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Wang R, Zhao H, Sun Z. Reactant-Product Decoupling Technique Using the Intermediate Coordinate Method. J Phys Chem A 2024; 128:3726-3741. [PMID: 38666315 DOI: 10.1021/acs.jpca.4c01148] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/12/2024]
Abstract
Although the reactant-product decoupling (RPD) technique was proposed over two decades ago, it remains an efficient approach for calculating product state-resolved information on some simple direct reactions using the quantum wave packet method. In the past, usually the RPD technique employed the collocation method to transform the wave function between reactant and product arrangements, which requires quite large computational efforts. In this work, the intermediate coordinate (IC) method is employed to realize the RPD technique. Numerical examples demonstrate that this new IC RPD (IRPD) technique has superior computational efficiency compared with the original method employing the collocation method. Especially, the new IRPD technique significantly saves disk space and computer memory. To illustrate the features of our new method, the total reaction probabilities of the H + H2, H + Br2, and F + H2 reactions with J = 0 and the differential cross sections of the H + H2 and F + H2 reactions at a series of collision energy are calculated and presented. With this efficient and effective new RPD technique, the Li + HF reaction, which involves sharp resonances with long-range wave functions in the van der Waals wells in both the reactant and product arrangements, is also calculated with several J at the product state-resolved level to reveal the ability of the RPD technique for describing resonance wave functions. With these numerical examples, it is found that, for the reaction with resonances, the RPD approach should be applied carefully. Otherwise, it is very possible that the resonances could disappear with the application of the RPD technique.
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Affiliation(s)
- Ransheng Wang
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Hailin Zhao
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China
| | - Zhigang Sun
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China
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2
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Jankunas J, Sneha M, Zare RN, Bouakline F, Althorpe SC. Disagreement between theory and experiment grows with increasing rotational excitation of HD(v′, j′) product for the H + D2 reaction. J Chem Phys 2013; 138:094310. [DOI: 10.1063/1.4793557] [Citation(s) in RCA: 12] [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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3
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Bouakline F, Althorpe SC, Larregaray P, Bonnet L. Strong geometric-phase effects in the hydrogen-exchange reaction at high collision energies: II. Quasiclassical trajectory analysis. Mol Phys 2010. [DOI: 10.1080/00268971003610218] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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4
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Li B, Chu TS, Han KL. Non-Born-Oppenheimer dynamics calculations using the coherent switching with decay of mixing method. J Comput Chem 2010; 31:362-70. [PMID: 19479734 DOI: 10.1002/jcc.21329] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
A theoretical investigation of the nonadiabatic processes that are involved in the full three-dimensional D+H(2), H+D(2), D(+)+H(2), and H(+)+D(2) reaction systems has been performed using the method of coherence switching with decay of mixing (CSDM) developed by Truhlar and coworkers. The electronic density matrix for each trajectory is fully coherent in the CSDM method, and a switching algorithm different to the original "decay of mixing" method is used to determine the pure state toward which the decoherent force drives the system. By solving the equations for the evolution of the electronic state populations along the semiclassical trajectory, the ensemble can present effective physical insight into nonadiabatic dynamics. The calculations for the D+H(2) and H+D(2) systems is based on the double many body expansion potential energy surface. The potential energy surface constructed by Kamisaka et al. is employed in the calculation of D(+)+H(2) and H(+)+D(2) reactions. The cross sections and the reaction probabilities for the total angular momentum J = 0 are calculated for all of these systems. The calculated results from the CSDM method are in good agreement with exact quantum mechanical calculations and experimental measurements.
