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Loreau J, van der Avoird A. Vibrational energy transfer in ammonia-helium collisions. Faraday Discuss 2024; 251:249-261. [PMID: 38787637 DOI: 10.1039/d3fd00180f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/26/2024]
Abstract
While the rotational energy transfer of ammonia by rare gas atoms and hydrogen molecules has been the focus of many studies, little is known about its vibrational relaxation, even though transitions involving the umbrella bending mode have been observed in many astrophysical environments. Here we explore the vibrational relaxation of the umbrella mode of ammonia induced by collisions with helium atoms by means of the close-coupling method on an ab initio potential energy surface. We compute cross sections up to kinetic energies of 1500 cm-1 and rate coefficients up to a temperature of 300 K for vibrational, rotational, and inversion transitions involving the lowest two vibrational states. We show that vibrational relaxation is much less efficient than rotation-inversion relaxation, although the rate coefficients for vibrational relaxation strongly increase with the temperature. We also observe important differences for vibrationally-elastic transitions within the lowest two vibrational states, i.e., for rotation-inversion transitions. These are a direct consequence of the difference in the tunnelling splitting of the lowest inversion levels.
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Affiliation(s)
- Jérôme Loreau
- KU Leuven, Department of Chemistry, B-3001 Leuven, Belgium.
| | - Ad van der Avoird
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
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2
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Leng JG, Sharples TR, Fournier M, McKendrick KG, Craciunescu L, Paterson MJ, Costen ML. Inelastic scattering of NO(A 2Σ +) + CO 2: rotation-rotation pair-correlated differential cross sections. Faraday Discuss 2024; 251:279-295. [PMID: 38757419 DOI: 10.1039/d3fd00162h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/18/2024]
Abstract
A crossed beam velocity-map ion-imaging apparatus has been used to determine differential cross sections (DCSs) for the rotationally inelastic scattering of NO(A2Σ+, v = 0, j = 0.5) with CO2, as a function of both NO(A, v = 0, N') final state and the coincident final rotational energy of the CO2. The DCSs are dominated by forward-peaked scattering for all N', with significant rotational excitation of CO2, and a small backward scattered peak is also observed for all final N'. However, no rotational rainbow scattering is observed and there is no evidence for significant product rotational angular momentum polarization. New ab initio potential energy surface calculations at the PNO-CCSD(T)-F12b level of theory report strong attractive forces at long ranges with significant anisotropy relative to both NO and CO2. The absence of rotational rainbow scattering is consistent with removal of low-impact-parameter collisions via electronic quenching, in agreement with the literature quenching rates of NO(A) by CO2 and recent electronic structure calculations. We propose that high-impact-parameter collisions, that do not lead to quenching, experience strong anisotropic attractive forces that lead to significant rotational excitation in both NO and CO2, depolarizing product angular momentum while leading to forward and backward glory scattering.
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Affiliation(s)
- Joseph G Leng
- Institute of Chemical Sciences, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK.
| | - Thomas R Sharples
- Institute of Chemical Sciences, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK.
| | - Martin Fournier
- Institute of Chemical Sciences, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK.
| | - Kenneth G McKendrick
- Institute of Chemical Sciences, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK.
| | - Luca Craciunescu
- Institute of Chemical Sciences, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK.
| | - Martin J Paterson
- Institute of Chemical Sciences, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK.
| | - Matthew L Costen
- Institute of Chemical Sciences, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK.
