phys Chem A 2018; 122:6381-6390. [DOI: 10.1021/acs.jpca.8b05235] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Steve Ndengué
- Department of Chemistry, Missouri University of Science and Technology, Rolla, Missouri 65409, United States
| | - Richard Dawes
- Department of Chemistry, Missouri University of Science and Technology, Rolla, Missouri 65409, United States
| | - Fabien Gatti
- Institut des Sciences Moléculaires d’Orsay, CNRS, Université Paris-Sud/Paris Saclay, F-91405 Orsay, France
| | - Hua Guo
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States
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14
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Otto F, Chiang YC, Peláez D. Accuracy of Potfit-based potential representations and its impact on the performance of (ML-)MCTDH. Chem Phys 2018. [DOI: 10.1016/j.chemphys.2017.11.013] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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15
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Ndengué S, Dawes R, Gatti F, Meyer HD. Atom-triatom rigid rotor inelastic scattering with the MultiConfiguration Time Dependent Hartree approach. Chem Phys Lett 2017. [DOI: 10.1016/j.cplett.2016.12.012] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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16
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Semenov A, Babikov D. Inelastic Scattering of Identical Molecules within Framework of the Mixed Quantum/Classical Theory: Application to Rotational Excitations in H2 + H2. J Phys Chem A 2016; 120:3861-6. [PMID: 27187769 DOI: 10.1021/acs.jpca.6b04556] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Theoretical foundation is laid out for description of permutation symmetry in the inelastic scattering processes that involve collisions of two identical molecules, within the framework of the mixed quantum/classical theory (MQCT). In this approach, the rotational (and vibrational) states of two molecules are treated quantum-mechanically, whereas their translational motion (responsible for scattering) is treated classically. This theory is applied to H2 + H2 system, and the state-to-state transition cross sections are compared versus those obtained from the full-quantum calculations and experimental results from the literature. Good agreement is found in all cases. It is also found that results of MQCT, where the Coriolis coupling is included classically, are somewhat closer to exact full-quantum results than results of the other approximate quantum methods, where those coupling terms are neglected. These new developments allow applications of MQCT to a broad variety of molecular systems and processes.
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Affiliation(s)
- Alexander Semenov
- Chemistry Department, Wehr Chemistry Building, Marquette University , Milwaukee, Wisconsin 53201-1881, United States
| | - Dmitri Babikov
- Chemistry Department, Wehr Chemistry Building, Marquette University , Milwaukee, Wisconsin 53201-1881, United States
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17
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Ndengué SA, Dawes R, Gatti F. Rotational Excitations in CO–CO Collisions at Low Temperature: Time-Independent and Multiconfigurational Time-Dependent Hartree Calculations. J Phys Chem A 2015; 119:7712-23. [DOI: 10.1021/acs.jpca.5b01022] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Steve A. Ndengué
- Department
of Chemistry, Missouri University of Science and Technology, 142 Schrenk
Hall, 400 West 11th Street, Rolla, Missouri 65409, United States
| | - Richard Dawes
- Department
of Chemistry, Missouri University of Science and Technology, 142 Schrenk
Hall, 400 West 11th Street, Rolla, Missouri 65409, United States
| | - Fabien Gatti
- CTMM,
Institut Charles Gerhardt, UMR 5253, Univeristé de Montpellier II, Place
Eugène Bataillon, 34095 Montpellier, France
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18
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Diaz-Torres A, Wiescher M. Relating molecular structure and low-energy fusion through time-dependent wave-packet dynamics: the 12C+ 12C collision. EPJ WEB OF CONFERENCES 2015. [DOI: 10.1051/epjconf/20159302017] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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19
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Montero S, Pérez-Ríos J. Rotational relaxation in molecular hydrogen and deuterium: Theory versus acoustic experiments. J Chem Phys 2014; 141:114301. [DOI: 10.1063/1.4895398] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- S. Montero
- Laboratory of Molecular Fluid Dynamics @ Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid, Spain
| | - J. Pérez-Ríos
- Physics Department, Purdue University, West Lafayette, Indiana 47907, USA
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20
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Zhao B, Zhang DH, Lee SY, Sun Z. Calculation of state-to-state cross sections for triatomic reaction by the multi-configuration time-dependent Hartree method. J Chem Phys 2014; 140:164108. [DOI: 10.1063/1.4872157] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
