Fully relativistic pseudopotentials generated by
the MBK (PRB 47, 6728 (1993)) scheme within LDA (CA13) and GGA (PBE13) which contain
a partial core correction and fully relativistic effects including spin-orbit coupling.
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 BCC bulk. The input files used for the orbital optimization can be found at
S_opt.dat
and
Sbcc_opt.dat .
Since S_CA13.vps and S_PBE13.vps include the 3s and 3p (6 electrons)
as the valence states, the minimal basis set is S*.*-s1p1.
Our recommendation for the choice of cutoff radius of basis functions is that
S7.0.pao is enough for bulks, but S8.0.pao or S9.0.pao is preferable
for molecular systems.
Benchmark calculations by the PBE13 pseudopotential with the various basis functions
(1) Calculation of the total energy as a function of lattice constant in the bcc structure,
where the total energy is plotted relative to the minimum energy for each case. a0
and B0 are the equilibrium lattice constant and bulk modulus obtained by fitting to
the Murnaghan equation of state. The difference between S7.0-s3p3d2f1 and S7.0-s4p3d3f2
in the total energy at the minimum point is 0.0118 eV/atom.
An input file used for the OpenMX calculations can be found at
Sbcc-EvsV.dat .
For comparison the result by the Wien2k code is also shown, where
the calculation was performed by default setting in the Ver. 10.1 of Wien2k except for
the use of RMT x KMAX of 12.
(2) Calculations of the band dispersion in the bcc structure,
where the non-spin polarized collinear calculation with the lattice constant of 4.10 Ang.
was performed using S_PBE13.vps and S7.0-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
Sbcc-Band.dat .
For comparison the result by the Wien2k code is also shown, where
the calculation was performed by default setting in the Ver. 10.1 of Wien2k
except for the use of RMT x KMAX of 12.
(3) Calculations of the S2 molecule with S=3,
where S_PBE13.vps and S9.0-s3p3d2f1 or S9.0-s4p3d3f2 were used.
The input files used for the OpenMX calculations can be found at
S2.dat ,
S.dat ,
and
S_CP.dat .
Equilibrium bond length (Ang.)
Atomization energy (eV)
Atomization energy (couterpoise corrected) (eV)
S9.0-s3p3d2f1
1.983
4.708
4.702
S9.0-s4p3d3f2
1.973
4.809
4.801
Other calc.
1.916 a
4.944 a
Expt.
1.889 b
4.41 c
a D.C. Patton, D.V. Porezag, and M.R. Pederson, Phys. Rev. B 55, 7454 (1997). b K.P. Huber and G. Herzberg, Constants of Diatomic Molecules
Van Nostrand Reinhold, New York, 1979. c Taken from Ref. (a)
Supplementary information for the GGA (PBE13) pseudopotential
