Fully relativistic pseudopotentials generated by
the MBK (PRB 47, 6728 (1993)) scheme within LDA (CA11) and GGA (PBE11) 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 a LiO molecule.
The input files used for the orbital optimization can be found at
Li_opt.dat ,
Li2_opt.dat ,
and
LiO_opt.dat .
Since Li_CA11.vps and Li_PBE11.vps include the 1s and 2s states (3 electrons)
as the valence states, the minimal basis set is Li*.*-s2.
Our recommendation for the choice of cutoff radius of basis functions is that
Li8.0.pao is enough for bulks, but Li10.0.pao or Li12.0.pao is preferable
for molecular systems.
Benchmark calculations by the PBE11 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 Li8.0-s3p2 and Li8.0-s3p3d2
in the total energy at the minimum point is 0.013 eV/atom.
An input file used for the OpenMX calculations can be found at
Libcc-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 bcc structure,
where the non-spin polarized collinear calculation with the lattice constant of 3.491 Ang.
was performed using Li_PBE11.vps, Li8.0-s3p2, and Li8.0-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
Libcc-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 the total energy as a function of lattice constant of LiCl in the rock salt 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 Cl7.0-s2p2d1 and Cl7.0-s3p3d2
in the total energy at the minimum point is 0.0112 eV/atom, where
Li8.0-s3p2d1 was used as basis functions for Li for both the cases.
An input file used for the OpenMX calculations can be found at
LiCl-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.
(4) Calculations of the band dispersion of LiCl in the rock salt structure,
where the non-spin polarized collinear calculation with the lattice constant of 5.106 Ang.
was performed using Li_PBE.vps, Cl_PBE11.vps, Li8.0-s3p2d1, and Cl7.0-s2p2d1,
and the origin of the energy is taken to be the top of the valence band.
The input file used for the OpenMX calculations can be found at
LiCl-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.
(5) Calculations of a lithium dimer molecule,
where Li_PBE11.vps, Li10.0-s3p2, and Li10.0-s3p3d2 were used.
The input files used for the OpenMX calculations can be found at
Li2.dat ,
Li_1.dat ,
Li_2.dat ,
Li_cp1.dat ,
and
Li_cp2.dat ,
Equilibrium bond length (Ang.)
Atomization energy (kcal/mol)
Atomization energy (couterpoise corrected) (kcal/mol)
Li10.0-s3p2
2.741
20.1
19.8
Li10.0-s3p3d2
2.731
20.4
20.1
Other calc.
2.730a
19.9b
Expt.
2.673c
24.4d
a M.M. Odashima and and K. Capelle, J. Chem. Theory Comput. 5 798 (2009). b S. Kurth et al., Int. J. of Quantum Chem. 75, 889 (1999). c K.P. Huber and G. Herzberg, Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979). d J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).
Supplementary information for the GGA (PBE11) pseudopotential
