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 (=0,1,2,3,4). The basis functions were generated by variationally
optimizing the corresponding primitive basis functions in the single atom.
The input file used for the orbital optimization can be found at
Ge_opt.dat .
Since Ge_CA13.vps and Ge_PBE13.vps include the 4s and 4p states (4 electrons)
as the valence states, the minimal basis set is Ge*.*-s1p1.
Our recommendation for the choice of cutoff radius of basis functions is that
Ge7.0.pao is enough for bulks, but Ge8.0.pao or Ge9.0.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 diamond 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 Ge7.0-s3p3d3f2 and Ge7.0-s4p4d3f2
in the total energy at the minimum point is 0.0067 eV/atom.
An input file used for the OpenMX calculations can be found at
Gedia-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 RMT x KMAX of 12.
(2) Calculations of the band dispersion in the diamond structure,
where the non-spin polarized collinear calculation with the lattice constant of 5.658 Ang.
was performed using Ge_PBE13.vps and Ge7.0-s3p3d3f2 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
Gadia-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 RMT x KMAX of 12.
(3) Calculations of a GeO molecule with S=1,
where Ge_PBE13.vps, O_PBE13.vps, Ge9.0-s3p3d3f2, Ge9.0-s4p4d3f2, and O7.0-s3p3d2 were used.
The input files used for the OpenMX calculations can be found at
GeO.dat ,
Ge_CP.dat ,
O_CP.dat ,
Ge.dat ,
and
O.dat .
Equilibrium bond length (Ang.)
Atomization energy (eV)
Atomization energy (couterpoise corrected) (eV)
Ga9.0-s3p3d3f2, O7.0-s3p3d2
1.663
7.434
7.429
Ga9.0-s4p4d3f2, O7.0-s3p3d2
1.663
7.447
7.441
Other calc.
1.653 a
Expt.
1.625 b
6.78 c
a BLYP result: J. Chem. Phys. 108, 8092 (1998). b G.A. Thompson, A.G. Maki, and A. Weber, J. Mol. Spectrosc. 116, 136 (1986). c K. P. Huber and G. Herzberg, Constants of Diatomic Molecules
(Van Nostrand, New York, 1979).
Supplementary information for the GGA (PBE13) pseudopotential
