Atom-condensed softness matrix
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