You raise a somewhat thorny question, but I’ll try to answer as clearly as possible.
What is being visualized in those cube files is the change in electron density between the zeroth-order monomer wavefunction(s) and the fully interacting monomer wavefunction(s). This will include higher-order induction effects, but not dispersion.
F-/ISAPT performs several SCF cycles, each of which contributes differently to the overall computation:
- Isolated monomer A wavefunction
- Isolated monomer B wavefunction
- Isolated monomer C wavefunction
- Monomer A orbital relaxation in presence of Monomer C, constrained orthogonal to Monomer B
- Forms zeroth-order monomer A wavefunction
- Monomer B orbital relaxation in presence of Monomer C, constrained orthogonal to Monomer A
- Forms zeroth-order monomer B wavefunction
- Fully interacting supersystem wavefunction (monomers A, B, & C all together)
- Used to compute the dHF correction
The difference in electron density between the zeroth-order wavefunctions for monomer A and B (formed in SCF cycles #3 & #4 above) and their density once localized from the fully interacting wavefunction (formed in SCF #6 above) is what is plotted in the cube files. Because all of this embedding is done at the Hartree–Fock level, it will include electrostatics, exchange, and higher-order induction, but it will unfortunately not include any dispersion.
I am pretty certain that there isn’t currently any mechanism available in the literature to visualize differences in electron density due exclusively to dispersion. You might be able to look at differences in natural orbital populations between the zeroth-order wavefunctions and fully interacting ones for a “dispersion-aware” change in electron density, but I’m not even sure if that is completely kosher.
Hope this explanation helps!