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21
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Otto F. Multi-layer Potfit: An accurate potential representation for efficient high-dimensional quantum dynamics. J Chem Phys 2014; 140:014106. [DOI: 10.1063/1.4856135] [Citation(s) in RCA: 47] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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dos Santos SF, Balakrishnan N, Forrey RC, Stancil PC. Vibration-vibration and vibration-translation energy transfer in H2-H2 collisions: A critical test of experiment with full-dimensional quantum dynamics. J Chem Phys 2013; 138:104302. [DOI: 10.1063/1.4793472] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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23
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Joubert-Doriol L, Lasorne B, Gatti F, Schröder M, Vendrell O, Meyer HD. Suitable coordinates for quantum dynamics: Applications using the multiconfiguration time-dependent Hartree (MCTDH) algorithm. COMPUT THEOR CHEM 2012. [DOI: 10.1016/j.comptc.2011.12.015] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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Otto F, Gatti F, Meyer HD. Rovibrational energy transfer in collisions of H2with D2: a full-dimensional wave packet propagation study. Mol Phys 2012. [DOI: 10.1080/00268976.2012.667165] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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BHATTACHARYA S, KIRWAI A, PANDA ADITYAN, MEYER HD. Full dimensional quantum scattering study of the H2 + CN reaction#. J CHEM SCI 2012. [DOI: 10.1007/s12039-011-0197-x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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26
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Giri K, Chapman E, Sanz CS, Worth G. A full-dimensional coupled-surface study of the photodissociation dynamics of ammonia using the multiconfiguration time-dependent Hartree method. J Chem Phys 2011; 135:044311. [DOI: 10.1063/1.3614038] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Santos SFD, Balakrishnan N, Lepp S, Quéméner G, Forrey RC, Hinde RJ, Stancil PC. Quantum dynamics of rovibrational transitions in H2-H2 collisions: Internal energy and rotational angular momentum conservation effects. J Chem Phys 2011; 134:214303. [DOI: 10.1063/1.3595134] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Marquardt R, Sanrey M, Gatti F, Le Quéré F. Full-dimensional quantum dynamics of vibrationally highly excited NHD2. J Chem Phys 2010; 133:174302. [DOI: 10.1063/1.3496374] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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29
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Schiffel G, Manthe U. On direct product based discrete variable representations for angular coordinates and the treatment of singular terms in the kinetic energy operator. Chem Phys 2010. [DOI: 10.1016/j.chemphys.2010.07.006] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Bhattacharya S, Panda AN, Meyer HD. Multiconfiguration time-dependent Hartree approach to study the OH+H2 reaction. J Chem Phys 2010; 132:214304. [DOI: 10.1063/1.3429609] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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31
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Garcia E, Saracibar A, Sánchez C, Laganà A. Effect of the Total Angular Momentum on the Dynamics of the H2 + H2 System. J Phys Chem A 2009; 113:14312-20. [DOI: 10.1021/jp903072j] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Affiliation(s)
- Ernesto Garcia
- Departamento de Quimica Fisica, Universidad del Pais Vasco, 01006 Vitoria, Spain, and Dipartimento di Chimica, Università di Perugia, 06123 Perugia, Italy
| | - Amaia Saracibar
- Departamento de Quimica Fisica, Universidad del Pais Vasco, 01006 Vitoria, Spain, and Dipartimento di Chimica, Università di Perugia, 06123 Perugia, Italy
| | - Carlos Sánchez
- Departamento de Quimica Fisica, Universidad del Pais Vasco, 01006 Vitoria, Spain, and Dipartimento di Chimica, Università di Perugia, 06123 Perugia, Italy
| | - Antonio Laganà
- Departamento de Quimica Fisica, Universidad del Pais Vasco, 01006 Vitoria, Spain, and Dipartimento di Chimica, Università di Perugia, 06123 Perugia, Italy
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32
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Jutier L, Léonard C, Gatti F. Renner–Teller effect in linear tetra-atomic molecules. I. Variational method including couplings between all degrees of freedom on six-dimensional potential energy surfaces. J Chem Phys 2009; 130:134301. [DOI: 10.1063/1.3089354] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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33
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Quéméner G, Balakrishnan N. Quantum calculations of H2–H2 collisions: From ultracold to thermal energies. J Chem Phys 2009; 130:114303. [DOI: 10.1063/1.3081225] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
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34
