 # Calculation of phonon eigenvector

Dear Julian,

I want to calculate the phonon eigenvector. When I included the keyword include_imaginary in input file, the eigenvector I got still has three columns of data. So I wonder if GULP can calculate the imaginary parts of phonon eigenvector.

Moreover, I got the following eigenvectors in which each mode has three columns. Can I understand these data as the displacement of atoms deviating from their equilibrium positions? Thanks very much.
Best regards,
Junwei

Hi Junwei,
The keyword you refer to isn’t connected to this - it’s to include imaginary modes in phonon dispersion and DOS plots. GULP definitely calculates imaginary phonon eigenvectors, but of course only if you’re not at the Gamma point (since what would be the point as they’re all zero). From your output I’d guess you’re at Gamma.
In terms of meaning, the eigenvectors aren’t displacements since in the harmonic approximation the atoms don’t move from their optimised positions. The eigenvectors represent the direction of motion during vibration, but they are normalised and as atoms vibrate the sign flips from + to -.
Hope that helps,
Julian

Dear Julian,
Thanks very much for your reply. I am asking you about atomic displacements because I want to calculate the phonon eigenvector periodicity (EP), according to the expression: where e and s are the real and imaginary parts of the eigenvector, respectively. ri0 is the optimized position of i-th atom, ri is the position of i-th in a given mode. As far as I understand, ri0, e and s can be calculated by GULP. Now my question is how to get the position ri of i-th atom in a given mode. As you replied, the eigenvectors represent the direction of motion during vibration. So I wonder if we can get the motion position ri according to the eigenvector.

Thanks very much for kind help.

I’m not familiar with this quantity and so I think you’ll have consult the article where you found it for more details I’m afraid. The only positions you have are the equilibrium atom coordinates. To go beyond this based on vibration would be time-dependent and since time doesn’t appear it’s hard to speculate as to the definitions. I’d recommend talking to whoever wrote the paper for more info.

Thanks very much for your kind help.
Best regards