Skip to main content

Quantum Mechanics of Electro-Nuclear Systems Towards a Theory of Chemical Reactions

  • Chapter
New Trends in Quantum Systems in Chemistry and Physics

Part of the book series: Progress in Theoretical Chemistry and Physics ((PTCP,volume 7))

Abstract

A new electronuclear separability approach is used to split global translational motion from the molecular hamiltonian (Hm) and to define state dependent molecular frames; an operator is obtained coupling the global translational momentum to the operators for linear momenta of nuclei and electrons. The method prompts for a different and hopefully sounder description of chemical processes. The electronic wave functions do not depend upon the instantaneous nuclear positions; they determine stationary geometric arrangements of sources of external Coulomb potential. For processes conserving charge and particle number, such as those intervening in a chemical reaction, reactants and products are eigenstates of Hm with momenta quantized by taking the system to be in a volume V with periodic boundary conditions. The physical and chemical processes are represented by changes in populations among the eigenstates of Hm. Such changes must be produced by a coupling to an external field (e.g. electromagnetic). One of the very new results is that chemical processes may even be affected by sound fields. Quantum mechanical conservation principles enter in a natural manner to describe chemical processes. They help define selection rules. In particular, parity plays a central role. If both reactant and product channels have the same parity, the theory requires the existence of a transition structure with different parity to mediate the interconversion. This rule is important since most of the chemical reactions in the ground electronic states of reactants and products belong to this class. Chemical processes can be described in the same general terms as Franck-Condon spectroscopy.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Born, M. and Huang, K.: Dynamical theory of crystal lattices, Clarendon, Oxford, 1954.

    Google Scholar 

  2. Aroeste, H.: Towards an analytical theory of chemical reactions, Adv. Chem. Phys., 6 (1964) 1–83.

    CAS  Google Scholar 

  3. Child, M. S.: Molecular collision theory, Academic Press, London, 1974.

    Google Scholar 

  4. Tapia, O.: (2000) Electro-nuclear quantum mechanics beyond de BO approximation: towards a quantum electronic theory of chemical reactions, in Hernandez-Laguna, A., Maruani. J., McWeeny, R. and Wilson, S. (eds), Quantum systems in chemistry and physics, Vol II: Advanced problems and complex system. Kluwer, Dordrecht, pp. 193–212.

    Google Scholar 

  5. Woolley, R. G.: Quantum theory and molecular structure, Adv. Phys., 25 (1976) 27–52.

    Article  CAS  Google Scholar 

  6. Woolley, R. G. and Sutcliffe, B. T.: Molecular structure and the Born-Oppenheimer approximation, Chem. Phys. Lett., 45 (1977) 393–398.

    Article  CAS  Google Scholar 

  7. Woolley, R. G.: Must a molecule have a shape ?, J. Am. Chem. Soc., 100 (1978) 1073–1078.

    Article  CAS  Google Scholar 

  8. Littlejohn, R. G. and Reinsch, M.: Gauge fields in the separation of rotations and internal motions in the n-body problem, Rev. Mod,Phys., 69 (1997) 213–275

    Article  Google Scholar 

  9. Flurry, R. L. and Siddall, I. T. H.: On the group of the independent-particle hamiltonian. Mol. Phys., 36 (1978) 1309–1320.

    CAS  Google Scholar 

  10. Goscinski, O. and Mujica, V. (1987) Adiabatic separation, broken symmetries and geometry optimization, in Erdahl, R. and Smith Jr, V. H. (eds); Density matrices and density functionals, Reidel, Dordrecht.

    Google Scholar 

  11. Witkowsh, A.: Separation of electronic and nuclear motions and the dynamical Schrodinger group, Phys. Rev.A, 41 (1990) 3511–3517.

    Google Scholar 

  12. Bransden, B. H. and Joachain, C. J.: Physics of atoms and molecules, Longman Scientific and Technical. New York, 1983.