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Affiliation(s)
- Bin Li
- State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China
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Chu TS, Han KL, Hankel M, Balint-Kurti GG, Kuppermann A, Abrol R. Nonadiabatic effects in the H+H2 exchange reaction: Accurate quantum dynamics calculations at a state-to-state level. J Chem Phys 2009; 130:144301. [DOI: 10.1063/1.3089724] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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6
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Bartlett NCM, Miller DJ, Zare RN, Sofikitis D, Peter Rakitzis T, Alexander AJ. Preparation of oriented and aligned H2 and HD by stimulated Raman pumping. J Chem Phys 2008; 129:084312. [DOI: 10.1063/1.2973628] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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7
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Althorpe SC, Juanes-Marcos JC, Wrede E. The Influence of the Geometric Phase on Reaction Dynamics. ADVANCES IN CHEMICAL PHYSICS 2008. [DOI: 10.1002/9780470259474.ch1] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/10/2023]
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8
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Bouakline F, Althorpe SC, Peláez Ruiz D. Strong geometric-phase effects in the hydrogen-exchange reaction at high collision energies. J Chem Phys 2008; 128:124322. [DOI: 10.1063/1.2897920] [Citation(s) in RCA: 71] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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9
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Monks PDD, Connor JNL, Althorpe SC. Nearside−Farside and Local Angular Momentum Analyses of Time-Independent Scattering Amplitudes for the H + D2 (vi = 0, ji = 0) → HD (vf = 3, jf = 0) + D Reaction. J Phys Chem A 2007; 111:10302-12. [DOI: 10.1021/jp073334k] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- P. D. D. Monks
- School of Chemistry, The University of Manchester, Manchester M13 9PL, England and Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, England
| | - J. N. L. Connor
- School of Chemistry, The University of Manchester, Manchester M13 9PL, England and Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, England
| | - S. C. Althorpe
- School of Chemistry, The University of Manchester, Manchester M13 9PL, England and Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, England
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10
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Koszinowski K, Goldberg NT, Zhang J, Zare RN, Bouakline F, Althorpe SC. Differential cross section for the H+D2→HD(v′=1,j′=2,6,10)+D reaction as a function of collision energy. J Chem Phys 2007; 127:124315. [PMID: 17902911 DOI: 10.1063/1.2771157] [Citation(s) in RCA: 23] [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 have measured differential cross sections (DCSs) for the HD (v(')=1,j(')=2,6,10) products of the H+D(2) exchange reaction at five different collision energies in the range 1.48< or =E(coll)< or =1.94 eV. The contribution from the less energetic H atoms formed upon spin-orbit excitation of Br in the photolysis of the HBr precursor is taken into account for two collision energies, E(coll)=1.84 and 1.94 eV, allowing us to disentangle the two different channels. The measured DCSs agree well with new time-dependent quantum-mechanical calculations. As the product rotational excitation increases, the DCSs shift from backward to sideward scattering, as expected. We also find that the shapes of the DCSs show only a small overall dependence on the collision energy, with a notable exception occurring for HD (v(')=1,j(')=2), which appears bimodal at high collision energies. We suggest that this feature results from both direct recoil and indirect scattering from the conical intersection.
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Affiliation(s)
- Konrad Koszinowski
- Department of Chemistry, Stanford University, Stanford, California 94305-5080, USA
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11
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Chu TS, Han KL, Hankel M, Balint-Kurti GG. Coriolis coupling effects in the calculation of state-to-state integral and differential cross sections for the H+D2 reaction. J Chem Phys 2007; 126:214303. [PMID: 17567192 DOI: 10.1063/1.2735624] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The quantum wavepacket parallel computational code DIFFREALWAVE is used to calculate state-to-state integral and differential cross sections for the title reaction on the BKMP2 surface in the total energy range of 0.4-1.2 eV with D2 initially in its ground vibrational-rotational state. The role of Coriolis couplings in the state-to-state quantum calculations is examined in detail. Comparison of the results from calculations including the full Coriolis coupling and those using the centrifugal sudden approximation demonstrates that both the energy dependence and the angular dependence of the calculated cross sections are extremely sensitive to the Coriolis coupling, thus emphasizing the importance of including it correctly in an accurate state-to-state calculation.
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Affiliation(s)
- Tian-Shu Chu
- State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China.
