Fully relativistic pseudopotentials

Fully relativistic pseudopotentials generated by the MBK (PRB 47, 6728 (1993)) scheme within LDA (CA19) and GGA (PBE19) which contain a partial core correction and fully relativistic effects including spin-orbit coupling.


• Ge_CA19.vps
• Ge_PBE19.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 (=0,1,2,3,4). The basis functions were generated by variationally optimizing the corresponding primitive basis functions in the single atom. The input file used for the orbital optimization can be found at Ge_opt.dat . Since Ge_CA19.vps and Ge_PBE19.vps include the 4s and 4p states (4 electrons) as the valence states, the minimal basis set is Ge*.*-s1p1. Our recommendation for the choice of cutoff radius of basis functions is that Ge7.0.pao is enough for bulks, but Ge8.0.pao or Ge9.0.pao is preferable for molecular systems.


• Ge7.0.pao
• Ge8.0.pao
• Ge9.0.pao

Benchmark calculations by the PBE19 pseudopotential with the various basis functions

(1) Calculation of the total energy as a function of lattice constant in the diamond 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 Ge7.0-s3p3d3f2 and Ge7.0-s4p4d3f2 in the total energy at the minimum point is 0.0067 eV/atom. An input file used for the OpenMX calculations can be found at Gedia-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 R_MT x K_MAX of 12.



(2) Calculations of the band dispersion in the diamond structure, where the non-spin polarized collinear calculation with the lattice constant of 5.658 Ang. was performed using Ge_PBE19.vps and Ge7.0-s3p3d3f2 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 Gedia-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 R_MT x K_MAX of 12.





(3) Calculations of a GeO molecule with S=1, where Ge_PBE19.vps, O_PBE19.vps, Ge9.0-s3p3d3f2, Ge9.0-s4p4d3f2, and O7.0-s3p3d2 were used. The input files used for the OpenMX calculations can be found at GeO.dat , Ge_CP.dat , O_CP.dat , Ge.dat , and O.dat .


	Equilibrium bond length (Ang.)	Atomization energy (eV)	Atomization energy (couterpoise corrected) (eV)
Ge9.0-s3p3d3f2, O7.0-s3p3d2	1.663	7.434	7.429
Ge9.0-s4p4d3f2, O7.0-s3p3d2	1.663	7.447	7.441
Other calc.	1.653 a	-	-
Expt.	1.625 b	6.78 c	-

^a BLYP result: J. Chem. Phys. 108, 8092 (1998).
^b G.A. Thompson, A.G. Maki, and A. Weber, J. Mol. Spectrosc. 116, 136 (1986).
^c K. P. Huber and G. Herzberg, Constants of Diatomic Molecules (Van Nostrand, New York, 1979).

Supplementary information for the GGA (PBE19) pseudopotential