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

  • Dmitri Sokolovski
  • Elena Akhmatskaya
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8579)

Abstract

In numerical modelling of chemical reactions one calculates the scattering matrix for the required values of energy and angular momentum. Having done so, one still faces the non-trivial task of extracting detailed information about the reaction mechanism. We discuss the methods and numerical tools for such an analysis in terms of resonance poles and semiclassical trajectories. Our approach avoids calculating the scattering matrix in semiclassical approximation, and employs its numerical values computed previously by an accurate scattering code.

Keywords

chemical reactions complex angular momentum analysis semiclassical methodsTuesday 
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References

  1. 1.
    Skouteris, D., Castillo, J.F., Manolopoulos, D.E.: ABC: a quantum reactive scattering problem. Comp. Phys. Commun. 133, 128 (2000)CrossRefMATHGoogle Scholar
  2. 2.
    Althorpe, S.C., Fernández-Alonso, F., Bean, B.D., Ayers, J.D., Pomerantz, A.E., Zare, R.N., Wrede, E.: Observation and interpretation of a time-delayed mechanism in hydrogen exchange reaction. Nature 416, 67 (2002)CrossRefGoogle Scholar
  3. 3.
    Aquilanti, V., Cavalli, S., De Fazio, D.: Hyperquantization algorithm. I. Theory for triatomic systems. J. Chem. Phys. 109, 3792 (1998)CrossRefGoogle Scholar
  4. 4.
    Alexander, A.J., Blunt, D.A., Brouard, M., Simons, J.P., Aoiz, F.J., Baares, L., Fujimura, Y., Tsubouchi, M.: O(1 D 2)+H 2 → OH|v′ ≤ 4,N′ > + H: the anatomy of a reaction. Faraday Discuss. Chem. Soc. 108, 375 (1997)CrossRefGoogle Scholar
  5. 5.
    Miller, W.H.: Classical-Limit Quantum Mechanics and the Theory of Molecular Collisions. Adv. Chem. Phys. 25, 69 (1974)Google Scholar
  6. 6.
    Miller, W.H.: The Semiclassical Initial Value Representation: A Potentially Practical Way for Adding Quantum Effects to Classical Molecular Dynamics Simulations. J. Phys. Chem. 105, 2942 (2001)CrossRefGoogle Scholar
  7. 7.
    Sokolovski, D., Connor, J.N.L.: Semiclassical nearside-farside theory for inelastic and reactive atom-diatom collisions. Chem. Phys. Lett. 305, 238 (1999)CrossRefGoogle Scholar
  8. 8.
    Brink, D.M.: Semi-classical Methods in Nucleus-Nucleus Scattering. Cambridge University Press, Cambridge (1985)Google Scholar
  9. 9.
    Sokolovski, D., Sen, S.K., Aquilanti, V., Cavalli, S., De Fazio, D.: Interacting resonances in the F + H2 reaction revisited: Complex terms, Riemann surfaces, and angular distributions. J. Chem. Phys. 126, 084305 (2007)CrossRefGoogle Scholar
  10. 10.
    Connor, J.N.L.: New theoretical methods for molecular collisions: The complex angular momentum approach. Chem. Soc. Faraday Trans. 86, 1627 (1990)CrossRefGoogle Scholar
  11. 11.
    Sokolovski, D., Msezane, A.Z., Felfli, Z., Ovchinnikov, S.Y., Macek, J.H.: What can one do with Regge poles? Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 261, 133 (2007)CrossRefGoogle Scholar
  12. 12.
    Sokolovski, D.: Complex-angular-momentum (CAM) route to reactive scattering resonances: from a simple model to the F + H2 → HF + H reaction. Phys. Scr. 78, 58118 (2008)CrossRefGoogle Scholar
  13. 13.
    Connor, J.N.L.: Resonance Regge poles and the state-to-state F + H2 reaction: QP decomposition, parametrized S matrix, and semiclassical complex angular momentum analysis of the angular scattering. J. Chem. Phys. 138, 124310 (2013)CrossRefGoogle Scholar