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12
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Jayachander Rao B, Padmanaban R, Mahapatra S. Nonadiabatic quantum wave packet dynamics of H+H2 (HD) reactions. Chem Phys 2007. [DOI: 10.1016/j.chemphys.2007.01.012] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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13
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Juanes-Marcos JC, Althorpe SC, Wrede E. Effect of the geometric phase on the dynamics of the hydrogen-exchange reaction. J Chem Phys 2007; 126:044317. [PMID: 17286480 DOI: 10.1063/1.2430708] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A recent puzzle in nonadiabatic quantum dynamics is that geometric phase (GP) effects are present in the state-to-state opacity functions of the hydrogen-exchange reaction, but cancel out in the state-to-state integral cross sections (ICSs). Here the authors explain this result by using topology to separate the scattering amplitudes into contributions from Feynman paths that loop in opposite senses around the conical intersection. The clockwise-looping paths pass over one transition state (1-TS) and scatter into positive deflection angles; the counterclockwise-looping paths pass over two transition states (2-TS) and scatter into negative deflection angles. The interference between the 1-TS and 2-TS paths thus integrates to a very small value, which cancels the GP effects in the ICS. Quasiclassical trajectory (QCT) calculations reproduce the scattering of the 1-TS and 2-TS paths into positive and negative deflection angles and show that the 2-TS paths describe a direct insertion mechanism. The inserting atom follows a highly constrained "S-bend" path, which allows it to avoid both the other atoms and the conical intersection and forces the product diatom to scatter into high rotational states. By contrast, the quantum 2-TS paths scatter into a mainly statistical distribution of rotational states, so that the quantum 2-TS total ICS is roughly twice the QCT ICS at 2.3 eV total energy. This suggests that the S-bend constraint is relaxed by tunneling in the quantum system. These findings on H+H(2) suggest that similar cancellations or reductions in GP effects are likely in many other reactions.
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Affiliation(s)
- Juan Carlos Juanes-Marcos
- Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, P.O. Box 9502, 2300 RA Leiden, The Netherlands
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14
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Hankel M, Smith SC, Allan RJ, Gray SK, Balint-Kurti GG. State-to-state reactive differential cross sections for the H+H2→H2+H reaction on five different potential energy surfaces employing a new quantum wavepacket computer code: DIFFREALWAVE. J Chem Phys 2006; 125:164303. [PMID: 17092069 DOI: 10.1063/1.2358350] [Citation(s) in RCA: 73] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
State-to-state differential cross sections have been calculated for the hydrogen exchange reaction, H+H2-->H2+H, using five different high quality potential energy surfaces with the objective of examining the sensitivity of these detailed cross sections to the underlying potential energy surfaces. The calculations were performed using a new parallel computer code, DIFFREALWAVE. The code is based on the real wavepacket approach of Gray and Balint-Kurti [J. Chem. Phys. 108, 950 (1998)]. The calculations are parallelized over the helicity quantum number Omega' (i.e., the quantum number for the body-fixed z component of the total angular momentum) and wavepackets for each J,Omega' set are assigned to different processors, similar in spirit to the Coriolis-coupled processors approach of Goldfield and Gray [Comput. Phys. Commun. 84, 1 (1996)]. Calculations for J=0-24 have been performed to obtain converged state-to-state differential cross sections in the energy range from 0.4 to 1.2 eV. The calculations employ five different potential energy surfaces, the BKMP2 surface and a hierarchical family of four new ab initio surfaces [S. L. Mielke, et al., J. Chem. Phys. 116, 4142 (2002)]. This family of four surfaces has been calculated using three different hierarchical sets of basis functions and also an extrapolation to the complete basis set limit, the so called CCI surface. The CCI surface is the most accurate surface for the H3 system reported to date. Our calculations of differential cross sections are the first to be reported for the A2, A3, A4, and CCI surfaces. They show that there are some small differences in the cross sections obtained from the five different surfaces, particularly at higher energies. The calculations also show that the BKMP2 performs well and gives cross sections in very good agreement with the results from the CCI surface, displaying only small divergences at higher energies.
