Errors while running scf: "ERROR! Current core has no plane waves! Please reduce the cores." and "psi_norm <= 0."

[xinchenhou]

Describe the bug

When performing SCF calculations for 1000g/cm³ deuterium with single-process single-thread configuration on CPU, different errors occur with different values of ecutwfc (plane-wave cutoff energy in INPUT file):

1. When ecutwfc = 50Ry / 60Ry, the calculation aborts with error "ERROR! Current core has no plane waves! Please reduce the cores."
2. When ecutwfc = 70Ry ~ 130Ry, the calculation aborts with the error "psi_norm <= 0.0."
   All tests use the same input structure and computational parameters except for ecutwfc, and the parallel configuration (1 proc, 1 thread) remains unchanged.

Expected behavior

No response

To Reproduce

input_files.zip

Environment

Device: CPU / Intel(R) Xeon(R) Gold 6132 CPU @ 2.60GHz (x2)
Parallel mode: 1 process, 1 thread
Calculation type: SCF
Material: 1000g/cm³ deuterium

Additional Context

No response

Task list for Issue attackers (only for developers)

• Verify the issue is not a duplicate.
• Describe the bug.
• Steps to reproduce.
• Expected behavior.
• Error message.
• Environment details.
• Additional context.
• Assign a priority level (low, medium, high, urgent).
• Assign the issue to a team member.
• Label the issue with relevant tags.
• Identify possible related issues.
• Create a unit test or automated test to reproduce the bug (if applicable).
• Fix the bug.
• Test the fix.
• Update documentation (if necessary).
• Close the issue and inform the reporter (if applicable).

[Cstandardlib]

In practice, this means that certain k-points end up with no plane waves assigned due to an insufficient wavefunction cutoff energy (ecutwfc) and/or a small simulation cell. Specifically, k-points located far from reciprocal lattice points (i.e., those requiring large |k+G| vectors) may fall outside the kinetic energy cutoff sphere, resulting in zero plane waves being included for those k-points.

[Cstandardlib]

After analyzing the logs and behavior across different ecutwfc values, I believe the root cause is that the number of plane waves (npwx) becomes smaller than nbands, leading to numerical instabilities during the Kohn-Sham equation solving. Here's a breakdown:

1. Low ecutwfc regime (50–60 Ry): "Current core has no plane waves"

Under high compression (small lattice), the reciprocal space grid becomes very sparse. At low energy cutoffs, the spherical cutoff in G-space may contain zero (k+G) vectors for certain k-points, triggering the "no plane waves" error immediately during basis construction.

2. Medium ecutwfc regime (70–130 Ry): psi_norm <= 0.0 in diago_cg.cpp:536

In this range, plane waves do exist, but the basis set remains too small or ill-conditioned. A key piece of evidence from the 130 Ry log:

NBANDS = 10, but npwx = 8

When npwx < nbands, the subspace for wavefunctions is rank-deficient. During CG diagonalization, the orthogonalization step becomes numerically unstable, causing psi_norm to collapse and triggering the early exit at diago_cg.cpp:536.

After all, you cannot extract 10 mutually orthogonal vectors from an 8-dimensional space. The subspace simply does not have enough degrees of freedom.

3. Higher ecutwfc: Issue disappears

As ecutwfc increases further, npwx grows sufficiently to satisfy npwx >= nbands, restoring numerical stability in orthogonalization .