Geometric Phase and Interference Effects in Ultracold Chemical Reactions

  • N. Balakrishnan
  • B. K. Kendrick
Conference paper
Part of the Progress in Theoretical Chemistry and Physics book series (PTCP, volume 31)


Electronically non-adiabatic effects play an important role in many chemical reactions and light induced processes. Non-adiabatic effects are important, when there is an electronic degeneracy for certain nuclear geometries leading to a conical intersection between two adiabatic Born-Oppenheimer electronic states. The geometric phase effect arises from the sign change of the adiabatic electronic wave function as it encircles the conical intersection between two electronic states (e.g., a ground state and an excited electronic state). This sign change requires a corresponding sign change on the nuclear motion wave function to keep the overall wave function single-valued. Its effect on bimolecular chemical reaction dynamics remains a topic of active experimental and theoretical interrogations. However, most prior studies have focused on high collision energies where many angular momentum partial waves contribute and the effect vanishes under partial wave summation. Here, we examine the geometric phase effect in cold and ultracold collisions where a single partial wave, usually the s-wave, dominates. It is shown that unique properties of ultracold collisions, including isotropic scattering and an effective quantization of the scattering phase shift, lead to large geometric phase effects in state-to-state reaction rate coefficients. Illustrative results are presented for the hydrogen exchange reaction in the fundamental H+H\(_2\) system and its isotopic counterparts.


Geometric phase Ultracold molecules Ultracold chemistry Ultracold collisions 



N. B. acknowledges support from the Army Research Office, MURI grant No. W911NF-12-1-0476 and the National Science Foundation, grant No. PHY-1505557. B. K. K. acknowledges that part of this work was done under the auspices of the US Department of Energy under Project No. 20140309ER of the Laboratory Directed Research and Development Program at Los Alamos National Laboratory. Los Alamos National Laboratory is operated by Los Alamos National Security, LLC, for the National Security Administration of the US Department of Energy under contract DE-AC52-06NA25396.