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Affiliation(s)
- Marlies Hankel
- Centre for Computational Molecular Science, The University of Queensland, Queensland QLD 4072, Australia.
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15
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Monks PDD, Xiahou C, Connor JNL. Local angular momentum-local impact parameter analysis: derivation and properties of the fundamental identity, with applications to the F+H2, H+D2, and Cl+HCl chemical reactions. J Chem Phys 2006; 125:133504. [PMID: 17029487 DOI: 10.1063/1.2210480] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The technique of local angular momentum-local impact parameter (LAM-LIP) analysis has recently been shown to provide valuable dynamical information on the angular scattering of chemical reactions under semiclassical conditions. The LAM-LIP technique exploits a nearside-farside (NF) decomposition of the scattering amplitude, which is assumed to be a Legendre partial wave series. In this paper, we derive the "fundamental NF LAM identity," which relates the full LAM to the NF LAMs (there is a similar identity for the LIP case). Two derivations are presented. The first uses complex variable techniques, while the second exploits an analogy between the motion of the scattering amplitude in the Argand plane with changing angle and the classical mechanical motion of a particle in a plane with changing time. Alternative forms of the fundamental LAM-LIP identity are described, one of which gives rise to a CLAM-CLIP plot, where CLAM denotes (Cross section) x LAM and CLIP denotes (Cross section) x LIP. Applications of the NF LAM theory, together with CLAM plots, are reported for state-to-state transitions of the benchmark reactions F+H2-->FH+H, H+D2-->HD+D, and Cl+HCl-->ClH+Cl, using as input both numerical and parametrized scattering matrix elements. We use the fundamental LAM identity to explain the important empirical observation that a NF cross section analysis and a NF LAM analysis provide consistent (and complementary) information on the dynamics of chemical reactions.
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Affiliation(s)
- P D D Monks
- School of Chemistry, The University of Manchester, Manchester M13 9PL, England
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16
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Teslja A, Valentini JJ. State-to-state reaction dynamics: A selective review. J Chem Phys 2006; 125:132304. [PMID: 17029423 DOI: 10.1063/1.2354466] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A selective review of state-to-state reaction dynamics experiments is presented. The review focuses on three classes of reactions that exemplify the rich history and illustrate the current state of the art in such work. These three reactions are (1) the hydrogen exchange reaction, H+H2-->H2+H and its isotopomers; (2) the H+RH-->H2+R reactions, where RH is an alkane, beginning with H+CH4-->H2+CH3 and extending to much larger alkanes; and (3) the Cl+RH-->HCl+R reactions, principally Cl+CH4-->HCl+CH3. We describe the experiments, discuss their results, present comparisons with theory, and introduce heuristic models.
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Affiliation(s)
- Alexey Teslja
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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17
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Lu RF, Chu TS, Zhang Y, Han KL, Varandas AJC, Zhang JZH. Nonadiabatic effects in the H+D2 reaction. J Chem Phys 2006; 125:133108. [PMID: 17029434 DOI: 10.1063/1.2202826] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The state-to-state dynamics of the H+D2 reaction is studied by the reactant-product decoupling method using the double many-body expansion potential energy surface. Two approaches are compared: one uses only the lowest adiabatic sheet while the other employs both coupled diabatic sheets. Rotational distributions for the reaction H+D2 (upsilon = 0, j = 0)-->HD(upsilon' = 3, j')+D are obtained at eight different collision energies between 1.49 and 1.85 eV; no significant difference are found between the two approaches. Initial state-selected total reaction probabilities and integral cross sections are also given for energies ranging from 0.25 up to 2.0 eV with extremely small differences being observed between the two sets of results, thus showing that the nonadiabatic effects in the title reaction are negligible at least for small energies below 2.0 eV.
