Theoretical background: The reduced density gradient

NCI (Non-Covalent Interactions) is a visualization index based on the density and its derivatives. It enables identification of non-covalent interactions. It is based on the peaks that appear in the reduced density gradient (RDG) at low densities.

There is a crucial change in the RDG at the critical points in between molecules due to the annihilation of the density gradient at these points. When we plot the RDG as a function of the density across a molecule, we see that the main difference between the monomer (Figure 1a) and dimer (Figure 1b) cases is the appearance of steep peaks at low density.

a) Formic acid	b) Formic acid dimer

Figure 1

When we search for the points in 3D space giving rise to these peaks, non covalent regions clearly appear in the (supra)molecular complex (insets in Figure 1a and Figure 1b).