I am running phonon calculations at finite q-points. I noticed in the ABINIT output that the reciprocal lattice vectors are defined using the crystallographic convention, where \mathbf{R}_i \cdot \mathbf{G}_j = \delta_{ij} (rather than the physics convention of 2\pi\delta_{ij}).
My question is: When ABINIT outputs the final absolute wavevector (e.g., in Cartesian coordinates in the output file or netCDF files), is the 2\pi factor automatically multiplied back into the physical q-point, or are the outputted Cartesian coordinates strictly in units of 1/\text{Bohr}?
I wanted to overlay some points from a Neutron scattering experiment onto my finite-q points and is having some trouble with the unit conversion.
good question, this is a delicate point with many conventions in experiments as well. Abinit gives you Cartesian q vectors by taking q_red and multiplying by gprimd, the dimensionful (bohr-1) reciprocal lattice vectors G which you define above. These do not contain the 2 pi factor, which is added in when needed for exponential phase factors etc. If you tell us more precisely which output you are looking at we can point you to the corresponding source file to check.
To be specific about my workflow: I am calculating phonon dispersions by explicitly defining reduced q-points in my input file using the qpt variable (e.g., scanning a path like qpt 2K 0.0 K for a body-centered tetragonal STO cell, K = 1/10).
I am overlaying my calculated phonon frequencies directly against Inelastic Neutron Scattering (INS) data. The experimentalists plot their data using the reciprocal lattice index H as their X-axis, where their absolute momentum is defined using the physics convention: \mathbf{Q} = \frac{2\pi}{a_{cub}}(H, H, 0) for the cubic cell, which becomes tetragonal in the temperature they do the measurements of the phonon dispersion.
Based on your answer, here is my conclusion—could you confirm if this is mathematically correct?
Because my input qpt values (K) and the experimental values (H) are both reduced, dimensionless coordinates representing a fraction of the Brillouin Zone (where 0.5 reaches the physical zone boundary in both cases), I can map my qpt values \sqrt{2}:1 with the experimental H values for the overlay(to correct for the tetragonal cell oriented along the diagonals of the cubic cell). The missing 2\pi factor in ABINIT only becomes an issue if I try to convert both datasets into absolute Cartesian space (e.g., 1/\text{\AA} vs 2\pi/\text{\AA}).
Is it correct that as long as I stick to comparing reduced qpt coordinates to experimental H indices, no 2\pi scaling factor is required?