Secret of Covalent Chemical Bonding by RealQM

RealQM offers an easily understandable explanation on clear physical grounds of covalent chemical bonding, which has remained a mystery within Standard text book QM (see PS below).

To exhibit the physical mechanism forming a covalent bond, let us here as an exercise consider a 2d model of a X2 molecule formed by two X atoms, each with a +1 kernel surrounded by -1 electron charge density. We can think of X as 2d model of an H atom. The model is described in this post and is realised in this code. The real case in 3d is considered in this post.  The essential physics is Coulomb interaction between charges of same/different sign. The question is how a Coulomb chemical bond can be formed between two neutral atoms? 

We start running the code with the atoms separated (D=50) to get this output:

We see two essentially non-interacting 2d charge densities (red) together with mid line crosscuts of charge density (red), kernel potentials (blue) and electron potentials (light-blue, different sign) with a total energy of -0.9068. We see that the electron potentials (light-blue) are roughly half of the kernel potentials (blue), reflecting two-way interaction between electrons and one-way interaction between kernel and electron. The 2d energy here of -0.9068 is not the 3d energy -1.

We next run the code with smaller kernel distance (D=20) to get a smaller total energy  -1.05443:

We see that the left and right electron wave functions/charge densities now interact and meet at line orthogonal to the line between the kernels with continuity (and small/zero derivative). We understand that the decrease of total energy has two sources:

• Decrease of kinetic energy from the fact the electron charges meet with non-zero value at the free boundary, which does not require decay to zero with kinetic energy cost.
• Decrease of potential energy from the shaded region between the left kernel potential (blue) and left electron potential (light-blue) in interaction with the right electron charge density (red) and vice versa.

We decrease the distance further (D=15) to get essentially the same total energy as minimum, as the kernel repulsion takes over, running this code:

Altogether, RealQM offers an explanation on clear physical grounds in the form of Coulomb potentials of covalent chemical bonding. The essence is the Bernoullli free boundary between electron charges allowing concentration of electron charge between kernels without cost of kinetic energy. The secret is the decrease of potential energy from the above shaded area combined with large charge density at the free boundary. We understand that the bond is formed from a subtle interplay between electron charge distributions of substantial width with kernels of much smaller width. This is a new revelation by RealQM. Text book explanations struggle with “charge concentration”combined with “charge decentralisation” which appears contradictory.

PS chatGPT admits that there is no explanation in real physical terms of covalent bond.