Chemical Bonding: StdQM vs RealQM

The basic problem of chemistry is how molecules as stable composites are formed through chemical bonding between collections of atoms consisting of positively charged nuclei surrounded by negatively charged electrons. The total energy $TE$ of a stable molecule is smaller than the sum of the energies of the atoms involved, with $TE$ the sum of 

• electron-nucleus potential energy $E_{en}$ negative
• electron-electron potential energy $E_{ee}$ positive
• nucleus-nucleus potential energy $E_{nn}$  positive
• electron kinetic energy $E_{ke}$ positive.

Standard Quantum Mechanics StdQM seeks to explains chemical bonding as an effect of: 

1. Localisation of electrons between nuclei giving maximal decrease of $E_{en}$.
2. Delocalisation of electrons over the whole molecule compensating for increases of $E_{ke}$ from localisation.  

We see a combined process of localisation-delocalisation, which is contradictory and requires intricate explanation to make sense forming a vast literature. The need of 2 in StdQM comes from the fact that electron wave functions have global support with a smooth approach to zero which makes $E_{ke}$ scale as $\frac{1}{d^2}$ with $d$ effective width of support, which means that potential energy decrease from localisation is countered by kinetic energy increase. 

In RealQM as an alternative to StdQM electron wave functions have non-overlapping local supports meeting with continuity without need of approaching zero. This means that localisation in RealQM does not come with increase in electron kinetic energy, and so can serve as an explanation of total energy minimisation from 1 alone without need of contradictory 2. For details see these articles.

Connecting to the previous post, recall that the main role of the Periodic Table is to support understanding of chemical bonding.