# Phonon eigenvectors

Hi Dr. Gale,

Apologies for asking so many questions recently. I modified example5 to print out the phonon eigenvectors for MgO, but I find they are all zero except at the Gamma point. Do you know what the reason for this is? I’m running v6.1.1. Input file and .eig file attached.

Connor

example5.gin (538 Bytes)
example5.eig (48.4 KB)

Hi Connor,
No need to apologise for asking questions and especially this one. Unfortunately there was a bug in the code related to changes made when the option to phase or unphase eigenvectors (as well as mass weighting options) were added. At some point the logic of a variable was inverted, but this got missed in one location and so the problem was caused by 5 missing characters for a “.not.”.
This is now fixed in the general tar file 6.1 and I’ve added 6.1.2 as a fixed point release to capture the correction.
Best regards,
Julian

Hi Dr. Gale,

Thank you very much - I updated to 6.1.2 and GULP now prints all the eigenvectors. I did have one more question about this: forgive me if I’m wrong, but I thought eigenvectors at +k and -k are related by complex conjugation. To confirm this, I evaluated the eigenvectors at (0.25,0.25,0.25) and (-0.25,-0.25,-0.25) in MgO. The rule holds for modes 3 and 6 in the .eig file attached, but not for the other 4 modes. Could you let me know if I’m missing a keyword somewhere?

Thank you for all your help,

Connor

example5.eig (2.1 KB)
example5.gin (616 Bytes)

Hi Connor
You are correct in that the eigenvectors should be related by the fact that one set is the complex conjugate of the other since they only differ in the sign of k. If you look at the modes at 368.5 and 776.6 cm^-1 then this is indeed true, as you say, because they are non-degenerate. The problem with degenerate modes is that you can take an arbitrary linear combination of the modes (subject to remaining orthonormal) to create two new modes. Because of this mixing the exact eigenvectors are sensitive to numerical noise and other factors during the diagonalisation. What is happening is that the two k points are ending up with different mixtures of the eigenvectors, which leads to them not being related by the complex conjugate property. However, if you were to take the complex conjugate at one k point and apply it to the dynamical matrix of the other then it should be a valid set of eigenvectors to diagonalise the matrix. If you break the symmetry of the system slightly to remove the degeneracy then this should also lead to a set of eigenvectors that have the appearance you are seeking.
Best regards,
Julian