Non-relativistic pseudopotentials

These pseudo potentials were generated by the TM scheme. PCC below the symbol means that the pseudo potentials were generated under the partial core correction.



• Ti_TM.vps

• Ti_TM_PCC.vps

Pseudo atomic orbitals for the non-relativistic pseudopotentials

The number below the symbol means a cutoff radius (a.u.) of the confinement potential. These file includes five radial parts for each angular momentum quantum number l (=0,1,2,3). Since the non-relativistic pseudopotentials include 3p, 3d, 4s, and 4p states as the valence states, the minimal basis set is Ti*.*-s1p2d1, and the number of valence electrons is 10.



• Ti5.5.pao

• Ti6.0.pao

• Ti6.5.pao

• Ti7.0.pao

• Ti7.5.pao

• Ti8.0.pao

Convergence properties with respect to basis sets

Figures (a) and (b) show the convergence properties of the total energy and the equilibrium bond length for a titanium dimer, which are calculated using the basis sets in the database, respectively. The energy cutoff of 146 (Ryd) was used in the numerical integrations and the solution of Poisson's equations. The pseudo potential used in these calculations was Ti_TM_PCC.vps which is stored in the vps database. The local spin density approximation (LSDA) was used for the exchange-correlation interaction.

Fully relativistic pseudopotentials

Fully relativistic pseudopotentials generated by the TM scheme within LDA and GGA which contain
• partial core correction
• full relativistic effects including spin-orbit coupling



• Ti_LDA.vps

• Ti_GGA.vps

Pseudo atomic orbitals for the fully relativistic pseudopotentials

The number below the symbol means a cutoff radius (a.u.) of the confinement potential. These file includes five radial parts for each angular momentum quantum number l (=0,1,2,3). Since the relativistic pseudopotentials include 3s, 3p, 3d, 4s, and 4p states as the valence states, the minimal basis set is Ti*.*-s2p2d1, and the number of valence electrons is 12.



• Ti5.5R.pao

• Ti6.0R.pao

• Ti6.5R.pao

• Ti7.0R.pao

• Ti7.5R.pao

• Ti8.0R.pao

Some results calculated by the relativistic pseudopontentials

Lattice constant vs. Total energy in Ti hcp bulk

Density of states of rutile TiO2

Refs.

Band gap of rutile TiO2 (Expt.)	J. Pascual et al., PRL 39, 1490 (1977).
Band gap of rutile of TiO2 (Theory)	K. M. Glassford and J. R. Chelikowsky, PRB 45, 3874 (1992).




Calculation conditions
Version	OpenMX3.0
Basis set	Ti6.0R-s2p2d1, O5.0-s2p2d1
Pseudo potential	Ti_LDA.vps, Ti_GGA, and O_LDA.vps as scalar relativistic VPS
Functional	LDA and GGA-PBE
spin-orbit coupling	None
Spin non-collinearity	None
Ecut for hcp Ti	32 x 32 x 32 (about 450 Ryd, the fixed scheme is used)
Ecut for rutile TiO2	180 Ryd
k-point	7 x 7 x 7