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Pasin G, Iung C, Gatti F, Richter F, Léonard C, Meyer HD. Theoretical investigation of intramolecular vibrational energy redistribution in HFCO and DFCO induced by an external field. J Chem Phys 2008; 129:144304. [DOI: 10.1063/1.2991411] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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35
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Wang XG, Carrington T. Using a nondirect product discrete variable representation for angular coordinates to compute vibrational levels of polyatomic molecules. J Chem Phys 2008; 128:194109. [DOI: 10.1063/1.2918498] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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36
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Otto F, Gatti F, Meyer HD. Rotational excitations in para-H2+para-H2 collisions: Full- and reduced-dimensional quantum wave packet studies comparing different potential energy surfaces. J Chem Phys 2008; 128:064305. [DOI: 10.1063/1.2826379] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
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37
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Panda AN, Otto F, Gatti F, Meyer HD. Rovibrational energy transfer in ortho-H2+para-H2 collisions. J Chem Phys 2007; 127:114310. [PMID: 17887840 DOI: 10.1063/1.2776266] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present the results of a full-dimensional quantum mechanical study of the rovibrational energy transfer in the collision between ortho-H2 and para-H2 in the energy range of 0.1-1.0 eV. The multiconfiguration time-dependent Hartree algorithm has been used to propagate the wave packets on the global potential energy surface by Boothroyd et al. [J. Chem. Phys. 116, 666 (2002)] and on a modification of this surface where the short range anisotropy is reduced. State-to-state attributes such as probabilities or integral cross sections are obtained using the formalism of Tannor and Weeks [J. Chem. Phys. 98, 3884 (1993)] by Fourier transforming the correlation functions. The effect of initial rotation of the diatoms on the inelastic and de-excitation processes is investigated.
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Affiliation(s)
- Aditya N Panda
- Theoretische Chemie, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany.
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38
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Lee TG, Balakrishnan N, Forrey RC, Stancil PC, Schultz DR, Ferland GJ. Erratum: “State-to-state rotational transitions in H2+H2 collisions at low temperatures” [J. Chem. Phys. 125, 114302 (2006)]. J Chem Phys 2007. [DOI: 10.1063/1.2730820] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Manzhos S, Carrington T. Using neural networks to represent potential surfaces as sums of products. J Chem Phys 2007; 125:194105. [PMID: 17129087 DOI: 10.1063/1.2387950] [Citation(s) in RCA: 129] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
By using exponential activation functions with a neural network (NN) method we show that it is possible to fit potentials to a sum-of-products form. The sum-of-products form is desirable because it reduces the cost of doing the quadratures required for quantum dynamics calculations. It also greatly facilitates the use of the multiconfiguration time dependent Hartree method. Unlike potfit product representation algorithm, the new NN approach does not require using a grid of points. It also produces sum-of-products potentials with fewer terms. As the number of dimensions is increased, we expect the advantages of the exponential NN idea to become more significant.
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Affiliation(s)
- Sergei Manzhos
- Département de chimie, Université de Montréal, Case Postale 6128, succursale Centre-ville, Montréal, (Québec) H3C 3J7, Canada.
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41
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Pasin G, Iung C, Gatti F, Meyer HD. Theoretical investigation of highly excited vibrational states in DFCO: Calculation of the out-of-plane bending states and simulation of the intramolecular vibrational energy redistribution. J Chem Phys 2007; 126:024302. [PMID: 17228949 DOI: 10.1063/1.2402920] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A previously developed modified Davidson scheme [C. Iung and F. Ribeiro, J. Chem. Phys. 121, 174105 (2005)] is applied to compute and analyze highly excited (nu2,nu6) eigenstates in DFCO. The present paper is also devoted to the simulations of the intramolecular vibrational energy redistribution (IVR) initiated by an excitation of the out-of-plane bending vibration (nnu6, n=2,4,6, . . . ,18, and 20). The multiconfiguration time-dependent Hartree method is exploited to propagate the corresponding six-dimensional wave packets. A comprehensive comparison with experimental data as well as with previous simulations of IVR in HFCO [G. Pasin et al. J. Chem. Phys. 124, 194304 (2006)] is presented.
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Affiliation(s)
- Gauthier Pasin
- Equipe de Chimie Théorique Méthodologies et Modélisations, Institut Gerhardt, UMR 5253 CNRS-UM II-ENSCM, CC 014, Université Montpellier II, F-34095 Montpellier, Cedex 05, France.
