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