Fully relativistic pseudopotentials

Fully relativistic pseudopotentials generated by the MBK (PRB 47, 6728 (1993)) scheme within LDA (CA11) and GGA (PBE11) which contain a partial core correction and fully relativistic effects including spin-orbit coupling.



• O_CA11.vps

• O_PBE11.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 in three environments: the single atom, a water molecule, and the dimer molecule. The input files used for the orbital optimization can be found at O_opt.dat , H2O_opt.dat, and O2_opt.dat . Since O_CA11.vps and O_PBE11.vps include the 2s and 2p states (6 electrons) as the valence state, the minimal basis set is O*.*-s1p1. Our recommendation for the choice of cutoff radius of basis functions is that O5.0.pao is enough for bulks, but O6.0.pao or O7.0.pao is preferable for molecular systems.



• O5.0.pao

• O6.0.pao

• O7.0.pao

Benchmark calculations by the PBE11 pseudopotential with the various basis functions

(1) Calculations of a oxygen molecule, where O_PBE11.vps and O7.0-s2p2d1, O7.0-s3p3d2, or O7.0-s3p3d2f1 were used. The input files used for the OpenMX calculations can be found at O2.dat , O.dat , and O_cp.dat .



	Equilibrium bond length (Ang.)	Atomization energy (eV)	Atomization energy (couterpoise corrected) (eV)
O7.0-s2p2d1	1.264	6.06	6.06
O7.0-s3p3d2	1.235	6.57	6.57
O7.0-s3p3d2f1	1.234	6.58	6.57
Other calc.	1.23a	6.24b
Expt.	1.208c	5.12c


^a S.F. Li et al., Phys. Lett. A 352, 526 (2006).
^b S. Kurth et al., Int. J. of Quantum Chem. 75, 889 (1999).
^c K.P. Huber and G. Herzberg, Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979).


(2) Calculations of a water molecule, where O_PBE11.vps, H_PBE11, O7.0-s2p2d1, O7.0-s3p3d2, H7.0-s2p1, and H7.0-s3p2 were used. The input files used for the OpenMX calculations can be found at H2O.dat .



	Equilibrium H-O bond length (Ang.)	Equilibrium H-O-H bond angle (Deg.)	Dipole moment (Debye)
O7.0-s2p2d1, H7.0-s2p1	0.971	103.7	1.82
O7.0-s3p3d2, H7.0-s3p2	0.970	103.8	1.83
Other calc.	0.969a	104.2a	1.81b
Expt.	0.957c	104.5d	1.86 c


^a A.E. Mattsson and T.R. Mattsson, J. Chem. Theory Comput. 5, 887 (2009).
^b X. Xu and W.A. Goddard III, J. Phys. Chem. A 108, 2305 (2004).
^c W. S. Benedict, N. Gailar, and E. K. Plyler, J. Chem. Phys. 24, 1139 (1956).
^d S. A. Clough, Y. Beers, G. P. Klein, and L. S. Rothman, J. Chem. Phys. 59, 2254 (1973).


(3) Calculations of a water dimer, where O_PBE11.vps, H_PBE11, O7.0-s2p2d1, O7.0-s3p3d2, H7.0-s2p1, and H7.0-s3p2 were used. The input files used for the OpenMX calculations can be found at H2O.dat , d-H2O.dat , H2O_cp1.dat , and H2O_cp2.dat ,



	Equilibrium O-O distance (Ang.)	Dipole moment (Debye)	Binding energy (kcal/mol)	Binding energy (couterpoise corrected) (kcal/mol)
O7.0-s2p2d1, H7.0-s2p1	2.899	2.54	5.57	5.21
O7.0-s3p3d2, H7.0-s3p2	2.897	2.45	5.48	5.48
Other calc.	2.893a		5.15 a
Expt.	2.98b	2.60b	5.44 b


^a A.E. Mattsson and T.R. Mattsson, J. Chem. Theory Comput. 5, 887 (2009).
^b F. Sim, A. St.-Amant, I. Papai, and D. R. Salahub, J. Am. Chem. Soc. 114, 4391 (1992).

Supplementary information for the GGA (PBE11) pseudopotential