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Lasorne B, Robb MA, Worth GA. Direct quantum dynamics using variational multi-configuration Gaussian wavepackets. Implementation details and test case. Phys Chem Chem Phys 2007; 9:3210-27. [PMID: 17579730 DOI: 10.1039/b700297a] [Citation(s) in RCA: 80] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
We present here a direct quantum dynamics method using variational multi-configuration Gaussian wavepackets. Based on the efficient multi-configuration time-dependent Hartree wavepacket propagation algorithm, it uses on-the-fly quantum chemical calculation of the potential energy and its derivatives rather than fitted surfaces. Intermediate results are stored in a database so that expensive quantum chemical computations can be recycled. This method is intended to treat quantum effects in the photochemistry of large molecules and the use of Cartesian coordinates to perform direct dynamics is discussed with a comparison between Cartesian coordinates of Jacobi vectors and Cartesian coordinates of the nuclei, using various free and constrained approaches depending on the way the rotation is treated. As a test calculation to be compared to full quantum dynamics it is applied here to the computation of the photodissociation spectrum of nitrosyl chloride (NOCl).
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Affiliation(s)
- B Lasorne
- Department of Chemistry, Imperial College London, South Kensington, London, UKSW7 2AZ.
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43
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Montero S, Thibault F, Tejeda G, Fernández JM. Rotranslational state-to-state rates and spectral representation of inelastic collisions in low-temperature molecular hydrogen. J Chem Phys 2006; 125:124301. [PMID: 17014168 DOI: 10.1063/1.2353121] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
Inelastic collisions in natural H2 are studied from the experimental and theoretical points of view between 10 and 140 K. Rotational populations and number densities measured by Raman spectroscopy along supersonic expansions of H2 provide the link between experimental and theoretical rotranslational state-to-state rate coefficients of H2 in the vibrational ground state. These rates are calculated in the close-scattering approach with the MOLSCAT code employing a recent ab initio H2-H2 potential. The calculated rates are assessed by means of a master equation describing the time evolution of the experimental rotational populations. The feasibility for obtaining the rates on the sole basis of the experiment is discussed. The dominant processes j(1)j(2)-->j'(1)j'(2) in the investigated thermal range are found to be 21-->01 >30-->12 >31-->11, proving the importance of double processes such as 30-->12. Good agreement is found between theory and experiment, as well as with earlier ultrasonic measurements of relaxation times. A spectral representation is proposed in order to visualize quantitatively the collisional contributions in any nonequilibrium time evolving process.
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Affiliation(s)
- S Montero
- Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid, Spain.
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Lee TG, Balakrishnan N, Forrey RC, Stancil PC, Schultz DR, Ferland GJ. State-to-state rotational transitions in H2+H2 collisions at low temperatures. J Chem Phys 2006; 125:114302. [PMID: 16999469 DOI: 10.1063/1.2338319] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
We present quantum mechanical close-coupling calculations of collisions between two hydrogen molecules over a wide range of energies, extending from the ultracold limit to the superthermal region. The two most recently published potential energy surfaces for the H(2)-H(2) complex, the so-called Diep-Johnson (DJ) [J. Chem. Phys. 112, 4465 (2000); 113, 3480 (2000)] and Boothroyd-Martin-Keogh-Peterson (BMKP) [J. Chem. Phys. 116, 666 (2002)] surfaces, are quantitatively evaluated and compared through the investigation of rotational transitions in H(2)+H(2) collisions within rigid rotor approximation. The BMKP surface is expected to be an improvement, approaching chemical accuracy, over all conformations of the potential energy surface compared to previous calculations of H(2)-H(2) interaction. We found significant differences in rotational excitation/deexcitation cross sections computed on the two surfaces in collisions between two para-H(2) molecules. The discrepancy persists over a large range of energies from the ultracold regime to thermal energies and occurs for several low-lying initial rotational levels. Good agreement is found with experiment B. Mate et al., [J. Chem. Phys. 122, 064313 (2005)] for the lowest rotational excitation process, but only with the use of the DJ potential. Rate coefficients computed with the BMKP potential are an order of magnitude smaller.
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Affiliation(s)
- Teck-Ghee Lee
- Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA.
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46
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Sultanov RA, Guster D. State resolved rotational excitation cross-sections and rates in H2+H2 collisions. Chem Phys 2006. [DOI: 10.1016/j.chemphys.2006.03.038] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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