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3
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Sun ZF, Scheidsbach RJA, van Hemert MC, van der Avoird A, Suits AG, Parker DH. Imaging rotational energy transfer: comparative stereodynamics in CO + N 2 and CO + CO inelastic scattering. Phys Chem Chem Phys 2023. [PMID: 37377093 DOI: 10.1039/d3cp02229c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/29/2023]
Abstract
State-to-state rotational energy transfer in collisions of ground ro-vibrational state 13CO molecules with N2 molecules has been studied using the crossed molecular beam method under kinematically equivalent conditions used for 13CO + CO rotationally inelastic scattering described in a previously published report (Sun et al., Science, 2020, 369, 307-309). The collisionally excited 13CO molecule products are detected by the same (1 + 1' + 1'') VUV (Vacuum Ultra-Violet) resonance enhanced multiphoton ionization scheme coupled with velocity map ion imaging. We present differential cross sections and scattering angle resolved rotational angular momentum alignment moments extracted from experimentally measured 13CO + N2 scattering images and compare them with theoretical predictions from quasi-classical trajectories (QCT) on a newly calculated 13CO-N2 potential energy surface (PES). Good agreement between experiment and theory is found, which confirms the accuracy of the 13CO-N2 potential energy surface for the 1460 cm-1 collision energy studied by experiment. Experimental results for 13CO + N2 are compared with those for 13CO + CO collisions. The angle-resolved product rotational angular momentum alignment moments for the two scattering systems are very similar, which indicates that the collision induced alignment dynamics observed for both systems are dominated by a hard-shell nature. However, compared to the 13CO + CO measurements, the primary rainbow maximum in the DCSs for 13CO + N2 is peaked consistently at more backward scattering angles and the secondary maximum becomes much less obvious, implying that the 13CO-N2 PES is less anisotropic. In addition, a forward scattering component with high rotational excitation seen for 13CO + CO does not appear for 13CO-N2 in the experiment and is not predicted by QCT theory. Some of these differences in collision dynamics behaviour can be predicted by a comparison between the properties of the PESs for the two systems. More specific behaviour is also predicted from analysis of the dependence on the relative collision geometry of 13CO + N2 trajectories compared to 13CO + CO trajectories, which shows the special 'do-si-do' pathway invoked for 13CO + CO is not effective for 13CO + N2 collisions.
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Affiliation(s)
- Zhong-Fa Sun
- Anhui Province Key Laboratory of Optoelectric Materials Science and Technology, Department of Physics, Anhui Normal University, Wuhu, Anhui 241000, China.
| | - Roy J A Scheidsbach
- Department of Molecular and Laser Physics, Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands.
| | - Marc C van Hemert
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, Einsteinweg 55, 2333 CC Leiden, The Netherlands
| | - Ad van der Avoird
- Theoretical Chemistry, Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
| | - Arthur G Suits
- Department of Chemistry, University of Missouri, Columbia, MO 65211, USA
| | - David H Parker
- Anhui Province Key Laboratory of Optoelectric Materials Science and Technology, Department of Physics, Anhui Normal University, Wuhu, Anhui 241000, China.
- Department of Molecular and Laser Physics, Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands.
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4
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Wang XD, Robertson PA, Cascarini FJJ, Quinn MS, McManus JW, Orr-Ewing AJ. Observation of Rainbows in the Rotationally Inelastic Scattering of NO with CH 4. J Phys Chem A 2019; 123:7758-7767. [PMID: 31442046 DOI: 10.1021/acs.jpca.9b06806] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Using a combination of velocity-map imaging and resonance-enhanced multiphoton ionization detection with crossed molecular beam scattering, the dynamics of rotational energy transfer have been examined for NO in collisions with CH4 at a mean collision energy of 700 cm-1. The images of NO scattered into individual rotational (jNO') and spin-orbit (Ω) levels typically exhibit a single broad maximum that gradually shifts from the forward to the backward scattering direction with increasing rotational excitation (i.e., larger ΔjNO). The rotational rainbow angles calculated with a two-dimensional hard ellipse model show reasonable agreement with the observed angles corresponding to the maxima in the differential cross sections extracted from the images for higher ΔjNO transitions, but there are clear discrepancies for lower ΔjNO (in particular, final rotational levels with jNO' = 7.5 and 8.5). The sharply forward scattered angular distributions for these lower ΔjNO transitions better agree with the predictions of an L-type rainbow model. The more highly rotationally excited NO appears to coincide with low rotational excitation of the co-product CH4, indicating a degree of rotational product-pair anticorrelation in this bimolecular scattering.
