Fully relativistic pseudopotentials

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.



• Mg_CA13.vps

• Mg_PBE13.vps

Pseudo-atomic orbitals

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 Mg_opt.dat and Mgfcc_opt.dat . Since Mg_CA13.vps and Mg_PBE13.vps include the 2p and 3s state (8 electrons) as the valence states, the minimal basis set is Mg*.*-s1p1. Our recommendation for the choice of cutoff radius of basis functions is that Mg7.0.pao is enough for bulks, but Mg9.0.pao or Mg11.0.pao is preferable for molecular systems.



• Mg7.0.pao

• Mg9.0.pao

• Mg11.0.pao

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 Mg7.0-s3p3d2 and Mg7.0-s4p3d3 in the total energy at the minimum point is 0.0019 eV/atom. An input file used for the OpenMX calculations can be found at Mgfcc-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 R_MT x K_MAX of 12.



(2) Calculations of the band dispersion in the fcc structure, where the non-spin polarized collinear calculation with the lattice constant of 4.520 Ang. was performed using Mg_PBE13.vps and Mg7.0-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 Mgfcc-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 R_MT x K_MAX of 12.





(3) Calculations of a MgO molecule with S=1, where Mg_PBE13.vps and Mg9.0-s3p3d2, Mg9.0-s4p3d3, and O7.0-s3p3d2 were used. The input files used for the OpenMX calculations can be found at MgO.dat , Mg_CP.dat , O_CP.dat , Mg.dat , and O.dat .



	Equilibrium bond length (Ang.)	Dipole moment (Debye)	Atomization energy (eV)	Atomization energy (couterpoise corrected) (eV)
Mg9.0-s3p3d2, O7.0-s3p3d2	1.760	7.10	3.04	3.04
Mg9.0-s4p3d3, O7.0-s3p3d2	1.755	7.08	3.10	3.10
Other calc.	1.745 a	-	2.66 a
Expt.	1.749 b	6.2 c	2.56 d


^a G. Geneste, J. Morillo, an F. Finocchi, Applied Surface Sci. 188, 122 (2002).
^b K.P. Huber and G. Herzberg, Constants of Diatomic Molecules, Van Nostrand Reinhold, New York, 1979.
^c D.R. Lide, Ed. CRC Handbook of Chemistry and Physics, 86th ed.; Taylor and Francis: Boca Raton, FL, 2005.
^d L. Operti et al., J. Am. Chem. Soc. 111, 9152 (1989).

Supplementary information for the GGA (PBE13) pseudopotential