Question: a rough test indicates the accuracy of grid integration cannot converge to < 1 kcal/mol level smoothly

[kirk0830]

Describe the bug

I am working on exploring the possibility to evaluate energies with ABACUS LCAO with so-called chemical accuracy (< 1 kcal/mol). The keyword ecutwfc in LCAO case is for controlling the precision of grid integration. However, I find the following behavior:

regular scale. If we plot in logscale, we can find ...

I generate some spherical waves (with different kinetic energy. Higher kinetic energy indicates the basis function oscillates more significantly) as basis functions, then use vion_in_h 0 to explicitly exclude the local term in pseudopotential (which is the term also involves grid integration). Then I can evaluate the precision and convergence behavior of grid integration straightforwardly.

The range I vary the ecutwfc is from 50 to 200 Ry. The energy difference w.r.t. the last point (with the highest ecutwfc) can not smoothly decrease, this is quite unexpected and indicates now the data yield from ABACUS LCAO calculation has uncertainty of 1 kcal/mol. I think this is a numerical problem that needs more developers focus on.

Expected behavior

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To Reproduce

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Environment

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Additional Context

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