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Affiliation(s)
- Xu-Dong Wang
- School of Chemistry , University of Bristol , Cantock's Close , Bristol , BS8 1TS , United Kingdom
| | - Patrick A Robertson
- School of Chemistry , University of Bristol , Cantock's Close , Bristol , BS8 1TS , United Kingdom
| | - Frederick J J Cascarini
- School of Chemistry , University of Bristol , Cantock's Close , Bristol , BS8 1TS , United Kingdom
| | - Mitchell S Quinn
- School of Chemistry , University of Bristol , Cantock's Close , Bristol , BS8 1TS , United Kingdom
| | - Joseph W McManus
- School of Chemistry , University of Bristol , Cantock's Close , Bristol , BS8 1TS , United Kingdom
| | - Andrew J Orr-Ewing
- School of Chemistry , University of Bristol , Cantock's Close , Bristol , BS8 1TS , United Kingdom
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5
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Gao Z, Loreau J, van der Avoird A, van de Meerakker SYT. Direct observation of product-pair correlations in rotationally inelastic collisions of ND 3 with D 2. Phys Chem Chem Phys 2019; 21:14033-14041. [PMID: 30649107 DOI: 10.1039/c8cp07109h] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present a combined experimental and theoretical study of state-to-state inelastic scattering of ND3(j = 11-) with D2 (j = 0, 1, 2, 3) molecules at collision energies around 800 cm-1. Using a crossed molecular beam apparatus which employs the combination of Stark deceleration and velocity map imaging, we observe the correlated rotational excitations of both collision partners. For D2, both elastic (ΔjD2 = 0), inelastic excitation (j = 0 →j = 2) and inelastic de-excitation (j = 2 →j = 0) processes are observed. For a number of final ND3 states, inelastic channels in which D2 is rotationally excited or de-excited appear surprisingly strong. The experimental results are in excellent agreement with the predictions from quantum scattering calculations which are based on an ab initio ND3-D2 potential energy surface.
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Affiliation(s)
- Zhi Gao
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands.
| | - Jérôme Loreau
- Service de Chimie Quantique et Photophysique, Université libre de Bruxelles, CP 160/09, 1050 Brussels, Belgium.
| | - Ad van der Avoird
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands.
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Gao Z, Karman T, Tang G, van der Avoird A, Groenenboom GC, van de Meerakker SYT. Correlated energy transfer in rotationally and spin-orbit inelastic collisions of NO(X 2Π 1/2, j = 1/2f) with O 2(X 3Σ g-). Phys Chem Chem Phys 2018; 20:12444-12453. [PMID: 29697730 DOI: 10.1039/c8cp01784k] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present a combined experimental and theoretical study of state-to-state inelastic scattering of NO(X2Π1/2, j = 1/2f) with O2(X3Σg-) molecules at a collision energy of 480 cm-1, focusing in particular on the observation and interpretation of correlated excitations in both NO and O2. Various final states of the NO radical, in both spin-orbit manifolds, were measured with high resolution using a crossed molecular beam apparatus which employs a combination of Stark deceleration and velocity map imaging. Velocity map imaging directly measures both the angular distribution and the radial velocity distribution of the scattered NO molecules, which probes the kinetic energy uptake or release and hence correlated excitations of NO-O2 pairs. Simultaneous excitations of NO and O2 were resolved for all studied final states of NO. In all cases, the experimental results excellently agree with the results of simulations based on quantum scattering calculations. Trends are discussed by analyzing the scattering wave functions from the calculations.
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Affiliation(s)
- Zhi Gao
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands.
