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.
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 dimer,
and the BCC bulk.
The input files used for the orbital optimization can be found at
V_opt.dat ,
V2_opt.dat ,
and
Vbcc_opt.dat .
Since V_CA19.vps and V_PBE19.vps include the 3s, 3p, 3d, and 4s states (13 electrons)
as the valence states, the minimal basis set is V*.*-s2p1d1.
Our recommendation for the choice of cutoff radius of basis functions is that
V6.0.pao is enough for bulks, but V8.0.pao or V10.0.pao is preferable
for molecular systems.
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 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 V6.0-s3p3d2 and V6.0-s3p3d3f1
in the total energy at the minimum point is 0.044 eV/atom.
An input file used for the OpenMX calculations can be found at
Vbcc-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 bcc structure,
where the non-spin polarized collinear calculation with the lattice constant of 3.030 Ang.
was performed using V_PBE19.vps and V6.0-s3p3d2,
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
Vbcc-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 the V2 molecule,
where V_PBE19.vps and V8.0-s3p3d3f1 were used.
The input files used for the OpenMX calculations can be found at
V2.dat ,
V_CP.dat ,
and
V.dat ,
Equilibrium bond length (Ang.)
Atomization energy (eV)
Atomization energy (couterpoise corrected) (eV)
V8.0-s3p3d3f1
1.801
2.698
2.633
Other calc.
1.654 a
3.092 a
-
Expt.
1.783 b
2.788 b
-
a F. Furche and J.P. Perdew, J. Chem. Phys. 124, 044103 (2006). b Taken from Ref.(a)
Supplementary information for the GGA (PBE19) pseudopotential