  1. 1.
    Mead CA, Truhlar DG (1979) J Chem Phys 70:2284; 78:6344E (1983)Google Scholar
  2. 2.
    Simon B (1983) Phys Rev Lett 51:2167CrossRefGoogle Scholar
  3. 3.
    Bohm A, Boya LJ, Kendrick B (1991) Phys Rev A 43:1206CrossRefPubMedGoogle Scholar
  4. 4.
    Mead CA (1992) Rev Mod Phys 64:51CrossRefGoogle Scholar
  5. 5.
    Berry MV (1984) Proc R Soc Lon Ser A 392:45CrossRefGoogle Scholar
  6. 6.
    Aharonov Y, Bohm D (1959) Phys Rev 115:485CrossRefGoogle Scholar
  7. 7.
    Mead CA (1980) Chem Phys 49:23Google Scholar
  8. 8.
    Kendrick BK (1997) Phys Rev Lett 79:2431CrossRefGoogle Scholar
  9. 9.
    Kendrick BK (1997) Int J Quantum Chem 64:581CrossRefGoogle Scholar
  10. 10.
    Babikov D, Kendrick BK, Zhang P, Morokuma K (2005) J Chem Phys 122:044315CrossRefGoogle Scholar
  11. 11.
    Kuppermann A, Wu YSM (1993) Chem Phys Lett 205:577; 213:636E (1993)Google Scholar
  12. 12.
    Wu YSM, Kuppermann A (1995) Chem Phys Lett 235:105CrossRefGoogle Scholar
  13. 13.
    Kuppermann A, Wu YSM (1995) Chem Phys Lett 241:229CrossRefGoogle Scholar
  14. 14.
    Kendrick BK (2001) J Chem Phys 114:8796CrossRefGoogle Scholar
  15. 15.
    Kendrick B, Pack RT (1996) J Chem Phys 104:7475CrossRefGoogle Scholar
  16. 16.
    Kendrick B, Pack RT (1996) J Chem Phys 104:7502CrossRefGoogle Scholar
  17. 17.
    Kendrick BK, (2000) J Chem Phys 112:5679; 114:4335E (2001)Google Scholar
  18. 18.
    Kendrick BK (2003) J Phys Chem 107:6739CrossRefGoogle Scholar
  19. 19.
    Kendrick BK (2003) J Chem Phys 118:10502CrossRefGoogle Scholar
  20. 20.
    Juanes-Marcos C, Althorpe SC (2005) J Chem Phys 122:204324CrossRefPubMedGoogle Scholar
  21. 21.
    Juanes-Marcos JC, Althorpe SC, Wrede E (2005) Science 309:1227CrossRefPubMedGoogle Scholar
  22. 22.
    Althorpe SC (2006) J Chem Phys 124:084105CrossRefPubMedGoogle Scholar
  23. 23.
    Althorpe SC, Stecher T, Bouakline F (2008) J Chem Phys 129:214117CrossRefPubMedGoogle Scholar
  24. 24.
    von Busch H, Eckel V, Dev H, Kasahara S, Wang J, Demtröder W, Sebald P, Meyer W (1998) Phys Rev Lett 81:4584CrossRefGoogle Scholar
  25. 25.
    Keil M, Krämer H-G, Kudell A, Baig MA, Zhu J, Demtröder W, Meyer W (2000) J Chem Phys 113:7414CrossRefGoogle Scholar
  26. 26.
    Rohlfing EA, Valentini JJ (1986) Chem Phys Lett 126:113CrossRefGoogle Scholar
  27. 27.
    Kliner DAV, Adleman DE, Zare RN (1991) J Chem Phys 95:1648CrossRefGoogle Scholar
  28. 28.
    Adelman DE, Shafer NE, Kliner DAV, Zare RN (1992) J Chem Phys 97:7323CrossRefGoogle Scholar
  29. 29.
    Kitsopoulos TN, Buntine MA, Baldwind DP, Zare RN, Chandler DW (1993) Science 260:1605CrossRefPubMedGoogle Scholar
  30. 30.
    Jankunas J, Sneha M, Zare RN, Bouakline F, Althorpe SC (2013) J Chem Phys 139:144316CrossRefPubMedGoogle Scholar
  31. 31.
    Jankunas J, Sneha M, Zare RN, Bouakline F, Althorpe SC, Phys Z (2013) Chemistry 227:1281Google Scholar
  32. 32.
    Jankunas J, Sneha M, Zare RN, Bouakline F, Althorpe SC, Herráez-Aguilar D, Aoiz FJ (2014) PNAS 111:15CrossRefPubMedGoogle Scholar
  33. 33.
    Sneha M, Gao H, Zare RN, Jambrina PG, Menéndez M, Aoiz FJ (2016) J Chem Phys 145:024308CrossRefPubMedGoogle Scholar
  34. 34.
    Krems RV, Stwalley WC, B. Friedrich B (eds) (2009) Cold molecules: theory, experiment, applications. CRC Press, Taylor & Francis GroupGoogle Scholar
  35. 35.
    Carr LD, DeMille D, Krems RV, Ye J (2009) New J Phys 11:055049Google Scholar
  36. 36.
    Ospelkaus S, Ni K-K, Wang D, de Miranda MHG, Neyenhuis B, Quéméner G, Julienne PS, Bohn JL, Jin DS, Ye J (2010) Science 327:853CrossRefPubMedGoogle Scholar
  37. 37.
    Knoop S, Ferlaino F, Berninger M, Mark M, Nägerl H-C, Grimm R, D’Incao JP, Esry BD (2010) Phys Rev Lett 104:053201CrossRefPubMedGoogle Scholar
  38. 38.
    Balakrishnan N (2016) J Chem Phys 145:150901CrossRefPubMedGoogle Scholar
  39. 39.
    Levinson N (1949) Kgl. Danske Videnskab Selskab Mat Fys Medd 25:9Google Scholar
  40. 40.
    Kendrick BK, Hazra J, Balakrishnan N (2015) Nat Commun 6:7918CrossRefPubMedPubMedCentralGoogle Scholar
  41. 41.
    Hazra J, Kendrick BK, Balakrishnan N (2015) J Phys Chem A 119:12291CrossRefPubMedGoogle Scholar
  42. 42.
    Kendrick BK, Hazra J, Balakrishnan N (2015) Phys Rev Lett 115:153201CrossRefPubMedGoogle Scholar
  43. 43.
    Hazra J, Kendrick BK, Balakrishnan N (2016) J Phys B At Mol Opt Phys 49:194004CrossRefGoogle Scholar
  44. 44.
    Kendrick BK, Hazra J, Balakrishnan N (2016) New J Phys 18:123020CrossRefGoogle Scholar
  45. 45.
    Kendrick BK, Hazra J, Balakrishnan N (2016) J Chem Phys 145:164303CrossRefPubMedGoogle Scholar
  46. 46.
    Simbotin I, Ghosal S, Côté R (2011) Phys Chem Chem Phys 13:19148CrossRefPubMedGoogle Scholar
  47. 47.
    Simbotin I, Ghosal S, Côté R (2014) Phys Rev A 89:040701CrossRefGoogle Scholar
  48. 48.
    Simbotin I, Côté R (2015) N J Phys 17:065003CrossRefGoogle Scholar
  49. 49.
    Pack RT, Parker GA (1987) J Chem Phys 87:3888CrossRefGoogle Scholar
  50. 50.
    Kendrick BK, Pack RT, Walker RB, Hayes EF (1999) J Chem Phys 110:6673CrossRefGoogle Scholar
  51. 51.
    Mead CA (1980) J Chem Phys 72:3839CrossRefGoogle Scholar
  52. 52.
    Boothroyd AI, Keogh WJ, Martin PG, Peterson MR (1996) J Chem Phys 104:7139CrossRefGoogle Scholar
  53. 53.
    Mielke SL, Garrett BC, Peterson KA (2002) J Chem Phys 116:4142CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of NevadaLas VegasUSA
  2. 2.Los Alamos National LaboratoryTheoretical Division (T-1, MS B221)Los AlamosUSA

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