Is it in principle possible to calculate the dispersion relation of phonons in a crystal from the crystal structure?

  • $\begingroup$ From just the crystal structure? Compare silicon with germanium (fairly easy to find). They are both diamond cubic semiconductors, and neither the electronic band structure nor the phonon dispersion curves are identical. Similar, yes, not identical. $\endgroup$
    – Jon Custer
    Sep 21, 2023 at 21:29

1 Answer 1


It is impossible to calculate the phonon dispersion relation from only information about the crystal structure. Phonons originate from the quantization of the normal mode approximation of the atomic dynamics in a crystalline solid. The normal mode approximation, in turn, is derived from a linearization of the interatomic forces. Therefore, forces are a critical ingredient, and it is impossible to obtain interatomic forces by only knowing the crystalline structure.

  • $\begingroup$ Isn't the input to a DFT calculation just the crystal structure? $\endgroup$ Sep 21, 2023 at 22:48
  • $\begingroup$ @HiddenBabel Not only the crystal structure. Ionic charges, electron-ion pseudopotentials, and exchange-correlation potentials are the key ingredients that allow the difference between phonon spectra in different materials with the same crystalline structure. $\endgroup$ Sep 22, 2023 at 5:57
  • $\begingroup$ I also mean that I know the location of all the atoms in the structure and know roughly all bond lengths and approximate strengths $\endgroup$
    – I'm Batman
    Sep 26, 2023 at 14:26
  • 1
    $\begingroup$ @I'mBatman bond lengths and location of the atoms are not required. One needs the force constants in harmonic approximation and masses. $\endgroup$ Sep 26, 2023 at 15:41

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