Physics of the Covalent Bond Still Debated!

The article The Basics of the Covalent Bond in Terms of Energy and Dynamics by Nordholm and Bacskay from 2020 opens with the following surprising revelation as Abstract:

• We address the paradoxical fact that the concept of a covalent bond, a cornerstone of chemistry which is well resolved computationally by the methods of quantum chemistry, is still the subject of debate, disagreement, and ignorance with respect to its physical origin. 
• Our aim here is to unify two seemingly different explanations: one in terms of energy, the other dynamics. 
• We summarize the mechanistic bonding models and the debate over the last 100 years, with specific applications to the simplest molecules: H2+ and H2.
• In particular, we focus on the bonding analysis of Hellmann (1933) that was brought into modern form by Ruedenberg (from 1962 on). 
• We and many others have helped verify the validity of the Hellmann–Ruedenberg proposal that a decrease in kinetic energy associated with interatomic delocalization of electron motion is the key to covalent bonding but contrary views, confusion or lack of understanding still abound. 
• In order to resolve this impasse we show that quantum mechanics affords us a complementary dynamical perspective on the bonding mechanism, which agrees with that of Hellmann and Ruedenberg, while providing a direct and unifying view of atomic reactivity, molecule formation and the basic role of the kinetic energy, as well as the important but secondary role of electrostatics, in covalent bonding.

We learn that that the most basic of all of chemistry, the covalent bond of the H2 molecule, is still under debate, disagreement and ignorance within the accepted form of quantum mechanics. What to say about that?

We compare with RealQM as a new form of quantum mechanics, which captures the physics of the covalent bond in a very clear and easily understandable parameter-free mathematical form as described in this blog post and this computer code with more chemistry in these posts. What to say about that?

Hint: The key to the direct success without any manipulation of RealQM for H2 (connecting to the decrease of kinetic energy above), is that the two electron densities are localised to two half-spaces and meet at a plane perpendicular to the axis midway between the two proton kernels with continuity and zero normal derivative, and so do not have to decay to zero requiring kinetic energy. The electron density for H2 thus is roughly the double of that for H2+ with one electron, with corresponding roughly double binding energy in agreement with observation. RealQM thus has a clear direct physical meaning, which is not the case using standard methods for computing binding energies.  See output from RealQM code: