Computer Software for Understanding Resonances and Resonance-Related Phenomena in Chemical Reactions

Sokolovski, D.; Akhmatskaya, Elena

doi:10.1007/978-3-319-09144-0_36

Cited by 3 publications

(3 citation statements)

References 25 publications

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“…The QP decomposition is an exact decomposition of the PW S matrix . The P(ole) part of the decomposition consists of a PW sum of Regge poles obtained from a Padé reconstruction , together with a rapidly oscillating quadratic phase. ,− A Padé reconstruction derives a Padé interpolant, denoted S̃ ( J ), in a region of the CAM plane surrounding the Re J axis, starting from the discrete values, J = 0, 1, 2, .... The Q part of the decomposition is then constructed exactly by subtracting the rapidly oscillating phase and the PW Regge pole sum from the input PW S matrix.…”

Section: Qp Decomposition Of the Partial Wave S Matrixmentioning

confidence: 99%

“…The P(ole) term S̃ J (P) is obtained from a Padé reconstruction − of the S matrix, but note we only use it for J = 0, 1, 2, ..., J max + 1 in this section and section . The set { J n } for n = 0, 1, 2, ..., n max contains the Regge pole positions, which are located in the first quadrant of the CAM plane; the { ã n } are called the partial residues of the poles and are related to the full residues , r̃ n by We recall the physical meaning of J n and r̃ n . ,, The real part of J n approximately determines the radius of the reaction zone by, Re J n ≈ kR .…”

Section: Qp Decomposition Of the Partial Wave S Matrixmentioning

confidence: 99%

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State-to-State F + H₂ Reaction at E_trans = 0.04088 eV: QP Decomposition, Parametrized S Matrix Incorporating Regge Poles, and Uniform Asymptotic Complex Angular Momentum Analysis of the Angular Scattering

Xiao

Connor

2016

J. Phys. Chem. A

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We report two new contributions for understanding the quantum dynamics of the benchmark state-to-state reaction, F + H2(vi, ji, mi) → FH(vf, jf, mf) + H, where (vi, ji, mi) and (vf, jf, mf) are the initial and final vibrational, rotational, and helicity quantum numbers, respectively. We analyze product differential cross sections (DCSs) for the transitions, 000 → 300, 000 → 310, and 000 → 320, at a translational energy of 0.04088 eV using the potential energy surface of Fu-Xu-Zhang. The two new contributions are as follows: (1) We exploit the recently introduced QP decomposition of J. N. L. Connor [ J. Chem. Phys . 2013 , 138 , 124310 ] to transform numerical partial-wave scattering (S) matrix elements for the three transitions into parametrized (analytic) formulas, in which all terms in the three parametrized S matrices have a direct physical interpretation. In particular, they contain the positions and residues of Regge poles in the first quadrant of the complex angular momentum (CAM) plane. We obtain very close agreement between the values of the parametrized and numerical S matrix elements. (2) We then apply a uniform asymptotic Watson/CAM theory, which allows a Regge pole to be close to a saddle point. It uses the parametrized S matrices and is applied to the partial wave series (PWS) representation for the scattering amplitude to understand structure in a DCS in terms of three contributing subamplitudes. We prove using this powerful CAM theory that resonance Regge poles contribute to the small-angle scattering in the DCSs for all three transitions, with the oscillations at larger angles arising from nearside-farside interference. We obtain very good agreement between the uniform asymptotic Watson/CAM DCSs and the corresponding PWS DCSs, except for angles close to the forward and backward directions, where (as expected) the Watson/CAM formulas become nonuniform.

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Section: Qp Decomposition Of the Partial Wave S Matrixmentioning

confidence: 99%

Section: Qp Decomposition Of the Partial Wave S Matrixmentioning

confidence: 99%

State-to-State F + H₂ Reaction at E_trans = 0.04088 eV: QP Decomposition, Parametrized S Matrix Incorporating Regge Poles, and Uniform Asymptotic Complex Angular Momentum Analysis of the Angular Scattering

Xiao

Connor

2016

J. Phys. Chem. A

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“…All of the quantities in the P(ole) term S̃ J (P) are obtained from a Padé reconstruction ,− of the S matrix, but note we only use it for J = 0,1,2,... J max in this paper. The set { J n } for n = 0,1,2,..., n max contains the Regge pole positions , which are located in the first quadrant of the complex angular momentum (CAM) plane; the { a ̃ n } are called the partial residues of the poles.…”

Section: Qp Decomposition Of the Partial Wave S Matrix And Scattering...mentioning

confidence: 99%

Application of the Partial Wave QP Decomposition to the Angular Scattering of the State-to-State F + H₂ Reaction at E_trans = 0.04088 eV

