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Fully relativistic pseudopotentials

Fully relativistic pseudopotentials generated by
the MBK (PRB 47, 6728 (1993)) scheme within LDA (CA19) and GGA (PBE19) which contain
a partial core correction and fully relativistic effects including spin-orbit coupling.

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Pseudo-atomic orbitals

The number below the symbol means a cutoff radius (a.u.) of the confinement
potential. These file includes fifteen radial parts for each angular
momentum quantum number l (=0,1,2,3). The basis functions were generated by variationally
optimizing the corresponding primitive basis functions in the single atom, the FCC bulk,
and the dimer molecule.
The input files used for the orbital optimization can be found at
Hf_opt.dat,
Hffcc_opt.dat,
and
Hf2_opt.dat.
Since Hf_CA19.vps and Hf_PBE19.vps include the 5s, 5p, 5d, and 6s states (12 electrons)
as the valence states, the minimal basis set is Hf*.*-s2p1d1.
Our recommendation for the choice of cutoff radius of basis functions is that
Hf7.0.pao is enough for bulks, but Hf9.0.pao or Hf11.0.pao is preferable
for molecular systems.

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Benchmark calculations by the PBE19 pseudopotential with the various basis functions

**(1) Calculation of the total energy as a function of lattice constant in the fcc structure,**
where the total energy is plotted relative to the minimum energy for each case. a_{0}
and B_{0} are the equilibrium lattice constant and bulk modulus obtained by fitting to
the Murnaghan equation of state. The difference between Hf7.0-s3p2d2f1 and Hf7.0-s3p3d3f1
in the total energy at the minimum point is 0.0055 eV/atom.
An input file used for the OpenMX calculations can be found at
Hffcc-EvsV.dat.
For comparison the result by the Wien2k code is also shown, where
the calculation was performed by default setting in the Ver. 9.1 of Wien2k except for
the use of R_{MT} x K_{MAX} of 12.

**(2) Calculations of the band dispersion in the fcc structure,**
where the non-spin polarized collinear calculation with the lattice constant of 4.470 Ang.
was performed using Hf_PBE19.vps and Hf7.0-s3p2d2f1.
and the origin of the energy is taken to be the Fermi level.
The input file used for the OpenMX calculations can be found at
Hffcc-Band.dat.
For comparison the result by the Wien2k code is also shown, where
the calculation was performed by default setting in the Ver. 9.1 of Wien2k
except for the use of R_{MT} x K_{MAX} of 12.