Mathematics-Physics-Chemistry Hierarchy

(Quantum) Chemistry QC is based on (Quantum) Physics QP is based on Mathematics M in a hierarchy from fundamental to application of fundamental, where fundamental sets the rules for application.

QP thus has to use a certain form of M to describe atomic physics, and QC has to conform to QP in  chemistry viewed as applied atomic physics. 

The mathematician John von Neumann set the rules of M for QP in his monumental Mathematical Foundations of Quantum Mechanics MFQM from 1932 as a scene of atomic physics occupied by wave functions over configuration space as elements of a Hilbert space becoming observables when acted upon by Hermitian operators, leaving the interpretation as physics to Bohr-Born-Heisenberg BBH, who came up with the Copenhagen Interpretation CI filling textbooks also today representing StdQM, while leading physicists no longer support CI. 

QC viewed as an application of StdQM, was then left to chemists to sort out, based on the foundation laid by  physicists guided by M according to von Neumann. 

Is QC a success story? Physicists would say yes arguing that the reason for success in chemistry is the great success of StdQM, while confessing that they do not consider CI to be correct physics. Chemists feel the same discord, but have to struggle to make sense of QC ultimately based on CI and StdQM. 

It seems that QC does not even give an explanation of the real of physics of covalent bonding of H2, which is accepted by a majority of qualified chemists, which is hard to believe but nevertheless true and so can be viewed contrary to success.  

For a modern physicist trained by von Neumann's MFQM, it may not a big deal that the CI does not explain real atomic physics, since BBH opened the door to view physics as epistemology (what we can say) and give up the classical ideal of ontology (what is).

But for a modern quantum chemist lack of ontology or lack of realism, becomes a main hurdle since a chemical bond keeping a molecule together like the covalent bond of H2, is something very real and physical. 

RealQM offers an alternative version of QP with clearly stated ontology in terms of systems of non-overlapping one-electron charge densities in a setting of classical deterministic continuum physics. RealQM offers an alternative version of QC, where in particular covalent bonding has a clear explanation. 

Summary:

The main theme of chemistry is molecules as collections of positive atomic nuclei held together by attractive electrostatic forces between nuclei-electrons balanced by repulsive forces between electrons and between nuclei all taking place in 3d real physical space. RealQM delivers these forces and so gives an explanation of e g H2 in clear physical terms. StdQM does not deliver forces and so cannot explain the physics of H2.