Skip to main content
SpringerLink
Log in

Describing Molecules in Motion by Quantum Many-Body Methods

  • Chapter
  • First Online:
Frontiers of Quantum Chemistry

  • 1921 Accesses

Abstract

For a complete quantum description of molecular systems, it is necessary to solve Schrödinger equations for both electrons and nuclei. In this chapter, focus is given to approximate methods for solving the nuclear Schrödinger equation. Similarities and dissimilarities compared to the practice employed for the electronic case will be noted. A many-body view on potential energy surfaces will be used to motivate a many-body view on the general problem of solving the nuclear Schrödinger equation. A second quantization multimode formalism will be outlined and used to formulate many-body wave functions for nuclear motion. The vibrational self-consistent field (VSCF) method is introduced. Full vibrational configuration interaction (FVCI) is introduced as the reference, before primary attention is given to vibrational coupled cluster (VCC) theory. VCC theory is furthermore analysed from a tensor decomposition perspective and with a perspective to scaling with system size.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 219.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 279.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 279.99
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

References

  1. T. Helgaker, P. Jørgensen, J. Olsen, Molecular Electronic Structure Theory (Wiley, Chichester, 2000)

    Book  Google Scholar 

  2. F. Jensen, Introduction to Computational Chemstry, 2nd edn. (Wiley, Chichester, 2006)

    Google Scholar 

  3. J.K.G. Watson, Mol. Phys. 15, 479 (1968)

    Article  CAS  Google Scholar 

  4. S. Carter, S.J. Culik, J.M. Bowman, J. Chem. Phys. 107, 10458 (1997)

    Article  CAS  Google Scholar 

  5. G.C. Schatz, Rev. Mod. Phys. 61, 669 (1989)

    Article  CAS  Google Scholar 

  6. H. Rabitz, O.F. Aliş, J. Math. Chem. 25, 197 (1999)

    Article  CAS  Google Scholar 

  7. H.-D. Meyer, WIREs: Comput. Mol. Sci. 2, 351 (2012)

    Google Scholar 

  8. M. Griebel, Sparse grids and related approximation schemes for higher dimensional problems, in Foundations of Computational Mathematics (FoCM05), Santander, ed. by L. Pardo, A. Pinkus, E. Suli, M. Todd, (Cambridge University Press, 2006) pp. 106–161

    Google Scholar 

  9. J.O. Jung, R.B. Gerber, J. Chem. Phys. 105, 10332 (1996)

    Article  CAS  Google Scholar 

  10. K. Yagi, T. Taketsugu, K. Hirao, M.S. Gordon, J. Chem. Phys. 113, 1005 (2000)

    Article  CAS  Google Scholar 

  11. D. Toffoli, J. Kongsted, O. Christiansen, J. Chem. Phys. 127, 204106 (2007)

    Article  CAS  Google Scholar 

  12. M. Sparta, D. Toffoli, O. Christiansen, Theor. Chem. Acc. 123, 413 (2009)

    Article  CAS  Google Scholar 

  13. C. König, O. Christiansen, J. Chem. Phys. 145, 064105 (2016)

    Article  Google Scholar 

  14. C. König, M.B. Hansen, I.H. Godtliebsen, O. Christiansen, J. Chem. Phys. 144, 074108 (2016)

    Article  Google Scholar 

  15. O. Christiansen, J. Chem. Phys. 120, 2140 (2004)

    Article  CAS  Google Scholar 

  16. O. Christiansen, J. Chem. Phys. 120, 2149 (2004)

    Article  CAS  Google Scholar 

  17. J.M. Bowman, Acc. Chem. Res. 19, 202 (1986)

    Article  CAS  Google Scholar 

  18. R.B. Gerber, M.A. Ratner, Adv. Chem. Phys. 70, 97 (1988)

    CAS  Google Scholar 

  19. M.B. Hansen, M. Sparta, P. Seidler, O. Christiansen, D. Toffoli, J. Chem. Theo. Comp. 6, 235 (2010)

    Article  CAS  Google Scholar 

  20. J.M. Bowman, T. Carrington, H. Meyer, Mol. Phys. 106, 2145 (2008)

    Article  CAS  Google Scholar 

  21. D. Oschetzki, M. Neff, P. Meier, F. Pfeiffer, G. Rauhut, Croat. Chem. Acta. 85, 379 (2012)

    Article  CAS  Google Scholar 

  22. O. Christiansen, Phys. Chem. Chem. Phys. 14, 6672 (2012)

    Article  CAS  Google Scholar 

  23. J. Brown, T. Carrington, J. Chem. Phys. 145, 144104 (2016)

    Article  Google Scholar 

  24. P. Seidler, O. Christiansen, J. Chem. Phys. 131, 234109 (2009)

    Article  Google Scholar 

  25. S. Banik, S. Pal, M.D. Prasad, J. Chem. Phys. 129, 134111 (2008)

    Article  Google Scholar 

  26. J.A. Faucheaux, S. Hirata, J. Chem. Phys. 143, 134105 (2015)

    Article  Google Scholar 

  27. T.G. Kolda, B.W. Bader, SIAM Rev. 51(3), 455 (2009)

    Article  Google Scholar 

  28. S. Hirata, M. Keçeli, K. Yagi, J. Chem. Phys. 133, 034109 (2010)

    Article  Google Scholar 

  29. I.H. Godtliebsen, B. Thomsen, O. Christiansen, J. Chem. Phys. A 117, 7267–7279 (2013)

    Article  CAS  Google Scholar 

  30. I.H. Godtliebsen, M.B. Hansen, O. Christiansen, J. Chem. Phys. 142, 024105 (2015)

    Article  Google Scholar 

  31. C. König, O. Christiansen, J. Chem. Phys. 142, 144115 (2015)

    Article  Google Scholar 

Download references

Acknowledgements

This work has been supported by the Lundbeck Foundation and the Danish Natural Science Research Council. We acknowledge discussions with Ian Godtliebsen and Mads Bøttger Hansen. Support from the COST network Molecules in Motion is acknowledged.

Author information

Authors and Affiliations

  1. Department of Chemistry, Aarhus University, Aarhus, Denmark

    Ove Christiansen

Authors
  1. Ove Christiansen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ove Christiansen .

Editor information

Editors and Affiliations

  1. Jagiellonian University, Kraków, Poland

    Marek J. Wójcik

  2. Quantum Chemistry Research Institute, Nishikyo-ku, Kyoto, Japan

    Hiroshi Nakatsuji

  3. University of California, Santa Barbara, California, USA

    Bernard Kirtman

  4. School of Science and Technology, Kwansei Gakuin University, Sanda, Japan

    Yukihiro Ozaki

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Christiansen, O. (2018). Describing Molecules in Motion by Quantum Many-Body Methods. In: Wójcik, M., Nakatsuji, H., Kirtman, B., Ozaki, Y. (eds) Frontiers of Quantum Chemistry. Springer, Singapore. https://doi.org/10.1007/978-981-10-5651-2_9

Download citation

Publish with us

Policies and ethics

Search

Navigation