Towards Understanding of Chemical Bonding

RealQM based on a new form of Schrödinger's equation in terms of non-overlapping electron charge densities meeting at a Bernoulli free boundary, gives a new view on the physics of formation of molecules by groups of atoms coming together into states of lower energy than when apart by establishing chemical bonds.  

StdQM describes chemical bonds as either covalent by "sharing of electrons" or ionic with "transfer of electrons" creating Coulomb bonds between charged ions, but in general as some sort of mix.  

RealQM gives a different description as basically covalent where the "sharing of electrons" is realised through the Bernoulli free boundary, where electrons meet with continuity of charge density with corresponding wave functions having vanishing normal derivatives. "Sharing" is thus replaced by "meeting". This allows electrons to meet between atom kernels and so decrease potential energy, without increase of kinetic energy because the "meeting" does not require vanishing charge density only normal derivative of wave function. 

The basic case is the formation of a H2 molecule from two H atoms considered e g in this post .

Let us now consider molecules of the form HXH with X an atom with two valence electrons in two forms as the 2nd column of the periodic table: Be, Mg, Ca, Sr, Ba,Ra, and 5th column: O, S, Se, Te, Po, Lv. Here the 2nd column is linear molecule, while the 5th including HOH is a bent molecule. 

RealQM offers a reduced model of X in the form of two valence electrons outside an inner shell of certain radius R representing the net effect of the other electrons + kernel as a +2 kernel. Running this code we get for a molecule bent to 90 degrees we get for R=0.5 a dissociation energy of 0.3178 Hartree (compared with 0.354 for HOH) with this output (code 3d on regular mesh with mesh size 0.1 atomic unit thus about 20 mesh points between kernels):

For a linear molecule like HBeH, we get with this code 

We see in these pictures as sections of 3d output the following:

• X atom electrons in red connecting to two H atoms in green, in bent and linear configurations.
• H atom meeting X in a narrow overlap region from level set representation of free boundary.
• Line section through kernels show wave function in yellow with in particular continuity of non-zero charge density/wave function at the free boundary as expression of the binding effect of the meeting between kernels. 
• We see small dissociation energy for large radius R of inner shell. 

More precisely we may compare to the following list values of dissociation energies:

• HOH   0.35 Hartree
• HSH    0.247
• HSeH  0.221
• HTeH  0.193
• HPoH  0.176
• HBeH  0.17
• HMgH 0.10
• HCaH  0.079
• HSrH   0.070
• HBaH  0.064
• HRaH  0.059

to see that R = 0.5 corresponds to HOH and R = 1 to HMgH. 

It remains to explain why HOH is bent but HBeH not. We expect this to depend on the different electron configurations of O and Be, with two electrons in the outer shell for Be, but possibly up to 6 for O. Will return with details. This connects to the dipole quality of HOH with the outer part of O negative and those of H positive. 

Bottom line so far:

• In RealQM electrons meet at a free boundary between kernels which decreases potential energy without increase of kinetic energy, as something easy to understand.  
• In StdQM electrons are "shared" which is a complex subject. 

We may view electrons as rivals competing to come close to kernels while repelling each other. An idea of meeting of rivals as a form of coexistence keeping integrity, may seem to be more natural than an idea of "sharing" between rivals with loss of integrity.