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7
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Gao Z, Karman T, Vogels SN, Besemer M, van der Avoird A, Groenenboom GC, van de Meerakker SYT. Observation of correlated excitations in bimolecular collisions. Nat Chem 2018; 10:469-473. [DOI: 10.1038/s41557-018-0004-0] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2017] [Accepted: 12/20/2017] [Indexed: 11/09/2022]
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Luxford TFM, Sharples TR, McKendrick KG, Costen ML. Pair-correlated stereodynamics for diatom-diatom rotational energy transfer: NO(A2Σ+) + N2. J Chem Phys 2017; 147:013912. [DOI: 10.1063/1.4979487] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Thomas F. M. Luxford
- Institute of Chemical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - Thomas R. Sharples
- Institute of Chemical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - Kenneth G. McKendrick
- Institute of Chemical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - Matthew. L. Costen
- Institute of Chemical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
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10
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Luxford TFM, Sharples TR, McKendrick KG, Costen ML. Experimental testing of ab initio potential energy surfaces: Stereodynamics of NO(A 2Σ +) + Ne inelastic scattering at multiple collision energies. J Chem Phys 2016; 145:174304. [PMID: 27825214 DOI: 10.1063/1.4966688] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a crossed molecular beam velocity-map ion imaging study of state-to-state rotational energy transfer of NO(A2Σ+, v = 0, N = 0, j = 0.5) in collisions with Ne atoms. From these measurements, we report differential cross sections and angle-resolved rotational angular momentum alignment moments for product states N' = 3 and 5-10 for collisions at an average energy of 523 cm-1, and N' = 3 and 5-14 for collisions at an average energy of 1309 cm-1, respectively. The experimental results are compared to the results of close-coupled quantum scattering calculations on two literature ab initio potential energy surfaces (PESs) [Pajón-Suárez et al., Chem. Phys. Lett. 429, 389 (2006) and Cybulski and Fernández, J. Phys. Chem. A 116, 7319 (2012)]. The differential cross sections from both experiment and theory show clear rotational rainbow structures at both collision energies, and comparison of the angles observed for the rainbow peaks leads to the conclusion that Cybulski and Fernández PES better represents the NO(A2Σ+)-Ne interaction at the collision energies used here. Sharp, forward scattered (<10°), peaks are observed in the experimental differential cross sections for a wide range of N' at both collision energies, which are not reproduced by theory on either PES. We identify these as L-type rainbows, characteristic of attractive interactions, and consistent with a shallow well in the collinear Ne-N-O geometry, similar to that calculated for the NO(A2Σ+)-Ar surface [Kłos et al., J. Chem. Phys. 129, 244303 (2008)], but absent from both of the NO(A2Σ+)-Ne surfaces tested here. The angle-resolved alignment moments calculated by quantum scattering theory are generally in good agreement with the experimental results, but both experiment and quantum scattering theories are dramatically different to the predictions of a classical rigid-shell, kinematic-apse conservation model. Strong oscillations are resolved in the experimental alignment moments as a function of scattering angle, confirming and extending the preliminary report of this behavior [Steill et al., J. Phys. Chem. A 117, 8163 (2013)]. These oscillations are correlated with structure in the differential cross section, suggesting an interference effect is responsible for their appearance.
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Affiliation(s)
- Thomas F M Luxford
- Institute of Chemical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - Thomas R Sharples
- Institute of Chemical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - Kenneth G McKendrick
- Institute of Chemical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - Matthew L Costen
- Institute of Chemical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
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11
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Luxford TFM, Sharples TR, Townsend D, McKendrick KG, Costen ML. Comparative stereodynamics in molecule-atom and molecule-molecule rotational energy transfer: NO(A(2)Σ(+)) + He and D2. J Chem Phys 2016; 145:084312. [PMID: 27586927 DOI: 10.1063/1.4961258] [Citation(s) in RCA: 11] [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 crossed molecular beam scattering study, using velocity-map ion-imaging detection, of state-to-state rotational energy transfer for NO(A(2)Σ(+)) in collisions with the kinematically identical colliders He and D2. We report differential cross sections and angle-resolved rotational angular momentum polarization moments for transfer of NO(A, v = 0, N = 0, j = 0.5) to NO(A, v = 0, N' = 3, 5-12) in collisions with He and D2 at respective average collision energies of 670 cm(-1) and 663 cm(-1). Quantum scattering calculations on a literature ab initio potential energy surface for NO(A)-He [J. Kłos et al., J. Chem. Phys. 129, 244303 (2008)] yield near-quantitative agreement with the experimental differential scattering cross sections and good agreement with the rotational polarization moments. This confirms that the Kłos et al. potential is accurate within the experimental collisional energy range. Comparison of the experimental results for NO(A) + D2 and He collisions provides information on the hitherto unknown NO(A)-D2 potential energy surface. The similarities in the measured scattering dynamics of NO(A) imply that the general form of the NO(A)-D2 potential must be similar to that calculated for NO(A)-He. A consistent trend for the rotational rainbow maximum in the differential cross sections for NO(A) + D2 to peak at more forward angles than those for NO(A) + He is consistent with the NO(A)-D2 potential being more anisotropic with respect to NO(A) orientation. No evidence is found in the experimental measurements for coincident rotational excitation of the D2, consistent with the potential having low anisotropy with respect to D2. The NO(A) + He polarization moments deviate systematically from the predictions of a hard-shell, kinematic-apse scattering model, with larger deviations as N' increases, which we attribute to the shallow gradient of the anisotropic repulsive NO(A)-He potential energy surface.
