Non-covalent interactions index

NCI representation in 3D and 2D of a three water molecules cluster

NCI representation in 3D and 2D of a six water molecules cluster

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.^[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 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_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 of molecular orbitals. Furthermore, the electron density of a system can be calculated both by X-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

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

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

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

in which k_F is the Fermi momentum of the free electron gas.^[6]

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

1. Pastorczak, E.; Corminboeuf, C. (1 March 2017). "Perspective: Found in translation: Quantum chemical tools for grasping non-covalent interactions". The Journal of Chemical Physics. 146 (12): 120901. doi:10.1063/1.4978951. ISSN 0021-9606. PMID 28388098. Wikidata Q48042223.
2. Johnson, E. R.; Keinan, S.; Mori-Sánchez, P.; Contreras-García, J.; Cohen, A. J.; Yang, W. (1 May 2010). "Revealing noncovalent interactions". Journal of the American Chemical Society. 132 (18): 6498–6506. doi:10.1021/JA100936W. ISSN 0002-7863. PMC 2864795. PMID 20394428. Wikidata Q33830576.
3. Contreras-García, J.; Yang, W.; Johnson, E. R. (25 July 2011). "Analysis of hydrogen-bond interaction potentials from the electron density: integration of noncovalent interaction regions". The Journal of Physical Chemistry A. 115 (45): 12983–12990. doi:10.1021/JP204278K. ISSN 1089-5639. PMC 3651877. PMID 21786796. Wikidata Q36837200.
4. Saleh , G.; Gatti, C.; Presti, L. L.; Contreras-García, J. (4 October 2012). "Revealing non-covalent interactions in molecular crystals through their experimental electron densities". Chemistry: A European Journal. 18 (48): 15523–15536. doi:10.1002/CHEM.201201290. ISSN 0947-6539. PMID 23038653. Wikidata Q87412684.
5. Perdew, J. P., Burke, K. and Ernzerhof, M. (1996) ‘Generalized Gradient Approximation Made Simple’, Physical Review Letters 77, 3865, doi:10.1103/PhysRevLett.77.3865
6. Hohenberg, P.; Kohn, W. (9 November 1964). "Inhomogeneous Electron Gas". Physical Review. 136 (3B): B864 – B871. Bibcode:1964PhRv..136..864H. doi:10.1103/PHYSREV.136.B864. ISSN 0031-899X. Wikidata Q21709392.