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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 and the FCC bulk.
The input files used for the orbital optimization can be found at
Co_opt.dat,
and
Cofcc_opt.dat.
Since Co_CA19H.vps and Co_PBE19H.vps include the 3s, 3p, 3d, and 4s states (17 electrons)
as the valence states, the minimal basis set is Co*.*H-s2p1d1.
Our recommendation for the choice of cutoff radius of basis functions is that
Co6.0H.pao is enough for bulks, but Co8.0H.pao or Co10.0H.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, a,
in the hcp structure,** where the total energy is plotted relative to the
minimum energy for each case, and the ratio of c/a is fixed to the experimental one (4.070/2.507).
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 Co6.0H-s3p3d2f1 and Co6.0H-s4p4d3f2
in the total energy at the minimum point is 0.0780 eV/atom.
An input file used for the OpenMX calculations can be found at
Cohcp-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 hcp structure,**
where the spin polarized collinear calculation with the lattice constants (a=2.507 Ang. and c=4.070 Ang.)
was performed using Co_PBE19H.vps and Co6.0H-s3p3d2f1,
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
Cohcp-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.