Inconsistency of nonlinear optical susceptibility between DFPT and Sum-over-States methods

Running Abinit Response calculations
1

Dear All,

Thanks for this wonderful platform. I recently am calculating frequency dependent nonlinear optical susceptibility, e.g., SHG. Previously I’ve calculated the same d_ij tensor using DFPT method (which is zero-freqency limit). I thought it would be good to see the consistent result in Sum-over-States method with frequency approaching to zero.

I am working on d_{33} (a half of \chi^2_{333}) component of AlN.

In both DFPT and Sum-over-States methods, I’ve testes the convergence of ngkpt, nband and ecut:

  1. In DFPT, I used ngkpt=16x16x10 and ecut=50 Ha, I got d_{33}=-4.147693 pm/V.
    tnlo_6.abi (4.5 KB)
    anaddb.in (835 Bytes)
    mrgddb.in (90 Bytes)
    nlo_files.in (97 Bytes)

  2. In Sum-over-States method, I used ngkpt=16x16x10, nband=80 and ecut=50 Ha (which already converges), I got d_{33}=-9.833838/2=-4.916919 pm/V.
    sum_over_states.abi (4.9 KB)
    post_sos_optic.abi (1.2 KB)

Two results are not very consistent, the error is almost 20%.

Thus I have the following confusion:

  • What causes this large deviation? I understand these two methods are intrinsically different. I also tested other materials and found this deivation seems to be general.

Below I attached my input files for both methods. I really appreciate if you could help out here. Thanks.

Best

Haochen