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 FCC bulk.
The input files used for the orbital optimization can be found at
Zr_opt.dat
and
Zrfcc_opt.dat .
Since Zr_CA13.vps and Zr_PBE13.vps include the 4s, 4p, 4d, and 5s states (12 electrons)
as the valence states, the minimal basis set is Zr*.*-s2p1d1.
Our recommendation for the choice of cutoff radius of basis functions is that
Zr7.0.pao is enough for bulks, but Zr9.0.pao or Zr11.0.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 fcc 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 Zr7.0-s3p2d2 and Zr7.0-s3p3d3f1
in the total energy at the minimum point is 0.083 eV/atom.
An input file used for the OpenMX calculations can be found at
Zrfcc-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 fcc structure,
where the non-spin polarized collinear calculation with the lattice constant of 4.530 Ang.
was performed using Zr_PBE13.vps, Zr7.0-s3p2d2, and Zr7.0-s3p3d3f1,
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
Zrfcc-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 a zirconium molecule with S=1,
where Zr_PBE13.vps and Zr9.0-s3p2d2 or Zr9.0-s3p3d3f1 were used.
The input files used for the OpenMX calculations can be found at
Zr2.dat ,
Zr.dat ,
and
Zr_cp.dat .
Equilibrium bond length (Ang.)
Atomization energy (eV)
Atomization energy (couterpoise corrected) (eV)
Zr9.0-s3p2d2
2.338
3.19
3.16
Zr9.0-s3p3d3f1
2.307
3.31
3.26
Other calc.
2.324a
2.42 a
Expt.
2.24 b
3.05 b
a B3LYP result: Z.J. Wu, Chem. Phys. Lett. 383, 251 (2004). b J.R. Lombardi, B. Davis, Chem. Rev. 102, 2431 (2002).
Supplementary information for the GGA (PBE13) pseudopotential
