energy cutoff for LCAO

[jinzx10]

Details

Currently the k mesh for LCAO radial Fourier transform (1D integration) is determined by ecutwfc and dk, where ecutwfc comes from INPUT having a typical value ~100, and dk by default is 0.01. For the nonlocal projector beta(r), I checked whether two successive transforms (carried out by Numerical_Nonlocal_Lm::get_kradial()) brings back the original beta(r), and plot the error below. The UPF file used for testing is PP_ORB/O_ONCV_PBE-1.0.upf, and all 4 beta projectors are tested.

The error shows that typical ecutwfc values, which is drawn from the 3D Fourier transform of charge density & wavefunction, might be inadequate for the radial Fourier transform. The convergence with respect to dk is yet to be studied.

[dyzheng]

What will you do with this issue?

[mohanchen]

I will discuss this with zx

[hongriTianqi]

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[jinzx10]

By switchiing to an FFT-based spherical Bessel transform method, this problem is systematically solved by https://github.com/deepmodeling/abacus-develop/pull/2904.