  14. 14.
    Sokolovski, D., Msezane, A.Z.: Semiclassical complex angular momentum theory and padé reconstruction for resonances, rainbows, and reaction thresholds. Phys. Rev. A. 70, 032710 (2004)CrossRefGoogle Scholar
  15. 15.
    Sokolovski, D., Akhmatskaya, E.: Classification of resonance Regge trajectories and a modified Mulholland formula. Phys. Lett. A 375, 3062 (2011), Please note that there is a typo in Eq.(5), which should read Open image in new window Google Scholar
  16. 16.
    Xiahou, C., Connor, J.N.L., Zhang, D.H.: Rainbows and glories in the angular scattering of the state-to-state F + H 2 reaction at E trans = 0.04088 eV. Phys. Chem. Chem. Phys. 13, 12981 (2011)CrossRefGoogle Scholar
  17. 17.
    Sokolovski, D.: Glory and thresholds effects in H + D2 reactive angular scattering. Chem. Phys. Lett. 370, 805 (2003)CrossRefGoogle Scholar
  18. 18.
    Xiahou, C., Connor, J.N.L.: The 6Hankel asymptotic approximation for the uniform description of rainbows and glories in the angular scattering of state-to-state chemical reactions: derivation, properties and applications. Phys. Chem. Chem. Phys. (2014) (in print)Google Scholar
  19. 19.
    Sokolovski, D.: Complex-angular-momentum analysis of atom-diatom angular scattering: Zeros and poles of the S matrix. Phys. Rev. A 62, 247 (2000)CrossRefGoogle Scholar
  20. 20.
    Bessis, D., Haffad, A., Msezane, A.Z.: Momentum-transfer dispersion relations for electron-atom cross sections. Phys. Rev. A 49, 3366 (1994)CrossRefGoogle Scholar
  21. 21.
    Sokolovski, D., Akhmatskaya, E., Sen, S.K.: Extracting resonance poles from numerical scattering data: type-II padé reconstruction. Comp. Phys. Comm. A 182, 448 (2011)CrossRefMATHGoogle Scholar
  22. 22.
    Regge, T.: Introduction to Complex Orbital Momenta. Nuovo Cimento 14, 951 (1959)CrossRefMATHMathSciNetGoogle Scholar
  23. 23.
    Macek, J.H., Krstic, P.S., Ovchinnikov, S.Y.: Regge oscillations in integral cross sections for proton impact on atomic hydrogen. Phys. Rev. Lett. 93, 183203 (2004)CrossRefGoogle Scholar
  24. 24.
    Sokolovski, D., De Fazio, D., Cavalli, S., Aquilanti, V.: Overlapping resonances and Regge oscillations in the state-to-state integral cross sections of the F + H2 reaction. J. Chem. Phys. 126, 12110 (2007)Google Scholar
  25. 25.
    Akhmatskaya, E., Sokolovski, D., Echeverría-Arrondo, C.: Numerical Regge pole analysis of resonance structures in elastic, inelastic and reactive state-to-state integral cross sections. Comp. Phys. Comm. 185, 2127 (2014)CrossRefGoogle Scholar
  26. 26.
    Sokolovski, D., De Fazio, D., Cavalli, S., Aquilanti, V.: On the origin of the forward peak and backward oscillations in the the F + H2(v=0) → HF(v’=2) + H reaction. Phys. Chem. Chem. Phys. 9, 1 (2007)CrossRefGoogle Scholar
  27. 27.
    Dobbyn, A.J., McCabe, P., Connor, J.N.L., Castillo, J.F.: Nearside-farside analysis of state-selected differential cross sections for reactive molecular collisions. Phys. Chem. Chem. Phys. 1, 1115 (1999)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Dmitri Sokolovski
    • 1
    • 3
  • Elena Akhmatskaya
    • 2
    • 3
  1. 1.Departmento de Química-FísicaUniversidad del País Vasco, UPV/EHULeioaSpain
  2. 2.Basque Center for Applied Mathematics (BCAM)BilbaoSpain
  3. 3.Basque Foundation for ScienceIKERBASQUEBilbaoSpain

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