Xiahou¹,

Xiao

Connor

2019

J. Phys. Chem. A

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We analyze the physical content of structures present in the product differential cross sections (DCSs) of the benchmark F + H 2 (v i , j i , m i ) → FH(v f , j f , m f ) + H reaction, where v, j, and m are the vibrational, rotational, and helicity quantum numbers, respectively, for the initial and final states. We analyze three state-to-state transitions: 000 → 300, 000 → 310, and 000 → 320. Accurate quantum S matrix elements are employed at a translational energy of 0.04088 eV for the Fu−Xu−Zhang potential energy surface. Our analysis of the DCSs uses a new technique called the QP decomposition; it makes an exact decomposition of the scattering (S) matrix into a Q part and a P part. The P part consists of a partial wave (PW) sum of Regge poles (involving both positions and residues) together with a rapidly oscillating quadratic phase. The Q part of the decomposition is then constructed exactly by subtracting the rapidly oscillating phase and the PW Regge pole sum from the input PW S matrix. In practice, it is convenient to make a small modification, which we call the QmodPmod decomposition. All our calculations use only integer values of the total angular momentum quantum number, namely, J = 0, 1, 2,... We find that the QmodPmod decomposition is successful and physically meaningful, in that the properties of Qmod matrix are simpler than those of the input S matrix. We then carry out a QmodPmod analysis of the DCSs, which provides novel insights into interference structures present in the angular scattering. In particular, we find for all three reactions that Regge resonances contribute across the whole angular range of the DCSs, being particularly pronounced at small angles. The techniques of nearside−farside decomposition and local angular momentum analysis for resummed Legendre PW series are also employed to provide additional insights into the angular scattering.

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A single resonance Regge pole dominates the forward-angle scattering of the state-to-state F + H₂ → FH + H reaction at E_trans = 62.09 meV

Xiahou,

Connor,

De Fazio

et al. 2024

Phys. Chem. Chem. Phys.

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Computer Software for Understanding Resonances and Resonance-Related Phenomena in Chemical Reactions

Cited by 3 publications

References 25 publications

State-to-State F + H₂ Reaction at E_trans = 0.04088 eV: QP Decomposition, Parametrized S Matrix Incorporating Regge Poles, and Uniform Asymptotic Complex Angular Momentum Analysis of the Angular Scattering

State-to-State F + H₂ Reaction at E_trans = 0.04088 eV: QP Decomposition, Parametrized S Matrix Incorporating Regge Poles, and Uniform Asymptotic Complex Angular Momentum Analysis of the Angular Scattering

Application of the Partial Wave QP Decomposition to the Angular Scattering of the State-to-State F + H₂ Reaction at E_trans = 0.04088 eV

A single resonance Regge pole dominates the forward-angle scattering of the state-to-state F + H₂ → FH + H reaction at E_trans = 62.09 meV

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Computer Software for Understanding Resonances and Resonance-Related Phenomena in Chemical Reactions

Cited by 3 publications

References 25 publications

State-to-State F + H2 Reaction at Etrans = 0.04088 eV: QP Decomposition, Parametrized S Matrix Incorporating Regge Poles, and Uniform Asymptotic Complex Angular Momentum Analysis of the Angular Scattering

State-to-State F + H2 Reaction at Etrans = 0.04088 eV: QP Decomposition, Parametrized S Matrix Incorporating Regge Poles, and Uniform Asymptotic Complex Angular Momentum Analysis of the Angular Scattering

Application of the Partial Wave QP Decomposition to the Angular Scattering of the State-to-State F + H2 Reaction at Etrans = 0.04088 eV

A single resonance Regge pole dominates the forward-angle scattering of the state-to-state F + H2 → FH + H reaction at Etrans = 62.09 meV

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State-to-State F + H₂ Reaction at E_trans = 0.04088 eV: QP Decomposition, Parametrized S Matrix Incorporating Regge Poles, and Uniform Asymptotic Complex Angular Momentum Analysis of the Angular Scattering

State-to-State F + H₂ Reaction at E_trans = 0.04088 eV: QP Decomposition, Parametrized S Matrix Incorporating Regge Poles, and Uniform Asymptotic Complex Angular Momentum Analysis of the Angular Scattering

Application of the Partial Wave QP Decomposition to the Angular Scattering of the State-to-State F + H₂ Reaction at E_trans = 0.04088 eV

A single resonance Regge pole dominates the forward-angle scattering of the state-to-state F + H₂ → FH + H reaction at E_trans = 62.09 meV