Open core pseudopotentials

The 4$f$-states in lanthanide elements are spin-polarized in many cases, and the majority states are located at below a few eV taken from the Fermi level. However, LDAs and GGAs cannot describe the feature of band structures for those materials. Although one way is to perform the plus U method by introducing on-site Coulomb repulsion for the 4$f$-states in such a case, OpenMX provides a simpler way that the spin-polarizaion of 4f-states is taken into account via a pseudopotential, so-called open core pseudopotential, while a few open core pseudopotentials are available in the database Ver. 2019. The open core pseudopotential of a lanthanide element is generated by assuming that the 4f-states are a part of core states, and the partial core correction charge is generated so that the radial shape resembles well the charge distribution of the 4f-states. Pseudopotentials: Nd_CA19_OC.vps and Nd_PBE19_OC.vps stored in the database Ver. 2019 were generated in this way.

Figure 4: (a) The total energy of NdCo$_5$ in the CaCu$_5$ structure as a function of lattice constant, calculated by the LDA, LDA+U (U=4 eV for 4f-states), and open core pseudopotential methods. (b) Spin magnetic moment per the formula unit of the same system as (a). The input files used for the calculations are 'NdCo5_4f.dat', 'NdCo5_4f+U.dat', and 'NdCo5_OC.dat', which can be found in the directory 'work'.

To illustrate how the open core pseudopotential can be used, a series of calculations for NdCo$_5$ in the CaCu$_5$ structure is shown in Fig. 4. It is found that the calculation with the open core pseudopotential qualitatively reproduces the result by the LDA+U method. When the open core pseudopotential is used by OpenMX, the partial core correction charge can be spin-polarized by the following keyword:

  <scf.pcc.opencore
    Nd  1
    Co  0
  scf.pcc.opencore>

The example is for the NdCo$_5$ calculation discussed above. The first column is the name of species which is defined by the keyword 'Definition.of.Atomic.Species', and the second is a flag to specify the spin direction, where '1' and '-1' mean that the partial core correction charge is fully spin-polarized upward and downward along the $z$-axis, respectively, and '0' means no spin-polarization. Using the keyword, one can control the spin direction of 4$f$ states being open core states site by site. It is also noted that the open core pseudopotential is valid if the overlap between the 4$f$-states and orbitals in the neighboring atoms is negligible, and if the occupation of the 4$f$-states is not largely different between the pseudopotential generation for an atom and the states in compounds.