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Affiliation(s)
- Rui-Feng Lu
- State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China
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18
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Abstract
We demonstrate a two-color reduced-Doppler probe for ion imaging that, in many applications, offers advantages over conventional 2+1 resonance-enhanced multiphoton ionization detection. Using counterpropagating beams of two different colors, one of which is broadband 266 nm, we achieve convenient and sensitive D atom detection without the need for Doppler scanning. We demonstrate the approach using 224 nm photodissociation of DBr. This method improves the sensitivity and signal-to-noise ratio and presents advantages and opportunities for use in the other systems.
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Affiliation(s)
- Cunshun Huang
- Department of Chemistry, Wayne State University, Detroit, MI 48202, USA
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Althorpe SC. General explanation of geometric phase effects in reactive systems: Unwinding the nuclear wave function using simple topology. J Chem Phys 2006; 124:084105. [PMID: 16512706 DOI: 10.1063/1.2161220] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We describe a simple topological approach which was used recently to explain geometric phase (GP) effects in the hydrogen-exchange reaction [Juanes-Marcos et al., Science 309, 1227 (2005)]. The approach is general and applies to any reactive system in which the nuclear wave function encircles a conical intersection (CI) and is confined to one adiabatic surface. The only numerical work required is to add and subtract nuclear wave functions computed with normal and GP boundary conditions. This is equivalent to unwinding the nuclear wave function onto a double cover space, which separates out two components whose relative sign is changed by the GP. By referring to earlier work on the Aharanov-Bohm effect, we show that these two components contain all the Feynman paths that follow, respectively, an even and an odd number of loops around the CI. These two classes of path are essentially decoupled in the Feynman sum, because they belong to different homotopy classes (meaning that they cannot be continuously deformed into one another). Care must be taken in classifying the two types of path when the system can enter the encirclement region from several different start points. This applies to bimolecular reactions with identical reagents and products, for which our approach allows a symmetry argument developed by Mead [J. Chem. Phys. 72, 3839 (1980)] to be generalized from nonencircling to encircling systems. The approach can be extended in order to unwind the wave function completely onto a higher cover space, thus separating contributions from individual winding numbers. The scattering boundary conditions are ultimately what allow the wave function to be unwound from the CI, and hence a bound state wave function cannot be unwound. The GP therefore has a much stronger effect on the latter than on the wave function of a reactive system.
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Affiliation(s)
- Stuart C Althorpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
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20
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Monks PDD, Connor JNL, Althorpe SC. Theory of Time-Dependent Reactive Scattering: Cumulative Time-Evolving Differential Cross Sections and Nearside−Farside Analyses of Time-Dependent Scattering Amplitudes for the H + D2 → HD + D Reaction. J Phys Chem A 2005; 110:741-8. [PMID: 16405348 DOI: 10.1021/jp0556254] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Nearside-farside (NF) theory, originally developed in the energy domain for the time-independent description of molecular collisions and chemical reactions, is applied to the plane wave packet (PWP) formulation of time-dependent scattering. The NF theory decomposes the partial wave series representation for the time-dependent PWP scattering amplitude into two time-dependent subamplitudes: one N, the other F. In addition, NF local angular momentum (LAM) theory is applied to the PWP scattering amplitude. The novel concept of a cumulative time-evolving differential cross section is introduced, in which the upper infinite time limit of a half-Fourier transform is replaced by a finite time. In a similar way, a cumulative energy-evolving angular distribution is defined. Application is made to the state-to-state reaction, H + D2(v(i) = 0, j(i) = 0) --> HD(v(f) = 3, j(f) = 0) + D, where v(i), j(i) and v(f), j(f) are vibrational and rotational quantum numbers for the initial and final states, respectively. This reaction exhibits time-direct and time-delayed (by about 25 fs) collision mechanisms. It is shown that the direct-time mechanism is N dominant scattering, whereas the time-delayed mechanism exhibits characteristics of NF interference. The NF and LAM theories provide valuable insights into the time-dependent properties of a reaction, as do snapshots from a movie of the cumulative time-evolving differential cross section.
