Atom-condensed softness matrix In the ACKS2 polarizable force field paper, I found a thing called the atom-condensed softness matrix. In another paper, I found this expression for it:


  $$
\chi_{kl} = 2 \sum_{i}^{\text{occ MOs}} \sum_{j}^{\text{unocc MOs}} \frac{\langle\psi_{i}|g_{k}|\psi_{j}\rangle\langle\psi_{j}|g_{l}|\psi_{i}\rangle}{\epsilon_{i} - \epsilon_{j}} \delta_{\sigma_{i}\sigma_{j}},
$$
  where
  
  
  $\epsilon_{i}$: orbital energy of the $i$th KS orbital
  $\chi$: (non-interacting) response matrix
  $\psi_{i}$: spatial orbital
  $g_{i}$: potential basis function
  



What is the physical meaning of it, or at least what information we can get from this matrix?
If in KS-DFT we consider the system as non-interacting, why do we consider interaction between two species in this equation? (if I understand it right - between molecules $i$ and $j$)
Your first misconception is what i and j mean. These are indices of molecular orbitals. 

A response matrix is something used in respone theory. It stems from Perturbation Theory.

Response Theory is a mathematical formalism to compute time-dependent molecular properties (in theoretical chemistry, that is). 

This pdf (no guarantee for anything) describes it pretty well and concise.
http://www.lct.jussieu.fr/pagesperso/toulouse/enseignement/molecular_properties.pdf