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Constructing quantum mechanical models starting from diabatic schemes: Quantum states for simulations bond break/formation—I. Feshbach-like quantum states and electronuclear wave functions

Abstract

A quantum description adapted to scrutinize chemical reaction mechanisms obtains by implementing an electronuclear separation via quantum numbers method; truly diabatic base states obtain that sustain quantum states expressed as linear superpositions. A proto-type bond breaking/formation case: \({H_{2}^{+}\Leftrightarrow H(1s)+H^{+}}\) test possibilities via mathematical modeling. Asymptotic states \({({\vert}{H}\rangle\otimes{\vert}{H}^{+}\rangle}\) and \({({\vert}{H}^{+}\rangle\otimes{\vert}{H}\rangle)}\) and basis states for quantized electromagnetic radiation complete the model; Feshbach-resonance-like quantum states obtain that play pivotal roles gating association/dissociation processes. A fixed grid of floating Gaussian orbitals permits actual computations compatible with this method. The information therefrom gleaned is used to construct model Hamiltonians easily adaptable to second quantization formalisms. Theoretical developments and non-routine computations results can directly be related to experiment.

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References

  1. 1

    Arteca G.A., Tapia O.: Phys. Rev. A 83, 032311 (2011)

    Article  Google Scholar 

  2. 2

    Tapia O.: Adv. Quantum Chem. 56, 31 (2009)

    Article  CAS  Google Scholar 

  3. 3

    Tapia O., Braña P.: J. Mol. Struct. (Theochem) 580, 9 (2002)

    Article  CAS  Google Scholar 

  4. 4

    Arteca G.A., Tapia O.: Int. J. Quantum Chem. 107, 382 (2007)

    Article  CAS  Google Scholar 

  5. 5

    Arteca G.A., Rank J.P., Tapia O.: J. Theor. Comput. Chem. 6, 869 (2007)

    Article  CAS  Google Scholar 

  6. 6

    Arteca G.A., Rank J.P., Tapia O.: Int. J. Quantum Chem. 108, 651 (2008)

    Article  CAS  Google Scholar 

  7. 7

    Arteca G.A., Tapia O.: J. Math. Chem. 37, 389 (2005)

    Article  CAS  Google Scholar 

  8. 8

    Arteca G.A., Tapia O.: J. Math. Chem. 35, 1 (2004)

    Article  CAS  Google Scholar 

  9. 9

    Arteca G.A., Tapia O.: J. Math. Chem. 35, 159 (2004)

    Article  CAS  Google Scholar 

  10. 10

    Cirac J.I., Zoller P.: Phys. Today 57, 38 (2003)

    Article  Google Scholar 

  11. 11

    Côté R.: Nat. Phys. 2, 583 (2006)

    Article  Google Scholar 

  12. 12

    DeMille D.: Phys. Rev. Lett. 88, 067901 (2002)

    Article  CAS  Google Scholar 

  13. 13

    André A., DeMille D, Doyle J.M., Lukin M.D., Maxwell S.E., Rabl P., Schoelkopf R.J., Zoller P.: Nat. Phys. 22, 636 (2006)

    Article  Google Scholar 

  14. 14

    Xia Y., Deng L., Yin J.: Appl. Phys. B 81, 459 (2005)

    Article  CAS  Google Scholar 

  15. 15

    Krems R.V.: Int. Rev. Phys. Chem. 24, 99 (2005)

    Article  CAS  Google Scholar 

  16. 16

    Krems R.V., Dalgarno A.: Phys. Rev. A 68, 013406 (2003)

    Article  Google Scholar 

  17. 17

    Cornish S.: Physics 1, 24 (2008)

    Article  Google Scholar 

  18. 18

    O. Tapia, in Beyond Standard Quantum Chemical Semi-classic Approaches: Towards a Quantum Theory of Enzyme Catalysis, ed. by P. Paneth, A. Dybala-Defratyka. Kinetics and Dynamics, Challenges and Advances in Computational Chemistry and Physics, vol. 12, pp. 267–298 (2010)

  19. 19

    Crespo R., Piqueras M.-C., Aulló J.M., Tapia O.: Int. J. Quantum Chem. 111, 263 (2011)

    Article  CAS  Google Scholar 

  20. 20

    Tapia O.: Adv. Quantum Chem. 61, 49 (2011)

    Article  CAS  Google Scholar 

  21. 21

    O. Tapia, Quantum Physical Chemistry: Basic Quantum Mechanics for Process Description. http://www.pac.uu.se/Fysikalisk_kemi/Personal/Emeritus/Orlando_Tapia-Olivares/

  22. 22

    Ballentine L.E.: Quantum Mechanics: A Modern Development. World Scientific, Singapore (1998)

    Google Scholar 

  23. 23

    M. Born, K. Huang, Dynamical Theory of Crystal Lattices (Oxford, 1956).

  24. 24

    Feshbach H.: Ann. Phys. 5, 357 (1958)

    Article  CAS  Google Scholar 

  25. 25

    Butler L.J.: Annu. Rev. Phys. Chem. 49, 125 (1998)

    Article  CAS  Google Scholar 

  26. 26

    Helgaker T., Almlöf J.: J. Chem. Phys. 89, 4889 (1988)

    Article  CAS  Google Scholar 

  27. 27

    Frisch M.J. et al.: Gaussian 98 [Revision A.7]. Gaussian Inc., Pittsburgh (USA) (1998)

    Google Scholar 

  28. 28

    Bates D.R., Reid R.H.G.: At. Mol. Phys. 4, 13 (1968)

    Article  CAS  Google Scholar 

  29. 29

    Hishikawa A., Iwamae A., Yamanouchi K.: Phys. Rev. Lett. 83, 1127 (1999)

    Article  CAS  Google Scholar 

  30. 30

    Posthumus H.: J. Rep. Prog. Phys. 67, 623 (2004)

    Article  CAS  Google Scholar 

  31. 31

    Giusti-Suzor A., Mies F.H., Di Mauro L.F., Charron E., Yang B.: J. Phys. B 28, 309 (1995)

    Article  CAS  Google Scholar 

  32. 32

    Stroe M., Fifiring M.: Mol. Phys. 109, 1617 (2011)

    Article  CAS  Google Scholar 

  33. 33

    Levis J.R., Menkir G.M., Rabitz H.: Science 292, 709 (2001)

    Article  CAS  Google Scholar 

  34. 34

    Gull E., Millis A.J., Lichtenstein A.I., Rubtsov A.N., Troyer M., Werner Ph.: Rev. Mod. Phys. 83, 349 (2011)

    Article  CAS  Google Scholar 

  35. 35

    Toutouni M.: Int. J. Quantum Chem. 111, 3475 (2011)

    Google Scholar 

Download references

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Arteca, G.A., Aulló, J.M. & Tapia, O. Constructing quantum mechanical models starting from diabatic schemes: Quantum states for simulations bond break/formation—I. Feshbach-like quantum states and electronuclear wave functions. J Math Chem 50, 949–970 (2012). https://doi.org/10.1007/s10910-011-9942-0

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Keywords

  • Feshbach states
  • Quantum states for chemical processes
  • Entanglements and reaction mechanisms
  • Floating Gaussian grid algorithm