View source for Non-covalent interactions index

[[File:Three water molecules cluster.jpg|thumb|NCI representation in 3D and 2D of a three water molecules cluster]] [[File:Six water molecules cluster.jpg|thumb|NCI representation in 3D and 2D of a six water molecules cluster]]
[[File:Eight water molecules cluster.jpg|thumb|NCI representation in 3D and 2D of an eight water molecules cluster]]

The '''Non-Covalent Interactions index''', commonly referred to as simply '''Non-Covalent Interactions (NCI)''' is a visualization index based in the [[Electron density]] (ρ) and the reduced density gradient (s). It is based on the empirical observation that [[Non-covalent interactions]] can be associated with the regions of small reduced density gradient at low electronic densities. In quantum chemistry, the '''non-covalent interactions index''' is used to visualize non-covalent interactions in three-dimensional space.<ref>{{Cite Q|Q48042223|author=Pastorczak, E.|author2=Corminboeuf, C.|author2-link=Clémence Corminboeuf}}</ref>

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{{sub|H}}) of the [[Hessian matrix|Hessian]] of the electron density in each point of the isosurface, with the attractive or repulsive character being determined by the sign of λ{{sub|H}}. This allows for a direct representation and characterization of non-covalent interactions in three-dimensional space, including hydrogen bonds and steric clashes.<ref>{{Cite Q|Q33830576|author=Johnson, E. R.|author2=Keinan, S.|author3=Mori-Sánchez, P.|author4=Contreras-García, J.|author5=Cohen, A. J.|author6=Yang, W.|author-link=Erin Johnson|author6-link=Weitao Yang}}</ref><ref>{{Cite Q|Q36837200|author=Contreras-García, J.|author2=Yang, W.|author3=Johnson, E. R.|author3-link=Erin Johnson|author2-link=Weitao Yang}}</ref> Being based on the electron density and derived scalar fields, NCI indexes are invariant with respect to the transformation of [[molecular orbital]]s. Furthermore, the electron density of a system can be calculated both by [[X-ray scattering techniques|X-ray diffraction]] experiments and theoretical wavefunction calculations.<ref>{{Cite Q|Q87412684|author=Saleh , G.|author2=Gatti, C.|author3=Presti, L. L.|author4=Contreras-García, J.}}</ref>

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

<math> s(\mathbf{r}) = \frac{\left | \nabla\rho(\mathbf{r}) \right | }{2 (3\pi^2)^{1/3} \rho(\mathbf{r})^{4/3} }</math>

Within the [[Density functional theory|Density Functional Theory]] framework the reduced density gradient arises in the definition of the Generalized Gradient Approximation of the exchange functional.<ref>Perdew, J. P., Burke, K. and Ernzerhof, M. (1996) ‘Generalized Gradient Approximation Made Simple’, ''Physical Review Letters'' '''77''', 3865, [https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.77.3865 doi:10.1103/PhysRevLett.77.3865]</ref> The original definition is

<math> s(\mathbf{r}) = \frac{\left | \nabla\rho(\mathbf{r}) \right | }{2k_F \rho(\mathbf{r}) }</math>

in which k{{sub|F}} is the [[Fermi energy|Fermi momentum]] of the [[Jellium|free electron gas]].<ref>{{Cite Q|Q21709392|author=Hohenberg, P.|author2=Kohn, W.|author-link=Pierre Hohenberg|author2-link=Walter Kohn}}</ref>

The NCI was developed by Canadian computational chemist [[Erin Johnson]] while she was a postdoctoral fellow at [[Duke University]] in the group of [[Weitao Yang]].

==References==
{{Reflist}}

[[Category:Chemical bonding]]