Anomalous large Ga forces for unperturbed 5×5×5 GaAs supercell in v3.10.1 using HSE functional

[spinodal2025]

Details

I encountered a possible issue in ABACUS v3.10.1 when performing calculation on unperturbed 5×5×5 GaAs supercell using HSE funtional with “cal_force” swithed on.

For 5×5×5 supercell, the calculated forces on Ga atoms are anomalously large, while the forces on As atoms are small and seem reasonable. However, when I run the same calculation with the same INPUT file for unperturbed 4×4×4 GaAs supercell, the forces on both Ga and As atoms are zero.

I wonder whether there may be some issue related to the HSE Hamiltonian for 5×5×5 GaAs supercell.

I have attached the input files for both cases, in GaAs supercell.zip:
Folder “444”: INPUT, KPT, STRU, abacus.std and running_scf.log for the 4×4×4 supercell
folder “555”: INPUT, KPT, STRU, abacus.std and running_scf.log for the 5×5×5 supercell
folder “dftdata”: pseudopotentials and atomic orbitals

Additional information:
Both the 4×4×4 and 5×5×5 unperturbed supercell STRU files were generated by phonopy
The unit cell was fully relaxed before supercell generation, and relaxation thresholds were “stress_thr”= 1e-4 and “force_thr”= 1e-6

GaAs supercell.zip

Have you read FAQ on the online manual http://abacus.deepmodeling.com/en/latest/community/faq.html

• Yes, I have read the FAQ part on online manual.

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[dyzheng]

Case: Non-zero Atomic Forces in 5×5×5 GaAs Supercell

Abnormal force calculation caused by a mismatch between the FFT grid and symmetry

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Problem Description

Phenomenon

Case	FFT Grid	Atomic Forces on Ga Atoms
Unit cell with 4×4×4 k-points	-	0
Unit cell with 5×5×5 k-points	-	0
4×4×4 supercell	200×200×200	0
5×5×5 supercell	243×243×243	Non-zero

Excluded Causes

• ✅ Point group and space group are fully consistent
• ✅ Dense k-point sampling
• ✅ SCF convergence

---

Root Cause Analysis

Mismatch Between FFT Grid and Symmetry

Core Issue: 243 is not a symmetry-friendly number

Analysis of FFT grids:
  4×4×4 supercell: 200×200×200
    - 200 = 8 × 25
    - Divisible by 2, 4, 5, 8, 10, etc.
    - Symmetry-friendly

  5×5×5 supercell: 243×243×243
    - 243 = 3^5
    - Only divisible by 3, 9, 27, 81
    - **Not divisible by 2!**

Problem Mechanism:

1. GaAs belongs to the T_d point group, which contains 4-fold rotation axes
2. 4-fold rotation requires the FFT grid to be a multiple of 4
3. 243 is not a multiple of 4
4. Grid points cannot be perfectly mapped during charge density symmetrization
5. Leading to errors in the local charge distribution
6. Introducing errors in the calculation of E_xc and atomic forces

Mathematical Verification

243 / 4 = 60.75  ← Not an integer!

90° rotation symmetry operation:
  Point → Rotated point
  If the grid is not a multiple of 4, points may not lie on grid nodes

---

Knowledge Base Association

Relationship with rho_symm

From wiki/concepts/physical-quantities/charge-density-states.md:

rho_mix --symmetrized_to(EXTRACTED)--> rho_symm

symmetrize_step:
  function: Symmetry_rho::begin()
  process:
    1. FFT: ρ(r) → ρ(G)  (Real space → Reciprocal space)
    2. Symmetrization: ρ(G) → ρ_symm(G)
    3. IFFT: ρ_symm(G) → ρ_symm(r)

Key Point: Symmetrization is performed in reciprocal space, but the result is transformed back to real space via IFFT. Incompatibility between the FFT grid and symmetry operations causes numerical errors.

Relationship with the symmetry parameter

From wiki/parameters/symmetry.md:

void Symmetry_rho::begin(...) {
    // Executed when symmetry = 1:
    real2recip(rho, rhog);    // FFT
    psymmg(rhog);             // Symmetrization (based on point group)
    recip2real(rhog, rho);    // IFFT
}

Issue: psymmg() yields errors if the FFT grid is incompatible with the applied symmetry.

---

Solutions

Solution 1: Adjust ecutwfc to obtain a suitable FFT grid

# Calculate appropriate ecutwfc
# Goal: FFT grid is a multiple of 4

# 5×5×5 supercell, assuming lattice constant a = 5.65 Å
# Target FFT grid: 244×244×244 (closest to 243 and a multiple of 4)

# Back-calculate ecutwfc
# FFT grid n = int(2 * sqrt(2 * ecutwfc) * a / π) + 1
# 244 ≈ 2 * sqrt(2 * ecutwfc) * 5.65 * 5 / π
# ecutwfc ≈ 85 Ry

# INPUT
ecutwfc = 85  # Adjust to set FFT grid to 244

Solution 2: Disable symmetry

# INPUT
symmetry = 0  # Disable charge density symmetrization

# Note: Increases computational cost but avoids symmetry-related errors

Solution 3: Use an even-multiple supercell

# Use 6×6×6 supercell instead
# FFT grid is more likely to be a multiple of 4

[dyzheng]

Another method of Solution 1 is setting nx 250 and ny 250 and nz 250 without change ecutwfc.