[QE-users] Issues SCAN functional for Cu slab

[Michele Giovanni Bianchi]

Dear QE users,
I am Michele Bianchi, a PhD student from Politecnico of Torino.
I am studying the Cu (111) surface using the meta-GGA SCAN exchange-correlation functional. I am using QE 7.2 version compiled with libxc library (version 6.1.0).
Since I did not find a Cu pseudopotential optimized for SCAN functional, I am using a Norm-Conserving pseudopotential optimized for PBE, as retrieved in the Pseudo Dojo library.
I am aware of the numerical instability issues of the SCAN functional. For that reason, I am using the improved r2SCAN version as proposed by Furness et al. (J. Phys. Chem. Lett.2020, 11, 19, 8208–8215).
Preliminary tests on Cu bulk phase gave me no problems and optimized lattice constant is reasonable.
Problems arise when I simulate a Cu (111) slab (dimension 4x4x6 with a vacuum space of about 15 A). SCF accuracy fluctuates and does not relevantly decrease (as visible below in the reported output file).
I tried to increase the ‘ecutrho’ parameter to get a denser FFT grid and use other Norm-Conserving pseudopotentials developed for PBE, but no visible improvements are achieved.
I believe that issues are associated with the use of the SCAN functional since the same simulation with PBE functional converges. From previous posts (e.g. https://lists.quantum-espresso.org/pipermail/users/2018-November/041688.html), I am aware that systems with exponentially decreasing densities might be tricky to simulate with SCAN functional.

Below I have reported a typical input file and an extract of the output file.
Any suggestion will be appreciated to solve my convergence problem.

Thank you in advance.

Michele Bianchi,
PhD student, Politecnico of Turin, Italy

TYPICAL INPUT SCRIPT:
&CONTROL
  calculation = 'scf'
  restart_mode='from_scratch',
  prefix='Cu_4x4x6_r2scan',
  pseudo_dir = '/pseudo/',
  outdir='./tmp/'
/
&SYSTEM
  ibrav=  4,
  celldm(1) = 19.38,
  celldm(3)= 2.5
  nat=  96,
  ntyp= 1,
  ecutwfc = 80.0,
  occupations='smearing',
  degauss=0.005
  smearing='gauss'
  input_dft = 'r2scan'
/
&ELECTRONS
  diagonalization='david'
  conv_thr =  1.0d-8
  mixing_mode = 'local-TF'
  mixing_beta=0.2
  diago_david_ndim=4
  electron_maxstep=200
/
ATOMIC_SPECIES
 Cu  63.55 Cu.ONCV.SR.v5.upf
ATOMIC_POSITIONS  { angstrom }
………
K_POINTS { automatic }
  3 3 1  1 1 1

EXTRACT OF OUTPUT:
Dense  grid:  1524959 G-vectors     FFT dimensions: ( 120, 120, 288)
     Initial potential from superposition of free atoms
     starting charge    1823.9693, renormalised to    1824.0000
     negative rho (up,down):  3.017E-05 0.000E+00
     Starting wfcs are  960 randomized atomic wfcs +  134 random wfcs
     total cpu time spent up to now is       66.6 secs
     Self-consistent Calculation
iteration #  1     ecut=    80.00 Ry     beta= 0.20
     Davidson diagonalization with overlap
     ethr =  1.00E-02,  avg # of iterations = 33.3
     negative rho (up,down):  9.728E+02 0.000E+00
     total cpu time spent up to now is     1189.7 secs
     total energy              =  283496.48467385 Ry
     estimated scf accuracy    < 3575348.00873053 Ry
iteration #  2     ecut=    80.00 Ry     beta= 0.20
     Davidson diagonalization with overlap
     ethr =  1.00E-02,  avg # of iterations = 54.0
     negative rho (up,down):  5.521E+02 0.000E+00
     total cpu time spent up to now is     3447.8 secs
     total energy              =  -56652.42746379 Ry
     estimated scf accuracy    < 1421161.66580171 Ry

……

iteration # 22     ecut=    80.00 Ry     beta= 0.20
     Davidson diagonalization with overlap
     ethr =  1.00E-02,  avg # of iterations =  2.0
     negative rho (up,down):  1.061E+01 0.000E+00
     total cpu time spent up to now is     6239.9 secs
     total energy              =  -35382.73785671 Ry
     estimated scf accuracy    <     661.23095918 Ry

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