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.


• Cu_CA19S.vps
• Cu_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 (=0,1,2,3,4). The basis functions were generated by variationally optimizing the corresponding primitive basis functions in the single atom and the monoxide molecule. The input file used for the orbital optimization can be found at Cu_opt.dat, and CuO_opt.dat. Since Cu_CA19S.vps and Cu_PBE19S.vps include the 3d and 4s states (11 electrons) as the valence states, the minimal basis set is Cu*.*-s1d1. Our recommendation for the choice of cutoff radius of basis functions is that Cu6.0S.pao is enough for bulks, but Cu8.0S.pao or Cu10.0S.pao is preferable for molecular systems.


• Cu6.0S.pao
• Cu8.0S.pao
• Cu10.0S.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 Cu6.0S-s2p2d2 and Cu6.0S-s3p3d3 in the total energy at the minimum point is 0.324 eV/atom. An input file used for the OpenMX calculations can be found at Cufcc-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 3.64 Ang. was performed using Cu_PBE19S.vps and Cu6.0S-s3p3d3, 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 Cufcc-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 Cu dimer molecule, where Cu_PBE19S.vps, Cu10.0S-s2p2d2, and Cu10.0S-s3p3d3 were used. The input files used for the OpenMX calculations can be found at Cu2.dat , Cu_cp1.dat , Cu_cp2.dat , and Cu.dat ,


	Equilibrium bond length (Ang.)	Atomization energy (eV)	Atomization energy (couterpoise corrected) (eV)
Cu10.0S-s2p2d2	2.227	2.259	2.258
Cu10.0S-s3p3d3	2.222	2.268	2.266
Other calc.	2.23 a	2.28 a	-
Expt.	2.2197 b	1.83 b	-

^a E.Yu. Zarechnaya et al., Comp. Mat. Sci. 43, 522530 (2008).
^b K.P. Huber and G. Herzberg, "Constants of Diatomic Molecules" (data prepared by J.W. Gallagher and R.D. Johnson, III) in NIST Chemistry WebBook, NIST Standard Reference Database Number 69, Eds. P.J. Linstrom and W.G. Mallard, National Institute of Standards and Technology, Gaithersburg MD, 20899, http://webbook.nist.gov, (retrieved January 12, 2011).

Supplementary information for the GGA (PBE19) pseudopotential