E2_pert

Q: Can I compute the 'E(2) energy' using the output of JANPA program?

A: No, but yes if you still insist ;)

In principle, CLPO procedure provides, under certain conditions, everything needed to compute a quantity similar to 'E(2) energy'. The needed ingredients are: (i) the transformation from NAO basis to localized orbital (e.g., CLPO) basis and (ii) the elements of Fock matrix in NAO basis.
In order to get the latter, -Fock_NAO_File option can be used to export Fock matrix in NAO basis to a text file, while -CLPO2LHO_File and -LHO2NAO_File options can be used to export the transformation matrices from LHO basis to CLPO basis as well as from NAO basis to LHO basis. The product of these two matrices will yield the ultimate transformation from NAO basis to CLPO basis, which is, in turn, needed to transform the Fock matrix from NAO basis into CLPO basis. As soon as this transformation is done, 'Fii', 'Fjj' and 'Fij' elements needed for evaluating the 'E(2) expression' become available.

Here is, however, why this should not be done.
Above all, the Fock matrix itself can only be well-defined within Hartree-Fock method, so that the one of two essential components of the scheme becomes unavailable for any post-SCF method (like MP2, CCSD etc). Needless to say, one rarely finds Hartree-Fock method enough for any practical applications, other than some special fundamental research topics related to physics of electrons in a molecules.
The only family of methods not mentioned above is thus DFT. Under Kohn-Sham formulation of DFT, an operator similar to the Fock one is readily available so that all of the required ingredients can formally be computed.
The problem arises, however, as soon as it comes to interpretation of the obtained quantities. The problem with interpreting the results obtained by using the 'E(2) formula' with matrix elements of 'Fock' (in fact, Kohn-Sham) matrix in localized orbitals basis is rooted in the fact that although the SCF scheme of DFT method in Kohn-Sham formulation uses (and allows exporting) the so-called first-order reduced density matrix (1RDM), this is not
1RDM of the true system, but instead the 1RDM of auxiliary system of non-interacting electrons. This fundamental difference contrasts the Kohn-Sham orbitals from the Hartree-Fock ones and makes the meaning of the entire transformation of orbitals, including their localization, questionable. In simple words, we do know the density from DFT, but we don't know the wavefunction!
Importance of all these issues stems from the fact that fundamentally 'E(2) energy' is merely the difference between the energy of the actual molecular system and the energy of 'artificial' 'reference' system in which a special hand-crafted perturbation (in form of modification of 1RDM) was introduced. Whether or not, and why, can such perturbation be attributed to the effect of some 'charge transfer' or 'non-covalent interaction' typically remains an opened question... The last but not least, 'E(2)' can not be measured experimentally.
Due to the above reasoning we did non implement 'E(2)' computation in JANPA (at least, in version 2.02).

Perhaps, the only more or less well-defined quantity, which is closely related to 'E(2)' and can still be computed in framework of DFT, is the amount of electron charge transferred between the localized orbitals due to the electron delocalization. Please, refer to Appendix A in [Yu. Nikolaienko, T., Kryachko, E. S., & Dolgonos, G. A. (2018). On the Existence of He-He Bond in the Endohedral Fullerene Hе2@ C60. Journal of computational chemistry, 39(18), 1090-1102, DOI: 10.1002/jcc.25061] for further details.

In short, we'd recommend avoid whenever possible using 'E(2)' estimations, for anything expect the true Hartree-Fock theory.