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Affiliation(s)
- P D D Monks
- School of Chemistry, The University of Manchester, Manchester M13 9PL, England
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21
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Pomerantz AE, Camden JP, Chiou AS, Ausfelder F, Chawla N, Hase WL, Zare RN. Reaction Products with Internal Energy beyond the Kinematic Limit Result from Trajectories Far from the Minimum Energy Path: An Example from H + HBr → H2 + Br. J Am Chem Soc 2005; 127:16368-9. [PMID: 16305203 DOI: 10.1021/ja055440a] [Citation(s) in RCA: 87] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The importance of reactive trajectories straying far from the minimum energy path is demonstrated for the bimolecular reaction H + HBr --> H2(v', j') + Br at 53 kcal/mol collision energy. Product quantum state distributions are measured and calculated using the quasi-classical trajectory technique, and the calculations indicate that highly internally excited H2 products result from indirect reactive trajectories with bent transition states. A general argument is made suggesting that reaction products with internal energy exceeding a kinematic constraint can, in general, be attributed to reactive collisions straying far from the minimum energy path.
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Affiliation(s)
- Andrew E Pomerantz
- Department of Chemistry, Stanford University, Stanford, California 94305-5080, USA
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Murray C, Pearce JK, Rudić S, Retail B, Orr-Ewing AJ. Stereodynamics of Chlorine Atom Reactions with Organic Molecules. J Phys Chem A 2005; 109:11093-102. [PMID: 16331891 DOI: 10.1021/jp054627l] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A series of recent experimental and computational studies has explored how the dynamics of hydrogen abstraction from organic molecules are affected by the presence of functional groups in the molecule and by basic structural motifs such as strained ring systems. Comparisons drawn between reactions of Cl atoms with alkanes such as ethane, Cl + CH3CH3--> HCl + CH3CH2, which serve as benchmark systems, and with functionalized molecules such as alcohols, amines, and alkyl halides, Cl + CH3X --> HCl + CH2X (X = OH, NH2, halogen, etc.) expose a wealth of mechanistic detail. Although the scattering dynamics, as revealed from measured angular distributions of the velocities of the HCl with quantum-state resolution, show many similarities, much-enhanced rotational excitation of the HCl products is observed from reactions of the functionalized molecules. The degree of rotational excitation of the HCl correlates with the dipole moment of the CH2X radical and is thus attributed, at least in part, to post-transition-state dipole-dipole interactions between the separating, polar reaction products. This interpretation is supported by direct dynamics trajectories computed on-the-fly, and the HCl rotation is thus argued to serve as an in situ probe of the angular anisotropy of the reaction potential energy surface in the post-transition-state region. Comparisons between the dynamics of reactions of dimethyl ether and the three- and four-membered-ring compounds oxirane (c-C2H4O) and oxetane (c-C3H6O) raise questions about the role of reorientation of the reaction products on a time scale commensurate with their separation. The shapes and structures of polyatomic molecules are thus demonstrated to have important consequences for the stereodynamics of these direct abstraction reactions.
