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 and the dimer molecule.
The input file used for the orbital optimization can be found at
Al_opt.dat
and
Al2_opt.dat.
Since Al_CA13.vps and Al_PBE13.vps include the 3s and 3p states (3 electrons)
as the valence states, the minimal basis set is Al*.*-s1p1.
Our recommendation for the choice of cutoff radius of basis functions is that
Al7.0.pao is enough for bulks, but Al8.0.pao or Al9.0.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 Al7.0-s3p3d2 and Al7.0-s4p4d2
in the total energy at the minimum point is 0.003 eV/atom.
An input file used for the OpenMX calculations can be found at
Alfcc-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 4.05 Ang.
was performed using Al_PBE13.vps and Al7.0-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
Alfcc-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 Al dimer molecule,
where Al_PBE13.vps, Al9.0-s3p3d2, and Al9.0-s4p4d2 were used.
The input files used for the OpenMX calculations can be found at
Al2.dat ,
Al_cp.dat ,
and
Al.dat ,