    Google Scholar 

  13. Gilbert, T. L.: Hohenberg-Kohn theorem for nonlocal external potentials, Phys. Rev.B, 12 (1975) 2111–2120.

    Article  Google Scholar 

  14. Mezey, P. G. (1989) Topology of molecular shape and chirality, in Bertran, J. and Csizmadia, I. G. (eds), New theoretical concepts for understanding organic reactions, Kluwer, Dordrecht, pp. 55–100.

    Google Scholar 

  15. Pack, R. T. and Hirschfelder, J. O.: Separation of rotational coordinates from the N-electron diatomic Schrödinger equation, J. Chem. Phys., 49 (1968) 4009–4020

    Article  CAS  Google Scholar 

  16. Mead, C. A. and Truhlar, D. G.: Conditions for a definition of a strictly diabatic electronic basis for molecular systems, J. Chem. Phys., 77 (1982) 6090–6098.

    Article  CAS  Google Scholar 

  17. Sakurai, J. J.: Modern Quantum Mechanics, Benjamin/Cummings, Menlo Park, 1985.

    Google Scholar 

  18. Smith, F. T.: Diabatic and adiabatic representations for atomic collision problems, Phys. Rev., 179 (1969) 111–123.

    Google Scholar 

  19. Steinfeld, J. I., Francisco, J. S. and Hase, W. T.: Chemical kinetics and dynamics, Prentice-Hall, New Jersey, 1989.

    Google Scholar 

  20. Omnès, R.: Understanding quantum mechanics, Princeton University Press, Princeton, New Jersey, 1999.

    Google Scholar 

  21. Tapia, O. (1982) Quantum theories of solvent-effect representation: an overview of methods and results, in Ratajczack, H. and Orville-Thomas, W. J. (eds), Molecular Interactions, Wiley, Chichester, pp. 47–117.

    Google Scholar 

  22. Tapia, O., Andres, J. and Stamato, F. M. G. (1996) Quantum theory of solvent effects and chemical reactions, in Tapia, O. and Bertran, J. (eds), Solvent effects and chemical reactivity, Kluwer, Dordrecht.

    Google Scholar 

  23. Golden S.: The quantum mechanics of chemical kinetics of homogeneous gas phase reactions, J. Chem. Phys., 17 (1949) 620–643.

    CAS  Google Scholar 

  24. Kleiman, V. D., Park. H., Gordon, R. J. and Zare. R. N.: Companion to Angular Momentum, Wiley and Sons, 1998.

    Google Scholar 

  25. Tully, J.C.: Diatomics-in-molecules potential energy surfaces. II. Nonadiabatic and spin-orbit interactions, J. Chem. Phys., 59 (1973) 5122–5134.

    Article  CAS  Google Scholar 

  26. Levine, R. D. and Bernstein, R. B.: Molecular reaction dynamics and chemical reactivity, Oxford University Press, New York, 1987.

    Google Scholar 

  27. Bohm, A., Antoniou, I. and Kielanowski, P.: The preparation-registration arrow of time in quantum mechanics, Phys. Lett.A, 189 (1994) 442–448.

    Article  Google Scholar 

  28. Bohm, A.: Quantum mechanics, Springer-Verlag, New York, 1993.

    Google Scholar 

  29. Feshbach. H.: Theoretical nuclear physics. Nuclear reactions, Wiley and Sons, New York, 1992.

    Google Scholar 

  30. Cimiraglia, R. (1992) Adiabatic and diabatic sets in molecular calculations, in Broeckhove. J. and Lathouwers, L. (eds), Time-dependent quantum molecular dynamics, Plenum Press, New York, pp. 11–26.

    Google Scholar 

  31. Sutcliffe, B. T.: The idea of a potential energy surface, J. Mol. Struct (Theochem), 341 (1995) 217–235.

    Article  CAS  Google Scholar 

  32. Goscinski, O. and Palma, A.: Electron and nuclear density matrices and the separation of electronic and nuclear motion, Int.J. Quantum Chem., 15 (1979) 197–205.

    Article  CAS  Google Scholar 

  33. Pack, R. T. and Hirschfelder, J. O.: Energy corrections to the Born-Oppenheimer approximation. The best adiabatic approximation, J. Chem. Phys., 52 (1970) 521–534.

