The 'jx', a postprocessing code for OpenMX, provides a way to calculate exchange coupling parameters between two localized spins based on Green's function representation of Liechtenstein formula [17]. In the standard distribution of OpenMX Ver. 3.9, the evaluation is supported for only the collinear calculations of cluster and bulk systems. To acknowledge in any publications by using the functionality, the citation of the references [18,19] would be appreciated.
The program provides three ways to calculate as explained below.
For cluster systems, the program computes exchange coupling constants between
atomic sites and from the following formula:
For bulk systems, the program computes exchange coupling constants
between individual sites and located at cells and , respectively,
from the following formula:
(6)  
(7) 
Alternatively, it is also possible to compute the summation of exchange coupling over
by the following formula:

For users, it might be helpful to explain the difference between Eqs. (5)
and (8) by schematics shown in Fig. 37.
Figure 37 (a) shows a schematic of interaction between individual sites,
which corresponds to Eq. (5).
Figure 37 (b) shows a schematic of interaction between periodic images,
which corresponds to Eq. (8).
When executing, this option can be specified by Flag.PeriodicSum
,
as explained in the latter subsection.