This post arose from a comment attached to the post on Na2He and relating to peculiar and rare topological features of the electron density in molecules called non-nuclear attractors. This set me thinking about other molecules that might exhibit this and one of these is shown below.
The topology of the electron density is described by just four basic types, designed formally by the notation [3,-3], [3,-1], [3,1] and [3,3] and more colloquially by the terms nuclear attractor (NNA), line (or bond) critical point, a ring critical point and a cage critical point respectively. Mostly, the nuclear critical points coincide exactly with the actual nuclear positions, but more rarely these points are not found centered at a nucleus. It was such an NNA that was suggested as a comment on the post on Na2He. There I replied that another example of an NNA is to be found in H3+ and so its a short step to take a look at H42+ in a tetrahedral arrangement (DOI: 10.14469/hpc/2165). Since only two electrons are available for bonding, it is tempting to represent it as below, with dashed partial bonds connnecting the six edges of the tetrahedron and is associated with real normal vibrational modes; ν 416, 1490 and 1861 cm-1. A brief search on Scifinder, which appears to reference this species as hydrogen, ion (H42+), does not identify any publications associated with it (there are studies on H41+ however); if any reader here knows of any discussion please alert us!
Analysing the density however gives a different result. A NNA is located at the centre of the tetrahedron and a line (bond) critical point connects this to each of the four hydrogen nuclei. This result is similar to the obtained for H3+. It is rather odd that these non-nuclear attractors have not entered into the vocabulary used to describe the bonding in simple molecules, but this picture is certainly different from the more empirical dashed lines between the four nuclei that one is instinctively drawn to use (above).
The ELF analysis (performed using multiWFN) is more interesting. The nuclear basins associated with the hydrogens reveal each has 0.425e, but the central one (green below) has its own basin with 0.301e.
The NICS value associated with the non-nuclear attractor is -27 ppm, which is indicative of strong spherical aromaticity.
All of which goes to show that even the simplest of molecular species may still have properties that are unexpected or certainly not well-known!