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Affiliation(s)
- Craig Murray
- School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, UK
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Shuman NS, Mihok M, Fistik M, Valentini JJ. Quasiclassical trajectory calculations to evaluate a kinematic constraint on internal energy in suprathreshold collision energy abstraction reactions. J Chem Phys 2005; 123:074312. [PMID: 16229575 DOI: 10.1063/1.1990122] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Experimentally observed product quantum state distributions across a wide range of abstraction reactions at suprathreshold collision energies have shown a strong bias against product internal energy. Only a fraction, sometimes quite a small fraction, of the energetically accessible product quantum states are populated. Picconatto et al. [J. Chem. Phys. 114, 1663 (2001)] noted a simple mathematical relationship between the highest-energy rovibrational states observed and the kinematics of the reaction system. They proposed a reaction model based on reaction kinematics that quantitatively explains this behavior. The model is in excellent agreement with measured quantum state distributions. The assumptions of the model invoke detailed characteristics of reactive trajectories at suprathreshold collision energies. Here we test those assumptions using quasiclassical trajectory calculations for the abstraction reactions H+HCl-->H2+Cl, D+HCl-->HD+Cl, and H+DCl-->HD+Cl. Trajectories were run on a potential-energy surface calculated with a London-Eyring-Polyani-Sato function with a localized 3-center term (LEPS-3C) previously shown to accurately reproduce experimentally observed product state distributions for the H+HCl abstraction reaction. The trajectories sample collision energies near threshold and also substantially above it. Although the trajectories demonstrate some aspects of the model, they show that it is not valid. However, the inadequacy of the proposed model does not invalidate the apparent kinematic basis of the observed energy constraint. The present results show that there must be some other molecular behavior rooted in the reaction kinematics that is the explanation and the source of the constraint.
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Affiliation(s)
- Nicholas S Shuman
- Department of Chemistry, Columbia University, New York, New York 10027, USA
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Aquilanti V, Cavalli S, De Fazio D, Simoni A, Tscherbul TV. Direct evaluation of the lifetime matrix by the hyperquantization algorithm: Narrow resonances in the F+H2 reaction dynamics and their splitting for nonzero angular momentum. J Chem Phys 2005; 123:054314. [PMID: 16108646 DOI: 10.1063/1.1988311] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose a new method for the direct and efficient evaluation of the Felix Smith's lifetime Q matrix for reactive scattering problems. Simultaneous propagation of the solution to a set of close-coupled equations together with its energy derivative allows one to avoid common problems pertinent to the finite-difference approach. The procedure is implemented on a reactive scattering code which employs the hyperquantization algorithm and the Johnson-Manolopoulos [J. Comput. Phys. 13, 455 (1973); J. Chem. Phys 85, 6425 (1986)] propagation to obtain the complete S matrix and scattering observables. As an application of the developed formalism, we focus on the total angular momentum dependence of narrow under-barrier resonances supported by van der Waals wells of the title reaction. Using our method, we fully characterize these metastable states obtaining their positions and lifetimes from Lorentzian fits to the largest eigenvalue of the lifetime matrix. Remarkable splittings of the resonances observed at J>0 are rationalized in terms of a hyperspherical model. In order to provide an insight on the decay mechanism, the Q-matrix eigenvectors are analyzed and the dominant channels populated during the decomposition of metastable states are determined. Possible relevance of the present results to reactive scattering experiments is discussed.
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Koszinowski K, Goldberg NT, Pomerantz AE, Zare RN, Juanes-Marcos JC, Althorpe SC. Collision-energy dependence of HD(ν′=1,j′) product rotational distributions for the H+D2 reaction. J Chem Phys 2005; 123:054306. [PMID: 16108638 DOI: 10.1063/1.1978871] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Product rotational distributions for the reaction H + D2 --> HD(nu'=1,j') + D have been measured for 16 collision energies in the range of 1.43 < or = E(coll) < or = 2.55 eV. Time-dependent quantum-mechanical calculations agree well in general with the experimental results, but they consistently yield slightly colder distributions. In terms of the average energy channeled into rotation, the differences between experiment and theory amount to approximately 10% for all collision energies sampled. No peculiarity is found for E(coll)=2.55 eV at which the system has sufficient energy to access the first HD2 electronically excited state.
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Affiliation(s)
- Konrad Koszinowski
- Department of Chemistry, Stanford University, Stanford, California 94305-5080, USA
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Juanes-Marcos JC, Althorpe SC. Geometric phase effects in the H+H2 reaction: Quantum wave-packet calculations of integral and differential cross sections. J Chem Phys 2005; 122:204324. [PMID: 15945741 DOI: 10.1063/1.1924411] [Citation(s) in RCA: 69] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report quantum wave-packet calculations on the H+H(2) reaction, aimed at resolving the controversy over whether geometric phase (GP) effects can be observed in this reaction. Two sets of calculations are reported of the state-to-state reaction probabilities, and integral and differential cross sections (ICSs and DCSs). One set includes the GP using the vector potential approach of Mead and Truhlar; the other set neglects the phase. We obtain unequivocal agreement with recent results of Kendrick [J. Phys. Chem. A 107, 6739 (2003)], predicting GP effects in the state-to-state reaction probabilities, which cancel exactly on summing the partial waves to yield the ICS. Our results therefore contradict those of Kuppermann and Wu [Chem. Phys. Lett. 349 537 (2001)], which predicted pronounced GP effects in the cross sections. We also agree with Kendrick in predicting that there are no significant GP effects in the full DCS at energies below 1.8 eV, and in the partial (0<or=J<or=10) DCS at energies above this. However, we find that in the full DCS above 1.8 eV (which was not reported by Kendrick), there are GP effects, which may be experimentally measurable.
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Aoiz * FJ, BaÑares L, Herrero VJ. The H+H2reactive system. Progress in the study of the dynamics of the simplest reaction. INT REV PHYS CHEM 2005. [DOI: 10.1080/01442350500195659] [Citation(s) in RCA: 92] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Pomerantz AE, Ausfelder F, Zare RN, Juanes-Marcos JC, Althorpe SC, Sáez Rábanos V, Aoiz FJ, Bañares L, Castillo JF. Rovibrational product state distribution for inelastic H+D2 collisions. J Chem Phys 2004; 121:6587-90. [PMID: 15473712 DOI: 10.1063/1.1804940] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Experimental measurements of rovibrational product state distributions for the inelastic scattering process H + D2(nu=0,j)-->H + D2(nu' = 1,2,j') are presented and compared with the results of quasiclassical and quantum mechanical calculations. Agreement between theory and experiment is almost quantitative. Two subtle trends are found: the relative amount of energy in product rotational excitation decreases slightly with increasing collision energy and increases slightly with increasing product vibrational excitation. These trends are the reverse of what has been found for reactive scattering in which the opposite trends are much more pronounced.
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Affiliation(s)
- Andrew E Pomerantz
- Department of Chemistry, Stanford University, Stanford, California 94305-5080, USA
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Murray C, Orr-Ewing * AJ. The dynamics of chlorine-atom reactions with polyatomic organic molecules. INT REV PHYS CHEM 2004. [DOI: 10.1080/01442350412331329166] [Citation(s) in RCA: 77] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Pomerantz AE, Ausfelder F, Zare RN, Huo WM. Line strength factors for E,F1Σ+g(v′ = 0, J′ = J′′) X1Σ+g (v′′, J′′) (2 + 1) REMPI transitions in molecular hydrogen. CAN J CHEM 2004. [DOI: 10.1139/v04-074] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Experimentally and theoretically determined line strengths are presented for E,F1Σ+g(v′ = 0, J′ = J′′) X1Σ+g (v′′, J′′) (2 + 1) REMPI transitions in H2, HD, and D2. The experimental technique employs a hot filament source of internally excited hydrogen that allows experimental determination of line strengths for the low rotational states of highly excited vibrational manifolds (v′′ ≤ 4). The line strengths are found to depend only weakly on J′′ for the states measured here, and theoretical results indicate that the line strengths depend strongly on v′′. These values are combined with previously measured and calculated line strengths for these transitions (K.-D. Rinnen, M.A. Buntine, D.A.V. Kliner, R.N. Zare, and W.M. Huo. J. Chem. Phys. 95, 214 (1991)), resulting in a more complete compilation of REMPI line strengths for molecular hydrogen. Key words: hydrogen, spectroscopy, REMPI, line strength, multiphoton.
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