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.



• Mn_CA13.vps

• Mn_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, the dimer, and a MnO molecule. The input files used for the orbital optimization can be found at Mn_opt.dat , Mn2_opt.dat , and MnO_opt.dat . Since Mn_CA13.vps and Mn_PBE13.vps include the 3s, 3p, 3d, and 4s states (15 electrons) as the valence states, the minimal basis set is Mn*.*-s2p1d1. Our recommendation for the choice of cutoff radius of basis functions is that Mn6.0.pao is enough for bulks, but Mn8.0.pao or Mn10.0.pao is preferable for molecular systems.



• Mn6.0.pao

• Mn8.0.pao

• Mn10.0.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 Mn6.0-s3p3d3 and Mn6.0-s3p3d3f1 in the total energy at the minimum point is 0.020 eV/atom. An input file used for the OpenMX calculations can be found at Mnfcc-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 14.



(2) Calculations of the band dispersion in the fcc structure, where the non-spin polarized collinear calculation with the lattice constant of 3.50 Ang. was performed using Mn_PBE13.vps and Mn6.0-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 Mnfcc-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 14.





(3) Calculations of a MnO molecule, where Mn_PBE13.vps, O_PBE13.vps, Mn10.0-s3p3d3, Mn10.0-s3p3d3f1, and O7.0-s3p3d2 were used. The input files used for the OpenMX calculations can be found at MnO_O1.dat , MnO_Mn1.dat , MnO_O2.dat , MnO_Mn2.dat , MnO_O_cp1.dat , MnO_Mn_cp1.dat , MnO_O_cp2.dat , and MnO_Mn_cp2.dat ,



	Equilibrium bond length (Ang.)	Dipole moment (Debye)	Atomization energy (eV)	Atomization energy (couterpoise corrected) (eV)
Mn10.0-s3p3d3, O7.0-s3p3d2	1.634	4.68	4.99	4.98
Mn10.0-s3p3d3f1, O7.0-s3p3d2	1.634	4.68	5.01	5.00
Other calc.	1.635 a		4.99a
Expt.	1.648b		3.70b


^a W.A. Al-Saidi, H. Krakauer, and S. Zhang, Phys. Rev. B 73, 075103 (2006).
^b H.P. Loock, B. Simard, S. Wallin, and C. Linton, J. Chem. Phys. 109, 8980 (1998).

Supplementary information for the GGA (PBE13) pseudopotential