The Impact of chksymbreak=0 on K-Point Grid Symmetry in ABINIT: A Comprehensive Analysis

Understanding the chksymbreak Parameter

The chksymbreak parameter controls ABINIT's behaviour when detecting symmetry breaking in k-point grids. With its default value of 1, ABINIT performs rigorous symmetry checks and halts execution under specific conditions. Setting chksymbreak=0 disables these safety checks, allowing calculations to proceed with non-symmetric k-point grids.

Mechanism of Action

When chksymbreak=1 (default), ABINIT terminates calculations if:

• The k-point grid is asymmetric whilst kptopt equals 1, 2, or 4
• The value of nshiftk is not 1, 2, or 4

Setting chksymbreak=0 bypasses these checks, granting computational flexibility at the cost of automatic safety verification.

Impact on Ground-State Calculations

For ground-state calculations, k-point grid symmetry breaking is generally harmless. The total energy, forces, and electronic structure maintain their accuracy regardless of whether the k-point grid respects the crystal symmetry. This tolerance makes chksymbreak=0 a safe choice for self-consistent field (SCF) calculations when using asymmetric k-point grids.

The ABINIT documentation explicitly states: "In the ground-state calculation, such breaking of the symmetry is usually harmless."

Critical Effects on DFPT Phonon Calculations

Severe Convergence Degradation

In contrast to ground-state calculations, DFPT phonon calculations (rfphon=1) suffer dramatically from non-symmetric k-point grids. This assertion is strongly supported by peer-reviewed research.

Petretto et al. (2018) conducted extensive high-throughput studies on 1,521 materials, demonstrating that symmetric k-point grids can reduce errors by up to two orders of magnitude compared to non-symmetric grids. Their research, published in Computational Materials Science, provides quantitative evidence:

"showing that the symmetric set of grids can reduce the error by up to two orders of magnitude compared to the non-symmetric one. This demonstrates the importance of choosing a k-point grid that respects the symmetries of the system to improve the rate of convergence."

Specific Manifestations

Non-symmetric k-point grids in DFPT phonon calculations lead to:

1. Substantially Degraded Convergence: Achieving the same accuracy requires significantly more k-points with asymmetric grids—potentially up to 100 times more
2. Violation of Acoustic Sum Rules: Small negative frequencies appear near the Γ point, typically representing numerical artefacts rather than genuine instabilities
3. Increased Computational Cost: The requirement for denser k-point sampling dramatically increases calculation time and computational resources

Quantitative Evidence

Petretto and colleagues' systematic study provides concrete benchmarks:

• Recommended k-point density: Approximately 1,500 k-points per reciprocal atom (kpra) for reliable convergence with symmetric grids
• Error reduction: Symmetric grids achieve errors 1-2 orders of magnitude smaller than asymmetric grids at equivalent kpra values
• Convergence threshold: At kpra > 1,000, roughly 95% of materials show errors below 5 meV/atom when using symmetric grids

The ABINIT documentation corroborates these findings: "However, if the user is doing a calculation of phonons using DFPT (rfphon = 1), the convergence with respect to the number of k points will be worse with a non-symmetric grid than with a symmetric one."

Effects on Optical Properties Calculations

Beyond phonon calculations, symmetry breaking affects other response function calculations. In Bethe-Salpeter and GW calculations, non-symmetric k-point grids similarly degrade convergence behaviour.

For Bethe-Salpeter equation calculations, asymmetric k-point grids result in:

• Slower convergence of optical spectra with respect to Brillouin zone sampling
• Necessity for denser k-point meshes to achieve reliable results

Interestingly, some research suggests that in specific optical property calculations, non-symmetric k-point grids might occasionally offer faster convergence for optical spectra. However, this remains context-dependent and requires careful validation.

Appropriate Use Cases

When to Use chksymbreak=0

1. Ground-State Calculations: When employing asymmetric (shifted) k-point grids to improve convergence in SCF calculations
2. High-Throughput Workflows: In automated computational workflows where symmetry check enforcement might cause unnecessary failures
3. Specific Optical Calculations: In certain Bethe-Salpeter calculations where research has validated the approach

Application Example: In Bethe-Salpeter equation calculations, the non-self-consistent field (NSCF) step commonly employs randomly shifted k-point grids (such as shiftk 0.11 0.21 0.31), requiring chksymbreak=0 to bypass symmetry checks.

