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 dimer.
The input files used for the orbital optimization can be found at
B_opt.dat
and
B2_opt.dat .
Since B_CA13.vps and B_PBE13.vps include the 2s and 2p states (3 electrons)
as the valence states, the minimal basis set is B*.*-s1p1.
Our recommendation for the choice of cutoff radius of basis functions is that
B7.0.pao is enough for bulks, but B8.0.pao or B9.0.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 B7.0-s2p2d1 and B7.0-s3p3d2
in the total energy at the minimum point is 0.036 eV/atom.
An input file used for the OpenMX calculations can be found at
Bfcc-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 2.87 Ang.
was performed using B_PBE13.vps, B7.0-s2p2d1, and B7.0-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
Bfcc-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 boron dimer molecule,
where B_PBE13.vps, B9.0-s2p2d1, and B9.0-s3p3d2 were used.
The input files used for the OpenMX calculations can be found at
B2.dat ,
B.dat ,
B_cp1.dat ,
and
B_cp2.dat ,
Equilibrium bond length (Ang.)
Atomization energy (kcal/mol)
Atomization energy (couterpoise corrected) (kcal/mol)
B9.0-s2p2d1
1.625
75.5
75.5
B9.0-s3p3d2
1.625
75.7
75.6
Other calc.
1.620a
76.7a
Expt.
1.590b
71.3c
a M.M. Odashima and and K. Capelle, J. Chem. Theory Comput. 5 798 (2009). b K.P. Huber and G. Herzberg, Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979). c M.T. Carrol, R.F.W. Bader, S.H. Vosko, J. Phys. B: At. Mol. Opt. Phys. 1987, 20, 3599.
Supplementary information for the GGA (PBE13) pseudopotential
