Conversion from phonon modes to force constants

[ajjackson]

One of Euphonic's main jobs is to efficiently convert force constants to phonon modes. This allows e.g. numerical powder averaging over many q-points to be performed given outputs of codes such as CASTEP or Phonopy that provide force constants.

However, the reverse transformation QpointPhononModes -> ForceConstants could also be very useful. A similar transformation from dynamical matrices to to force constants is made in e.g. CASTEP to convert from DFPT results on a Gamma-centered mesh to the force constants of an equivalent supercell. Converting from a non-commensurate lattice would be an interesting but more difficult (i.e. numerical fitting) problem, and is out-of-scope for this Issue.

This ability to convert a set of QpointPhononModes to ForceConstants would be especially useful with external codes like GULP or CRYSTAL which, as far as I can tell, do generate supercell force constants internally but do not expose them to the user in a useful format. With such a code one could specify a mesh (as though constructing a DOS...) and use the results to reconstruct the ForceConstants in Euphonic for further manipulation and interpolation.

This would benefit from input of @DBJochym and @krefson