I am interested in calculating the non-interacting non-local susceptibility for simple molecules.

In principle, if you have a single Slater determinant, then you should just take a sum over the occupied orbitals $ \{\phi_i\} $ as

$$ \chi(r,r') = \sum_{occ} \frac{\phi_i(r) \phi_j(r') \phi_i(r') \phi_j(r)}{\varepsilon_i-\varepsilon_j} $$

I believe if you have the representation of the wavefunctions in Cartesian space, then you can "simply" sum over them. In practice, however, I am not sure I want to write a code that does this, so I'm asking: does anyone know about a package that does this?

I think it should be possible, as $\chi$ is an intermediate property for RPA calculations as well as an interesting object in conceptual DFT (see this paper for example where they actually calculate this quantity, but they don't report their full function, neither do they provide their code...)

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    $\begingroup$ The paper you link suggests that the sum should be over occupied and virtual orbitals unless I'm missing some simplification implicit in your question. This library looks promising for computing these conceptual DFT quantities, though it only seems to work with Python2.7 and it's not entirely clear to me what electronic structure programs it can interface with. $\endgroup$
    – Tyberius
    Mar 24, 2022 at 23:52
  • $\begingroup$ Thanks, yes, you are right, virtual orbitals should be included. Either way, I think the practical implementation would almost be the same in this case. $\endgroup$
    – user4626
    Mar 28, 2022 at 5:52

1 Answer 1


After a few days of pondering this issue, I've realized that the code Multiwfn has the option to calculate this quantity that I am looking for.


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