[Phonopy-users] eigenvector and displacement of phonon

[김수란 <lor...@gm...>]

Hello

During the study of formulations page in phnonopy homepage,
I found a strange thing.

http://phonopy.sourceforge.net/theory.html#dynamical-matrix

In this section, until third equation,
[image: \sum_{j \alpha j' \beta}e_\alpha(j',\mathbf{q}\nu)^*
D_{\alpha\beta}(jj',\mathbf{q}) e_\beta(j',\mathbf{q}\nu') =
[\omega(\mathbf{q}\nu)]^2 \delta_{\nu\nu'}.]

eigenvector *e *follows Sigma(e*e)"m_j"=delta

However the output eigenvector in phononpy follows Sigma(e*e)=delta.
(Which is written in phonopy-workshop.pdf in homepage)
And this output eigenvector is used for calculating displacement using
forth equation.

Therefore eigenvectors in third equation and forth equation look different
i.e. eigenvector in third equation follows  Sigma(e*e)"m_j"=delta
eigenvector in  forth equation follows Sigma(e*e)=delta

Which one is the really calculated in phonopy??
eigenvector in third equation or eigenvector in forth?

p.s. minor bug report in moulation.yaml.
 I used phonopy 1.6.2 version. When I calculated the multi modulation,
e.g. MODULATION = 1 1 1, 1/2 0 1/2 1 1, 1/2 1/2 1/2 1 1
The q-position above the eigenvector not displacement
always is written last q position (in this case 1/2 1/2 12)

So I think there should be  q = mode[0] at line 248 in modulation.py.

Best regards
Sooran Kim