From He Atom and Proton to He+H Cation as First Molecule

Following up the previous post we now let RealQM simulate the formation of the He+H molecule believed to be the first chemical compound created after the Big Bang (article in Nature). 

The general idea is that Big Bang created the Helium atom as a +2 proton kernel surrounded by two electrons as well as free protons, and that the compound He+H subsequently was formed when one of the two electrons of He was somehow transferred to a proton to form an H atom.

We now let RealQM model this process in 3d (run code yourself also finer resolution), and thus start with a Helium atom of ground state energy E =-2.903 Hartree combined with a proton within the range of its electrons, as depicted in this mid section plot (the colors represent the supports of the electrons):

We see here the characteristic feature of RealQM for Helium with the two electrons occupying two separate non-overlapping half lobes meeting at a plane together with the +2 kernel in the middle, and we also see a proton inserted on the left. The energy of the system is the ground state energy E = -2.903 of He. We watch the dynamics when the left electron is attracted to the proton and the right electron gradually takes over the Helium kernel with energy increasing to E -2.546:

and discover the following final state with energy E = -2.490:

We understand that -2.500 is the energy of separate He+ (-2.000) and H atom (-0.500) and so the final state of He+H can easily dissociate into separate He+ and H, thus altogether forming H from He. 

We also understand that the formation of He+H from He and proton requires input of energy (from -2.90 to -2.50), which we (as maybe expected) find to be equal to the repulsion energy of 0.40 between the kernels (see updated code), that is the energy required to bring a proton close to the He atom (somehow supplied by Big Bang).

RealQM thus let us follow the (protonation) process when He delivers one of its electrons to an inserted proton to create the molecule He+H which can separate into He+ and H. We understand that the initial He atom with two electrons separated in space is instrumental in the subsequent passage of the left electron to surround the proton preparing formation of an H atom, while leaving the Helium kernel to the right electron.  

In stdQM electrons overlap and separation as above seems more farfetched, right?

Recall the shooting off an electron from He requires 0.903 Hartree, which is a lot, while the above process with instead a proton capturing an electron involves only 0.403 Hartree from -2.903 to -2.500.

Also recall the stdQM gives a completely different picture with the energy of He+H ranging from -2.93 to -2.97 indicting that He+H forms from He and proton under release of energy. We thus have a clear case to compare RealQM with stdQM. What is your verdict?

PS The experimental discovery of HeH+ in 2019: