Non-covalent interactions index

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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.{{Cite Q|Q48042223|author=Pastorczak, E.|author2=Corminboeuf, C.|author2-link=Clémence Corminboeuf}}

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 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.{{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}}{{Cite Q|Q36837200|author=Contreras-García, J.|author2=Yang, W.|author3=Johnson, E. R.|author3-link=Erin Johnson|author2-link=Weitao Yang}} Being based on the electron density and derived scalar fields, NCI indexes are invariant with respect to the transformation of molecular orbitals. Furthermore, the electron density of a system can be calculated both by X-ray diffraction experiments and theoretical wavefunction calculations.{{Cite Q|Q87412684|author=Saleh , G.|author2=Gatti, C.|author3=Presti, L. L.|author4=Contreras-García, J.}}

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

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

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

$s(\backslash mathbf\{r\})\; =\; \backslash frac\{\backslash left\; |\; \backslash nabla\backslash rho(\backslash mathbf\{r\})\; \backslash right\; |\; \}\{2k\_F\; \backslash rho(\backslash mathbf\{r\})\; \}$

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

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.