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Calculations of Local Properties of Luminescent Materials

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

Abstract

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.

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Notes

  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 \(\Delta Q_k = \Delta Q_{a_{1g}} = \sqrt{8}~\Delta d_\mathbf{Ln}-L \).

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Correspondence to Zoila Barandiarán .

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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. https://doi.org/10.1007/978-3-030-94984-6_3

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