Energy Difference Between OT and Diagonalization in CP2K

[yis...@163.com]

To the CP2K Development Team,

Hello!

      I  would like to raise another question: why is there a discrepancy in the calculated energies when using the OT (Orbital Transformation) method compared to the diagonalization method? 

        I started with the NiO₂ unit cell (5.6512 Å × 5.6512 Å × 4.3886 Å). Due to its small size, I expanded it into supercells and performed calculations using the OT method. As shown in the attached table, I constructed supercells of sizes 2×2×2, 3×3×3, 3×3×4, and 4×4×4. The energies per NiO₂ unit cell obtained were –805.2913786 Ha, –805.2931813 Ha, –805.2932437 Ha, and –805.2931291 Ha, respectively, with relative energy differences of –1.803×10⁻³ Ha, –6.232×10⁻⁵ Ha, and 1.145×10⁻⁴ Ha. The results indicate that the energy converges to –805.2932437 Ha per unit cell when the supercell is expanded to 3×3×4.

          Additionally, I tested the diagonalization method with k-point sampling. Using k-point grids of 4×4×4, 5×5×5, 6×6×6, and 7×7×7, the energies per NiO₂ unit cell were –805.2394556 Ha, –805.2394471 Ha, –805.2395249 Ha, and –805.2394426 Ha, respectively, with relative differences of 8.512×10⁻⁶ Ha, –7.782×10⁻⁵ Ha, and 8.234×10⁻⁵ Ha. The energy converges to –805.2394556 Ha per unit cell with a 4×4×4 k-point grid.
         Although both methods appear to converge individually, there is a significant discrepancy of about 0.0538 Ha (~1.46 eV) between the two results, which cannot be overlooked. Could you please help explain the possible reasons for this difference?
          For reference, I have attached the relevant test results and input/output files:
         cp2k_K444.inp and cp2k_K444.out: input and output files for the diagonalization calculation with a 5×5×5 k-point grid.
        cp2k_SP334.inp and cp2k_SP334.out: input and output files for the OT method calculation with a 3×3×4 supercell.
        nio2.cif: the unit cell file used in the calculations.

A figure summarizing the energy convergence with respect to supercell size and k-point sampling.

I welcome any feedback or suggestions from the developers. Thank you for your time and assistance!

Best regards,

yisichi

[Jürg Hutter]

Hi

Please note that you forgot to specify the vdW correction (D3) in the k-point
calculations.
Make sure that the vdW energy is also converged in both calculations (cutoff!).

best
JH

________________________________________
From: cp...@googlegroups.com <cp...@googlegroups.com> on behalf of yis...@163.com <yis...@163.com>
Sent: Monday, January 26, 2026 4:23 AM
To: cp2k
Subject: [CP2K:22065] Energy Difference Between OT and Diagonalization in CP2K

To the CP2K Development Team,

Hello!

I would like to raise another question: why is there a discrepancy in the calculated energies when using the OT (Orbital Transformation) method compared to the diagonalization method?
I started with the NiO₂ unit cell (5.6512 Å × 5.6512 Å × 4.3886 Å). Due to its small size, I expanded it into supercells and performed calculations using the OT method. As shown in the attached table, I constructed supercells of sizes 2×2×2, 3×3×3, 3×3×4, and 4×4×4. The energies per NiO₂ unit cell obtained were –805.2913786 Ha, –805.2931813 Ha, –805.2932437 Ha, and –805.2931291 Ha, respectively, with relative energy differences of –1.803×10⁻³ Ha, –6.232×10⁻⁵ Ha, and 1.145×10⁻⁴ Ha. The results indicate that the energy converges to –805.2932437 Ha per unit cell when the supercell is expanded to 3×3×4.

[微信图片_20260126112239_276_77.png]

Additionally, I tested the diagonalization method with k-point sampling. Using k-point grids of 4×4×4, 5×5×5, 6×6×6, and 7×7×7, the energies per NiO₂ unit cell were –805.2394556 Ha, –805.2394471 Ha, –805.2395249 Ha, and –805.2394426 Ha, respectively, with relative differences of 8.512×10⁻⁶ Ha, –7.782×10⁻⁵ Ha, and 8.234×10⁻⁵ Ha. The energy converges to –805.2394556 Ha per unit cell with a 4×4×4 k-point grid.
Although both methods appear to converge individually, there is a significant discrepancy of about 0.0538 Ha (~1.46 eV) between the two results, which cannot be overlooked. Could you please help explain the possible reasons for this difference?
For reference, I have attached the relevant test results and input/output files:
cp2k_K444.inp and cp2k_K444.out: input and output files for the diagonalization calculation with a 5×5×5 k-point grid.
cp2k_SP334.inp and cp2k_SP334.out: input and output files for the OT method calculation with a 3×3×4 supercell.
nio2.cif: the unit cell file used in the calculations.

A figure summarizing the energy convergence with respect to supercell size and k-point sampling.

I welcome any feedback or suggestions from the developers. Thank you for your time and assistance!

Best regards,
yisichi

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[yis...@163.com]

Thank your very much

[yis...@163.com]

Thank you for your reply. The issue was indeed due to inconsistent settings in the two input files—this was my oversight. I would also like to express my special thanks for the CP2K software you have developed. It performs remarkably fast in DFT calculations and offers comprehensive functionality.

However, I have a couple of questions I would like to ask:

1. When will the built-in OT algorithm in CP2K support k-point calculations?

2. Regarding the RI-HFX method currently used in CP2K for hybrid functional calculations, is it currently limited to systems with fewer than 10 atoms? When will it support larger systems, such as supercells with around 10 to 100 atoms?

在2026年1月26日星期一 UTC+8 17:21:55<Jürg Hutter> 写道：