[CP2K-user] [CP2K:22372] Help tuning HSE exact-exchange fraction for AlN band gap in CP2K

[Thomas Kühne]

Dear Asif,

there are two separate issues here: defining the functional consistently and
converging it.

First, alpha is not merely an SCF parameter. Standard HSE06 uses alpha = 0.25
and omega = 0.11 bohr^-1. If alpha is tuned, the short-range HF term and the
complementary short-range PBE exchange must be changed together.

When HYB_GGA_XC_HSE06 from LibXC is used, changing only &HF/FRACTION leaves
the semilocal HSE mixing at its original HSE06 value. This therefore no longer
defines a consistent tuned HSE functional.

A transparent native CP2K definition for alpha = 0.20 is:

&XC
  &XC_FUNCTIONAL
    &PBE
      SCALE_C 1.0
      SCALE_X 0.0
    &END PBE
    &XWPBE
      OMEGA 0.11
      SCALE_X -0.20
      SCALE_X0 1.0
    &END XWPBE
  &END XC_FUNCTIONAL
  &HF
    FRACTION 0.20
    &INTERACTION_POTENTIAL
      OMEGA 0.11
      POTENTIAL_TYPE SHORTRANGE
    &END INTERACTION_POTENTIAL
  &END HF
&END XC

The value in FRACTION and the negative value in XWPBE/SCALE_X must contain
the same alpha. Your existing screening and ADMM settings can be retained.

For convergence, I recommend continuation instead of jumping directly from
alpha = 0.15 to a fresh alpha = 0.20 calculation:

1. Converge PBE or alpha = 0.15.
2. Restart successively with alpha = 0.17, 0.19 and 0.20.
3. Use the converged wavefunction from each step as the initial guess for the
   next one.
4. First converge only the occupied ground state with OT, for example:

&SCF
  SCF_GUESS RESTART
  EPS_SCF 1.0E-7
  MAX_SCF 25
  &OT
    MINIMIZER CG
    PRECONDITIONER FULL_ALL
    ENERGY_GAP 0.001
    LINESEARCH 3PNT
  &END OT
  &OUTER_SCF
    EPS_SCF 1.0E-7
    MAX_SCF 10
  &END OUTER_SCF
&END SCF

5. After the occupied state has converged, perform a separate restart using
   conventional diagonalization and ADDED_MOS to calculate the conduction
   states and band gap. Do not combine OT and ADDED_MOS.

A NaN in the first SCF step is not ordinary slow convergence. Changing the
mixing method cannot repair invalid arithmetic. Remove a stale or incompatible
restart wavefunction, retry once with SCF_GUESS ATOMIC, and inspect the complete
output for overlap, basis-set or integration-grid problems.

I would also verify the ADMM auxiliary basis and repeat a smaller calculation
without ADMM as a reference.

Finally, do not calibrate alpha only until one Gamma-point supercell
eigenvalue difference equals 6.1 eV. First converge cutoff and REL_CUTOFF,
supercell or k-point sampling, ADMM, and the structural parameters. The
experimental gap also depends on temperature, electron-phonon effects and
whether it is being compared with a Kohn-Sham or quasiparticle gap.

If you attach the complete input and the output up to the first NaN, the
immediate numerical cause can be diagnosed more specifically.

Best regards,
Thomas

> Am 29.07.2026 um 06:32 schrieb Asif Billah <asifbillah010 at gmail.com>:
> 
> Hello CP2K community,
> 
> I am calculating the bulk AlN band gap using CP2K 2024.1 with HSE, ADMM, a 72-atom 3x3x2 wurtzite supercell, and Gamma point sampling. My target band gap is approximately 6.1 eV.
> 
> Using standard diagonalization, Broyden mixing, ADMM_PURIFICATION_METHOD NONE, and alpha=0.15, I obtained a converged gap of:
> 
> Band gap = 5.267211 eV
> However, when I used alpha=0.20, the SCF initially approached about 5.7 eV but later diverged catastrophically. A retry with DIRECT_P_MIXING and a level shift produced a NaN in the first SCF step.
> 
> Could you please advise: What is the recommended stable procedure or strategy so that the calculated bandgap reaches 6.1 eV using HSE calculations with ADMM? 
> 
> Any guidance would be greatly appreciated.
> 
> Thank you.
> 
> 
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