[QE-users] The grid for wave functions in real space;

[Taghipour, Zahra]

Dear developers,

I have a question regarding the grid QE uses to define the wave functions in real space.
After reading the developer’s manual and the conversations in the forum, I realize that the grid in which QE uses to express the wave functions is the “smooth grid” determined by nr1, nr2, nr3 (right?). On the other hand, looking at the file “gvectors.dat” which supposedly includes the G-vectors in the calculation (determined by the condition \hbar^{2} (\vec{k}+\vec{G})^2 <= 2m e_{cutoff_wfc} for each \vec{k}) I see that the number of these G-vectors is less than nr1*nr2*nr3.
If I understand correctly, the reason is QE generates a box (instead of the sphere in the cutoff condition, above) to do the FFT and Inverse FFT; So, it contains more points.
Now to my question:
I want to calculate the oscillator strength matrix elements, i.e. \langle n,k | e^{i \vec{q+G} \cdot \vec{r} } | m, k’ \rangle where |n,k \rangle are the KS wave functions. It should be straightforward to do this given the G-vectors in the gvectors.dat and the periodic part of wave functions in evc.dat but I have a hard time finding which grid point in real space to assign to each part of the wave function.
There are as many points for each wave function in real space as there are for G-vectors which makes sense I think because \vec{G} and \vec{r} are Fourier duals, but less than nr1*nr2*nr3. For my task, can I use the 3D-to-1D indexing method described in the developer’s manual (ind = i + (j - 1) * nr1 + (k - 1) * nr2 * nr1) to extract the grid points for the wave function, or is there another/better way?

I appreciate your help.
Zahra Taghipour
Research Scientist,
Electrical and Computer Engineering, Ohio State University, Columbus, OH

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