The Miracle of the H2 Molecule: StdQM vs RealQM

The H2 molecule formed by 2 neutral Hydrogen H atoms by a covalent chemical bond with a substantial binding energy of  0.17 Hartree, is according to chatGPT to be viewed as a miracle, and then also that two Helium He atoms do not form a bond. 

The textbook StdQM explanation starts out by noting that an H atom consists of a proton kernel of charge +1 which is surrounded by an electron charge density/cloud of total charge -1 which is attracted by the kernel. The total electronic energy has a contribution from Coulomb electron-kernel potential energy and so called kinetic energy measured by the gradient of the electron density.  

As two H atoms approach their electron densities start to interact into a total energy including (i) electron-kernel potential energies (negative), (ii) electron-electron potential energy (positive) and (iii) electron kinetic energies supplemented by (iv) kernel-kernel potential energy.  

As the distance between the kernels decreases, we expect that:

• (i) decreases because both electrons feel presence of both kernels, 
• (iv) increases because kernels come closer, 
• (ii) and (iii) is left open. 

With some knowledge of quantum mechanics, one would expect that at the same time: 

• (ii) increases because electrons come closer,
• (iii) increases because electron densities accumulate between kernels.  

Tendency of bonding by (i) would thus be counterbalanced by (ii)-(iv) and it would appear as a miracle that (i) could win.  

Since H2 is observed to form it is then up to the expert quantum physicist to explain the miracle, and this is done by claiming that both (ii) and (iii) are misconceptions. The expert argument goes as follows: 

• In fact (iii) decreases a little because electrons spread out over both kernels (delocalisation, Ruedenberg accepted argument)
• In fact (ii) decreases a little because electrons avoid each other even when accumulating between kernels (exchange, special StdQM effect) 
• Delocalisation and avoidance is not contradictory to accumulation between kernels. 

To a non-expert this would not make sense, and so the feeling of a miracle is undeniable.

RealQM as an alternative to StdQM gives a different explanation (displayed in article and book chap 31):

• (ii) increases only a little because electrons are kept separated into two half spaces
• (iii) decreases a little because the electron densities meet with non-zero density. 

H2 is a miracle in StdQM, which is deconstructed in RealQM (including non-existence of He2).