# Interpretation of phonon eigenvectors

Hi Dr. Gale,

I was reading through the attached forum post and I wanted to confirm the meaning of the “eigv mass” switch that was recently added to GULP. When

eigvector_type mass-unweighted

is added to a *.gin file, does GULP solve the equations of motion by assuming an ansatz such as (18) in the *.pdf attached, where all the displacements are weighted by the inverse square root of the masses? Does this in tum mean that the eigenvectors in the *.eig files are solutions of en equation such as (21) [ie. the dynamical matrix is weighted by

\frac{1}{\sqrt{m_b m_{b'}}}

and the eigenvectors are themselves dimensionless?]

Thank you for your help, as always,

Connor

715_ch4.pdf (316.4 KB)

Hi Connor
Normally the eigenvectors are those that diagonalise the second derivative matrix multiplied by the inverse square root masses (as per your formula). If you specify the new option then the eigenvectors are re-weighted by the mass of the atom, divided by the sqrt root of the sum of the squares of the masses times the eigenvectors squared (to renormalise). The code can be seen in peigen for example. Strictly speaking the eigenvectors are always unitless since it’s the eigenvalues which have the units. Hope this helps a bit. I can try to write the formal equations next week.
Best regards

Julian

Hi Dr. Gale,

Thank you for your reply. If you have time to write out the equations, that would be wonderful, but otherwise, I think everything is very clear from your answer.

Thank you again,

Connor

Hi Connor,
I’ll attach some text from a new section that will be added to the manual with the equations.
Best regards,
eigenvectors.pdf (117.7 KB)

Julian

Hi Dr. Gale,

This is excellent - thank you!

Connor