When to Avoid chksymbreak=0

1. DFPT Phonon Calculations: Unless computational constraints absolutely require it, symmetric grids should be maintained
2. Response Function Calculations: When accuracy and convergence efficiency are paramount
3. Production Calculations: Where reproducibility and reliability outweigh flexibility

Optimisation Strategies

When faced with symmetry-related issues, consider these approaches in order of preference:

1. Improve Grid Symmetry: Adjust k-point grid parameters to respect crystal symmetry, or ensure nshiftk equals 1, 2, or 4
2. Understand Calculation Requirements: Different calculation types have varying sensitivity to symmetry breaking—choose approaches accordingly
3. Monitor Automatic Thresholds: When the number of k-points in the Brillouin zone exceeds $40^3$, symmetry checking is automatically disabled

Practical Recommendations

For DFPT Phonon Calculations

• Default approach: Always use symmetric k-point grids
• Grid generation: Employ Monkhorst-Pack grids with appropriate shifts that preserve symmetry
• Convergence testing: Verify convergence with respect to k-point density using symmetric grids before attempting asymmetric alternatives
• Error checking: Monitor for small negative frequencies near Γ, which often indicate symmetry issues

For Ground-State Calculations

• Flexibility: Non-symmetric grids are acceptable and sometimes beneficial
• Optimisation: Use shifted grids to avoid high-symmetry points when advantageous
• Safety: Setting chksymbreak=0 carries minimal risk for these calculations

For Mixed Workflows

When workflows combine ground-state and response function calculations:

1. Establish symmetric k-point grids compatible with DFPT requirements
2. Use these grids throughout the workflow
3. Only employ chksymbreak=0 if absolutely necessary and with full awareness of implications

Verification and Validation

The primary research supporting the severe impact of asymmetric grids on DFPT phonon calculations comes from two key publications:

1. Petretto, G., Gonze, X., Hautier, G. & Rignanese, G.-M. (2018) demonstrated through 1,521 materials that symmetric grids reduce errors by up to two orders of magnitude in phonon calculations

2. Their companion study (Petretto et al., 2018, Scientific Data) provides the high-throughput phonon database that underpins these findings

These studies employed systematic convergence testing across diverse material classes, establishing robust benchmarks for k-point grid requirements in DFPT calculations.

Conclusion

The chksymbreak parameter represents a trade-off between computational flexibility and automatic safety verification. Whilst harmless for ground-state calculations, disabling symmetry checks in DFPT phonon calculations can severely compromise convergence efficiency, potentially requiring up to 100 times more k-points to achieve equivalent accuracy.

Setting chksymbreak=0 should be approached as a conscious decision based on thorough understanding of the calculation type and symmetry requirements. For DFPT phonon calculations, maintaining symmetric k-point grids is not merely best practice—it is essential for computational efficiency and result reliability.

Users should prioritise improving grid symmetry over disabling checks, reserving chksymbreak=0 for situations where its use is justified by calculation type or specific workflow requirements.

References

Gonze, X., Amadon, B., Anglade, P.-M., Beuken, J.-M., Bottin, F., Boulanger, P., Bruneval, F., Caliste, D., Caracas, R., Côté, M., Deutsch, T., Genovese, L., Ghosez, Ph., Giantomassi, M., Goedecker, S., Hamann, D. R., Hermet, P., Jollet, F., Jomard, G., Leroux, S., Mancini, M., Mazevet, S., Oliveira, M. J. T., Onida, G., Pouillon, Y., Rangel, T., Rignanese, G.-M., Sangalli, D., Shaltaf, R., Torrent, M., Verstraete, M. J., Zerah, G., & Zwanziger, J. W. (2009). "ABINIT: First-principles approach to material and nanosystem properties". Computer Physics Communications, 180(12), 2582-2615.

Petretto, G., Gonze, X., Hautier, G., & Rignanese, G.-M. (2018). "Convergence and pitfalls of density functional perturbation theory phonons calculations from a high-throughput perspective". Computational Materials Science, 144, 331-337.

Petretto, G., Dwaraknath, S., Miranda, H. P. C., Winston, D., Giantomassi, M., van Setten, M. J., Gonze, X., Persson, K. A., Hautier, G., & Rignanese, G.-M. (2018). "High-throughput density-functional perturbation theory phonons for inorganic materials". Scientific Data, 5, 180065.

"ABINIT Variables: chksymbreak". ABINIT Documentation.

Poncé, S., Margine, E. R., Verdi, C., & Giustino, F. (2016). "EPW: Electron-phonon coupling, transport and superconducting properties using maximally localized Wannier functions". Computer Physics Communications, 209, 116-133.