A benchmark for the non-covalent interaction (NCI) index or... is it really all in the geometry?

Describing non-covalent interactions (NCIs) has shown to be of paramount importance in many areas of theoretical chemistry and related disciplines, such as biochemistry and material science. However, non-covalent interactions are subtle effects, very difficult to reproduce from most common computational approaches. Electron density studies have shown to provide a good semiquantitative visual approach to such interactions, which are much less prone to method dependency. But to which extent? This is the question addressed in this contribution. The NCI approach based on the reduced density gradient is given the third degree so as to provide the user with a benchmark on how it is affected by the computational method and the basis set of choice. We have assessed the dependence of the NCI results on the geometry. This last question is addressed in detail to dissect how, why and when the NCI method can be used to understand dispersion interactions. Along various examples, we will show that the NCI index is very little dependent on the method and basis set used in the calculation of the electron density as long as the geometry is kept fixed. Indeed, the biggest variations in NCI come from changes in the geometry. Thus, methods which provide descriptions of a given interaction type of different accuracies will yield different electron density organizations. This gives no qualitative variations in the NCI 3D picture. But it is reflected in quantitative NCI measures even in very subtle cases. Moreover, in the case of a failure of the calculation method, NCI can also reveal the sources of its error. NCI volumes are able to locate the energetic ordering in various conformational situations, but always in a relative manner. Absolute values should not be used in comparisons, nor between compounds that do not belong to the same family.