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Affiliation(s)
- Thomas F M Luxford
- Institute of Chemical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - Thomas R Sharples
- Institute of Chemical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - Dave Townsend
- Institute of Chemical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - Kenneth G McKendrick
- Institute of Chemical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - Matthew L Costen
- Institute of Chemical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
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Song L, Groenenboom GC, van der Avoird A, Bishwakarma CK, Sarma G, Parker DH, Suits AG. Inelastic Scattering of CO with He: Polarization Dependent Differential State-to-State Cross Sections. J Phys Chem A 2015; 119:12526-37. [PMID: 26473516 DOI: 10.1021/acs.jpca.5b08472] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A joint theoretical and experimental study of state-to-state rotationally inelastic polarization dependent differential cross sections (PDDCSs) for CO (v = 0, j = 0, 1, 2) molecules colliding with helium is reported for collision energies of 513 and 840 cm(-1). In a crossed molecular beam experiment, velocity map imaging (VMI) with state-selective detection by (2 + 1) and (1 + 1') resonance enhanced multiphoton ionization (REMPI) is used to probe rotational excitation of CO due to scattering. By taking account of the known fractions of the j = 0, 1, and 2 states of CO in the rotationally cold molecular beam (Trot ≈ 3 K), close-coupling theory based on high-quality ab initio potential energy surfaces for the CO-He interaction is used to simulate the differential cross sections for the mixed initial states. With polarization-sensitive 1 + 1' REMPI detection and a direct analysis procedure described by Suits et al. ( J. Phys, Chem. A 2015 , 119 , 5925 ), alignment moments are extracted from the images and the latter are compared with images simulated by theory using the calculated DCS and alignment moments. In general, good agreement of theory with the experimental results is found, indicating the reliability of the experiment in reproducing state-to-state differential and polarization-dependent differential cross sections.
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Affiliation(s)
| | | | | | | | | | | | - Arthur G Suits
- Department of Chemistry, Wayne State University , Detroit, Michigan 48202, United States
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13
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Loreau J, van der Avoird A. Scattering of NH3 and ND3 with rare gas atoms at low collision energy. J Chem Phys 2015; 143:184303. [DOI: 10.1063/1.4935259] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- J. Loreau
- Service de Chimie Quantique et Photophysique, Université Libre de Bruxelles (ULB) CP 160/09, 50 av. F.D. Roosevelt, 1050 Brussels, Belgium
| | - A. van der Avoird
- Theoretical Chemistry, Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
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van der Avoird A, Loreau J, Alexander MH, van de Meerakker SYT, Dagdigian PJ. Resonances in rotationally inelastic scattering of NH3 and ND3 with H2. J Chem Phys 2015; 143:044312. [PMID: 26233134 DOI: 10.1063/1.4927074] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ad van der Avoird
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
| | - Jérôme Loreau
- Service de Chimie Quantique et Photophysique C. P. 160/09, Université Libre de Bruxelles (ULB), 50 Ave. F. D. Roosevelt, 1050 Brussels, Belgium
| | - Millard H. Alexander
- Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742-2021, USA
| | | | - Paul J. Dagdigian
- Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218-2685, USA
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