Empty atom scheme

The primitive and optimized PAO functions are usually assigned to atoms. Moreover, it is possible to assign basis functions in any vacant region using an empty atom. You will find the empty atom 'E' in the web site of the database (http://www.openmx-square.org/). Using the pseudopotential for the empty atom 'E', though the pseudopotential is a flat zero potential, you can put basis functions at any place independently of atomic position. To do that, you can define empty atoms by

   <Definition.of.Atomic.Species
     H    H5.0-s2p1      H_PBE13
     C    C5.0-s2p1      C_PBE13
     EH   H5.0-s2p1      E
     EC   C5.0-s2p1      E
   Definition.of.Atomic.Species>

In the example, two sorts of empty atoms are defined as 'EH' and 'EC' which have basis sets specified by 'H5.0-s2p1' and 'C5.0-s2p1', respectively, which means that one can use any basis functions for an empty atom as shown above. Then 'EH' and 'EC' can be put to any place by the keyword 'Atoms.SpeciesAndCoordinates', where the number of electrons for the empty atom is zero. To define an empty atom, only thing you have to do is to use 'E.vps' as pseudopotential for the empty atom. The empty atom scheme enables us not only to estimate the basis set superposition error (BSSE) using the counterpoise correction (CP) method [35,36], but also to treat a vacancy state and a nearly free electron state on metal surfaces within the linear combination of pseudo-atomic orbitals (LCPAO) method. As an example, a calculation of a F-center in NaCl with a Cl vacancy is shown in Fig. 3. We see that the highest occupied state at the $\Gamma$ point is the F-center state. You can follow the calculation using 'NaCl_FC.dat' in the directory 'work'.

Figure 3: The isosurface map of the highest occupied state at the $\Gamma$ point for NaCl with a Cl-site vacancy, which shows a F-center in NaCl with a Cl vacancy. The isosurface map was drawn using XCrySDen with the isovalue of 0.042 [66]. The calculation was done with the system charge of -1 using a keyword 'scf.system.charge'. The watery and silver colors correspond to sodium and chlorine atoms,respectively, and the yellow small ball shows the position of empty atom.