TheNon-Covalent Interactions index, commonly referred to as simplyNon-Covalent Interactions (NCI) is a visualization index based in theElectron density (ρ) and the reduced density gradient (s). It is based on the empirical observation thatNon-covalent interactions can be associated with the regions of small reduced density gradient at low electronic densities. In quantum chemistry, thenon-covalent interactions index is used to visualize non-covalent interactions in three-dimensional space.^[1]

Its visual representation arises from the isosurfaces of the reduced density gradient colored by a scale of strength. The strength is usually estimated through the product of the electron density and the second eigenvalue (λ_H) of theHessian of the electron density in each point of the isosurface, with the attractive or repulsive character being determined by the sign of λ_H. This allows for a direct representation and characterization of non-covalent interactions in three-dimensional space, including hydrogen bonds and steric clashes.^[2][3] Being based on the electron density and derived scalar fields, NCI indexes are invariant with respect to the transformation ofmolecular orbitals. Furthermore, the electron density of a system can be calculated both byX-ray diffraction experiments and theoretical wavefunction calculations.^[4]

The reduced density gradient (s) is a scalar field of the electron density (ρ) that can be defined as

${\displaystyle s(\mathbf{r})=\frac{\left|\mathrm{\nabla }\rho (\mathbf{r})\right|}{2(3{\pi }^2{)}^{1/3}\rho (\mathbf{r}{)}^{4/3}}}$

Within theDensity Functional Theory framework the reduced density gradient arises in the definition of the Generalized Gradient Approximation of the exchange functional.^[5] The original definition is

${\displaystyle s(\mathbf{r})=\frac{\left|\mathrm{\nabla }\rho (\mathbf{r})\right|}{2k_F\rho (\mathbf{r})}}$

in which k_F is theFermi momentum of thefree electron gas.^[6]

The NCI was developed by Canadian computational chemistErin Johnson while she was a postdoctoral fellow atDuke University in the group ofWeitao Yang.

• Chemical bonding