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.


• Zn_CA19S.vps
• Zn_PBE19S.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, the FCC bulk, and the monoxide molecule. The input file used for the orbital optimization can be found at Zn_opt.dat, Znfcc_opt.dat, and ZnO_opt.dat. Since Zn_CA19S.vps and Zn_PBE19S.vps include the 3d and 4s states (12 electrons) as the valence states, the minimal basis set is Zn*.*S-s1d1. Our recommendation for the choice of cutoff radius of basis functions is that Zn6.0S.pao is enough for bulks, but Zn8.0S.pao or Zn10.0S.pao is preferable for molecular systems.


• Zn6.0S.pao
• Zn8.0S.pao
• Zn10.0S.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 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 Zn6.0S-s2p2d2 and Zn6.0S-s3p3d3f1 in the total energy at the minimum point is 0.0697 eV/atom. An input file used for the OpenMX calculations can be found at Znfcc-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 fcc structure, where the non-spin polarized collinear calculation with the lattice constant of 3.939 Ang. was performed using Zn_PBE19S.vps and Zn6.0S-s2p2d2, 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 Znfcc-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 ZnO molecule, where Zn_PBE19S.vps, O_PBE19.vps, Zn10.0S-s2p2d2, Zn10.0S-s3p3d3f1, and O6.0-s3p3d3 were used. The input files used for the OpenMX calculations can be found at ZnO.dat , Zn_CP.dat , O_CP.dat , Zn.dat , and O.dat ,


	Equilibrium bond length (Ang.)	Atomization energy (eV)	Atomization energy (couterpoise corrected) (eV)
Zn10.0S-s2p2d2	1.698	1.876	1.859
Zn10.0S-s3p3d3f1	1.696	2.029	2.006
Other calc.	1.73 a	2.121 a	-
Expt.	-	1.61 b	-

^a B. Wang et al., J. Phys. Chem. C 111, 4956 (2007).
^b D.E. Clemmer, N.F. Dalleska, and P.B. Armentrout, J. Chem. Phys. 95, 7263 (1991).

Supplementary information for the GGA (PBE19) pseudopotential