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.


• Zr_CA19.vps
• Zr_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). 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 Zr_opt.dat and Zrfcc_opt.dat . Since Zr_CA19.vps and Zr_PBE19.vps include the 4s, 4p, 4d, and 5s states (12 electrons) as the valence states, the minimal basis set is Zr*.*-s2p1d1. Our recommendation for the choice of cutoff radius of basis functions is that Zr7.0.pao is enough for bulks, but Zr9.0.pao or Zr11.0.pao is preferable for molecular systems.


• Zr7.0.pao
• Zr9.0.pao
• Zr11.0.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 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 Zr7.0-s3p2d2 and Zr7.0-s3p3d3f1 in the total energy at the minimum point is 0.083 eV/atom. An input file used for the OpenMX calculations can be found at Zrfcc-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 4.530 Ang. was performed using Zr_PBE19.vps, Zr7.0-s3p2d2, and Zr7.0-s3p3d3f1, 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 Zrfcc-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 zirconium molecule with S=1, where Zr_PBE19.vps and Zr9.0-s3p2d2 or Zr9.0-s3p3d3f1 were used. The input files used for the OpenMX calculations can be found at Zr2.dat , Zr.dat , and Zr_cp.dat .


	Equilibrium bond length (Ang.)	Atomization energy (eV)	Atomization energy (couterpoise corrected) (eV)
Zr9.0-s3p2d2	2.338	3.19	3.16
Zr9.0-s3p3d3f1	2.307	3.31	3.26
Other calc.	2.324a	2.42 a	-
Expt.	2.24 b	3.05 b	-

^a B3LYP result: Z.J. Wu, Chem. Phys. Lett. 383, 251 (2004).
^b J.R. Lombardi, B. Davis, Chem. Rev. 102, 2431 (2002).

Supplementary information for the GGA (PBE19) pseudopotential