Help tuning HSE exact-exchange fraction for AlN band gap in CP2K

[Asif Billah]

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.

[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

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