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Fully relativistic pseudopotentials

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.

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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 diamond
structure. The input files used for the orbital optimization can be found at
Sn_opt.dat
and
Sndia_opt.dat .
Since Sn_CA13.vps and Sn_PBE13.vps include the 4d, 5s, and 5p states (14 electrons)
as the valence states, the minimal basis set is Sn*.*-s1p1d1.
Our recommendation for the choice of cutoff radius of basis functions is that
Sn7.0.pao is enough for bulks, but Sn9.0.pao or Sn11.0.pao is preferable
for molecular systems.

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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 diamond 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 Sn7.0-s2p2d3f1 and Sn7.0-s2p3d3f2
in the total energy at the minimum point is 0.0008 eV/atom.
An input file used for the OpenMX calculations can be found at
Sndia-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 diamond structure,**
where the non-spin polarized collinear calculation with the lattice constant of 6.49 Ang.
was performed using Sn_PBE13.vps and Sn7.0-s2p2d3f1 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
Sndia-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.