Primitive basis function

The primitive basis functions used in OpenMX are the ground and exited states of a pseudo-atom with a confinement pseudopotential [23] shown in Fig. 1. The functions are numerical table function stored in a file of which file extension is 'pao'. You will see that the ground state is nodeless and the first exited state has one node, and the number of nodes increases in the further excited states. The one-particle Kohn-Sham functions are expressed by the linear combination of the atomic type basis functions where each basis function is the product of the radial function and a real spherical harmonics function. The selection of the basis sets is one of important issues to perform reliable calculations. However, the use of a large number of basis orbitals requires an extensive computational resource such as memory size and computational time. So, users are required to use small but accurate basis sets at some level which depends on calculated properties and computer power. As a criterion of the selection, we offer databases (http://www.openmx-square.org/) of basis sets, and convergence properties of the total energy and the equilibrium bond length of dimer molecules. As an example, the convergence properties of a carbon dimer are shown in Fig. 2. You might find that the convergence properties are determined by two simple parameter: a cutoff radius of basis orbitals and the number of basis orbitals, which suggests a large cutoff radius and number of basis orbitals provide more accurate results with high computational demands. The database suggests that basis orbitals with a higher angular momentum are needed to achieve the sufficient convergence for elements, such as F and Cl, in the right side of the periodic table, and that a large cutoff radius of basis orbitals should be used for elements, such as Li and Na, in the left side of the periodic table.

Figure 1: Primitive basis functions for s-orbitals of a carbon pseudo-atom with a confinement pseudopotential.

If you want to use basis orbitals stored in the database, then copy them to the directory, 'openmx3.5/DFT_DATA/PAO/'. You can freely utilize these data in terms of GNU-GPL, but we cannot offer any warranty on these data. Also it is possible to generate pseudo-atomic basis functions using ADPACK by yourself. The basis set is specified by a keyword 'Definition.of.Atomic.Species' as follows:

   <Definition.of.Atomic.Species
     H   H4.0-s2p1        H_LDA
     C   C4.5-s2p2        C_LDA
   Definition.of.Atomic.Species>

where an abbreviation 'H4.0-s2p1' of the basis function is introduced, where H4.0 indicates the file name of the pseudo-atomic basis orbitals without the file extension which must exist in the directory 'DFT_DATA/PAO', and 's2p1' means that two s-orbitals and one p-orbital in the file are used. In this case, totally eight basis functions (2x1+1x3=5) are assigned for 'H'. See also the Section 'Input file' for the details.

Figure 2: Convergence properties of (a) the total energy and (b) the equilibrium bond length for a carbon dimer with respect to basis set