Uncovering Secrets of Chemical Bonds

In the previous post we used RealQM to uncover the formation of a H2 molecule as two Hydrogen H atoms at a kernel distance of 1.4 atomic units au find a electron configuration of minimal energy 0.17 Hartree below that of two separate atoms, thus forming a chemical bond with dissociation energy 0.17 Hartree.

RealQM also uncovered why two Helium He atoms do not form a chemical bond to a He2 molecule, that is why they find no kernel distance with lower energy than separate atoms. 

RealQM thus offers an explanation why H2 forms but not He2 and so reveals some of the secret of the chemical bond, which appears to be hidden in Standard Quantum Mechanics StdQM. 

Recall that the essence of the RealQM explanation of chemical bond is the presence of electron density accumulation between the kernels with two electrons meeting with non-zero density thus allowing decrease of potential energy forming a bond without increase of kinetic energy. 

In this post we let RealQM compute the dissociation energy E in Hartree of an X2 molecule with X an atom with 2 valence electrons outside a sphere around the kernel of varying radius R in au: 

• R = 0         E = 0
• R = 0.5      E = 0.09
• R = 1         E = 0.33
• R = 1.2      E = 0.28
• R = 1.5      E = 0.17 

which we can compare with the following experimental data for 2nd row of the periodic table

• Li2            E = 0.04
• Be2           E = 0.004
• C2             E = 0.23
• O2             E = 0.19

and for the 3rd row

• Na2           E = 0.027 
• Mg2          E = 0.00011
• Si2            E = 0.073
• S2             E = 0.11   

We see a qualitative match between RealQM and observation with dissociation energy starting at 0 for He slowly increasing to a maximum for C2 (R=1) and then decaying to O2 (R=1.2), with the same pattern in the 3rd row.

Let us now summarise RealQM for X2 molecules with 2 valence electrons recalling the previous post and starting by inspecting the following output (3d ab initio computation on uniform grid of mesh size 0.1 au with code link above):

We see two atomic kernels in black each surrounded by a 2-electron cloud/wave function in red (2d plot on plane trough the kermels), each 2-electron wave function  consisting of 2 half-spherical shell 1-electron wave functions meeting at a atomic free boundary slightly shifted outward from each kernel. We also see the inner half-spherical electron shell of each 2-electron meeting at a free boundary midway between the kernels. The yellow curve is a cross-cut of electron wave function with the dips showing the free boundaries. The radius of the inner shell system of X is 1 with 2 valence electrons outside which forms a chemical bond with dissociation energy 0.33 Hartree as shown above.

After proper inspection of the image, we can now understand the physics of chemical bonding of atoms with 2 valence electrons, as follows:

• Electron accumulation between the kernels add to binding.
• Electron accumulation between the kernels push the interatomic free boundary outwards to reach continuity with outer half-shell wave function, which subtracts from binding.
• There is a net binding effect which decreases proceding to the left in each row of the periodic table towards 0 for He and Neon. 
• In short: The presence of inner shells allow outer 2 valence shells to form a bond. 
• He does not have any inner shell and so does not bond to He2. 

The binding of atoms with 1 valence electron follows the physics of the H atom. We have thus reached some understanding of chemical binding of diatomic molecules with 1 or 2 valence electrons. 

It remains to consider the case with 3 valence electrons (Nitrogen N as 2+2+3) and 4 (Carbon C as 2+4), which can be expected to be similar to the case of 2 just considered. Together it will form a new theory of chemical bonding based on a new atom model in the form of RealQM. 

PS Concerning the state of the art of understanding of chemical bonding, let me quote from the recent article The Quantum Origin of the Periodic Table - The Role of Electrons Dynamics and Energy Degeneracy in Atomic Reactivity and Chemical Bonding by prof Sture Nordholm University of Gothenburg:

• It would be reasonable to also expect quantum chemistry to produce better understanding and more refined physical models of bonding but, unfortunately, this development has lagged behind high expectations. The access to rigorous and accurate quantum chemical methods has certainly helped understand but not greatly revise and improve, the simple models above, nor resolved the historical debate over the best physical interpretation of the computational results.

In short, chemical bonding does not appear to be well understood by expert chemists of today.