    CAS  Google Scholar 

  34. Levine, R. D.: Quantum mechanics of molecular rate processes, Clarendon Press, Oxford, 1969.

    Google Scholar 

  35. Roos, B. O. (edr), Lecture Notes in Chemistry, Springer-Verlag, Berlin, 1992.

    Google Scholar 

  36. Roos, B. O.: Theoretical studies of electronically excited states of molecular systems using multiconfigurational perturbation theory, Acc. Chem. Res., 32 (1999) 137–144.

    Article  CAS  Google Scholar 

  37. Deumens, E., Diz: A., Longo, R. and Öhrn, Y.: Time-dependent theoretical treatments of the dynamics of electrons and nuclei in molecular systems, Rev. Mod. Phys., 66 (1994) 917–953.

    Article  CAS  Google Scholar 

  38. Hohenberg, P. and Kohn, W.: Inhomogeneous electron gas; Phys. Rev., 136 (1964) B864–B871.

    Article  Google Scholar 

  39. Lieb, E. H. and Thirring, W. E.: Bound for the kinetic energy of fermions which proves the stability of matter, Phys. Rev. Lett., 35 (1975) 687–689.

    CAS  Google Scholar 

  40. Zewail, A. H.: Femtochemistry. Ultrafast dynamics of the chemical bond, World Scientific, Singapore, 1994.

    Google Scholar 

  41. Cohen-Tannoudji, C., Dupont-Roc, J. and Grynberg, G.: Photons and Atoms. Introduction to quantum electrodynamics, Wiley and Sons, New York, 1989

    Google Scholar 

  42. Feynman, R. P.: Quantum electrodynamics, Benjamin, New York, 1961.

    Google Scholar 

  43. Woolley, R. G.: Charged particles, gauge invariance and molecular electrodynamics, Int.J. Quant. Chem., 74 (1999) 531–545.

    Article  CAS  Google Scholar 

  44. Dunbar, R. C. and McMahon, T. B.: Activation of unimolecular reactions by ambient blackbody radiation, Science, 279 (1998) 194–197.

    Article  CAS  Google Scholar 

  45. Tapia, O. and Andres, J.: On a quantum theory of chemical reactions and the role of in vacuum transition structures. Primary and secondary sources of enzyme catalysis, J. Mol. Str.-Theochem, 335 (1995) 267–286.

    CAS  Google Scholar 

  46. Tapia, O., Andres, J., Moliner, V. and Stamato, F. L. M. G. (1997): Theory of solvent effects and the description of chemical reactions. Proton and hydride transfer processes, in Hadzi, D. (edr), Theoretical treatments of hydrogen bonding, John Wiley and Sons, New York, pp. 143–164

    Google Scholar 

  47. Tapia, O., Moliner, V. and Andres, J.: A quantum electronic theory of chemical processes. The inverted energy profile case: CH3+ + H2 reaction, I. J. Quantum Chem., 63 (1997) 373–391.

    CAS  Google Scholar 

  48. Tapia, O.: Quantum mechanics and the theory of hydrogen bond and proton transfer. Beyond a Born-Oppenheimer description of chemical interconversions, J. Mol. Str. Theochem, 433 (1998) 95–105.

    CAS  Google Scholar 

  49. Zewail, A. H.: Femtosecond transition-state dynamics, Faraday Disc. Chem. Soc., 91 (1991) 207–237.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Kluwer Academic Publishers

About this chapter

Cite this chapter

Tapia, O. (2000). Quantum Mechanics of Electro-Nuclear Systems Towards a Theory of Chemical Reactions. In: Maruani, J., Minot, C., McWeeny, R., Smeyers, Y.G., Wilson, S. (eds) New Trends in Quantum Systems in Chemistry and Physics. Progress in Theoretical Chemistry and Physics, vol 7. Springer, Dordrecht. https://doi.org/10.1007/0-306-46950-2_2

Download citation

  • DOI: https://doi.org/10.1007/0-306-46950-2_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-6709-3

  • Online ISBN: 978-0-306-46950-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics