Skip to main content

Calculations of Local Properties of Luminescent Materials

  • 354 Accesses

Part of the Springer Series in Materials Science book series (SSMATERIALS,volume 322)


The quantum chemical methods used in this book give electronic energies and wave functions as eigenvalues and eigenfunctions of the electronic Schrödinger equation at fixed nuclei positions, within the Born-Oppenheimer approximation. This process is typically repeated for multiple nuclear arrangements, leading to so-called potential energy surfaces. Their analyses, much helped with the use of symmetry, which may reduce the number of relevant normal vibrational modes to one in high-symmetry sites, leads to important properties of the luminescent centers such as equilibrium geometries, vibrational frequencies and spectral shapes for optical absorption and emission. This chapter summarizes how these properties are derived from quantum chemical calculations.

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

Buying options

USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and 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

Learn about institutional subscriptions


  1. 1.

    Note that the electronic Hamiltonian \(\hat{H}_\text {elec}\) is \(\hat{H}_\mathrm{EC}+ V_\mathrm{ECnuc-Host}\) in (1.4).

  2. 2.

    In non-linear free molecules, the number of internal nuclear coordinates is 3\(N_\text {nuc}\)–6, because three coordinates describe free translations and three coordinates describe free rotations (two in linear molecules); however, free translations and rotations do not exist in a cluster embedded in a solid host, hence the number of 3\(N_\text {nuc}\) internal nuclear coordinates.

  3. 3.

    Strictly speaking, contributions to the band shapes exist from all vibrational coordinates that make the energy differences non-parallel, but the differences in curvatures (i.e. vibrational frequencies) between states is usually so small that the only relevant contribution to the non-parallelism is the horizontal offset.

  4. 4.

    In the case of degenerate electronic states, there are always degenerate vibrations that give non-null linear coefficients. E.g. in the \(O_h\) group, \(E_g \otimes E_g \otimes E_g \ni A_{1g}\) and \(E_g\) electronic states \(\Phi _{E_g,\theta }\) and \(\Phi _{E_g,\epsilon }\) show horizontal offsets along the two \(E_g\) vibrations \(Q_{E_g,\theta }\) and \(Q_{E_g,\epsilon }\). Besides, the two degenerate electronic states are coupled with first and second derivative operators, all of it resulting in the so called \(E_g\otimes e_g\) Jahn-Teller or vibronic coupling [2]. The stabilizations achieved as a consequence of the horizontal shift along these degenerate vibration coordinates, known as Jahn-Teller energies \(E_\mathrm {JT}\), are usually small, as the horizontal shifts are themselves. This makes the Jahn-Teller active or vibronic modes important to understand some detailed spectroscopic features. Multiconfigurational ab initio calculations of Jahn-Teller problems demand the calculation of the potential energy surfaces along them [3, 4]. The result of the \(E_g\otimes e_g\) Jahn-Teller effect on a degenerate electronic state is displayed in Fig. 3.1c.

  5. 5.

    E.g., in a LnL\(_{8}\) cubic moiety, the effective mass is \(\mu _k = \mu _{a_{1g}} = m_\text {L}\) and the breathing mode distortion of the LnL\(_{6}\) moiety is given by \(\Delta Q_k = \Delta Q_{a_{1g}} = \sqrt{8}~\Delta d_\mathbf{Ln}-L \).


  1. R.P. Feynman, Phys. Rev. 56, 340 (1939)

    Article  CAS  Google Scholar 

  2. I.B. Bersuker, The Jahn-Teller Effect and Vibronic Interactions in Modern Chemistry (Plenum Press, New York and London, 1984)

    Book  Google Scholar 

  3. L. Seijo, Z. Barandiarán, J. Chem. Phys. 94, 8158 (1991)

    Article  CAS  Google Scholar 

  4. J.L. Pascual, L. Seijo, Z. Barandiarán, J. Chem. Phys. 98, 9715 (1993)

    Article  CAS  Google Scholar 

  5. J. Oddershede, Phys. Scr. 20, 587 (1979)

    Article  CAS  Google Scholar 

  6. R.C. Hilborn, Am. J. Phys. 50, 982 (1982)

    Article  CAS  Google Scholar 

  7. B. Henderson, G.F. Imbusch, Optical Spectroscopy of Inorganic Solids (Clarendon, Oxford, 1989)

    Google Scholar 

  8. M. de Jong, L. Seijo, A. Meijerink, F. Rabouw, Phys. Chem. Chem. Phys. 17, 16959 (2015)

    Article  Google Scholar 

  9. E.J. Heller, J. Chem. Phys. 62, 1544 (1975)

    Article  CAS  Google Scholar 

  10. E.J. Heller, Acc. Chem. Res. 14, 368 (1981)

    Article  CAS  Google Scholar 

  11. J.I. Zink, K.S. Shin, Advances in Photochemistry, vol. 16 (Wiley, New York, 1991), pp. 119–214

    Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Zoila Barandiarán .

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Barandiarán, Z., Joos, J., Seijo, L. (2022). Calculations of Local Properties of Luminescent Materials. In: Luminescent Materials. Springer Series in Materials Science, vol 322. Springer, Cham.

Download citation

Publish with us

Policies and ethics