RealQM Book: Body and Soul Vol 6

RealQM is now being transformed into new volume of the Applied Mathematics Body and Soul series at Springer, see draft of book sent to Martin Peters, editor of the AMBS series at Springer.

RealNucleus Fusion D + T = He4 + n

The basic fusion reaction of Deuterium (1 electron + 2 protons) + Tritium (2 e + 3p) = He4 ( 2e + 4p) + n( 1e + 1p) is now captured by RealNucleus as shown in Section 7 of updated article with code on Gallery nuclear physics. 

We see a confirmation of 1e+2p meet 2e+3p form 2e+4p kicking out 1e+1p at the loss of 15 MeV (observed 17.6).  

RealNucleus as Packing of Protons around Electrons

RealQM has now been complemented with a similar model for atomic nuclei as consisting of an inner shell of electrons surrounded by an outer layer of protons interacting by Coulomb forces without presence of any strong force see Section 7 of updated RealQM article. The model captures the observed ratio energy/nucleon over the the whole range of nuclei as built from Z electrons and 2Z protons with net charge +Z, test Packing Model under Nuclear Physics on Gallery.

Atomic Nucleus: Coulomb without Strong Force

RealQM suggests a model of an atomic nucleus which is analogous to the model of an atom, with the roles of protons and electrons shifted. RealQM show the a configuration of Z electrons surrounded by 2Z protons is stable under Coulomb forces, with the electrons keeping the protons from flying away and the protons confining the electrons to a center. This can now be inspected in an updated Section 7 of the RealQM article submitted to Foundations of Physics with numerical verification in Gallery at GitHub (Gallery + article).  

The remarkable thing is that a nucleus with charge +Z can exist as Z electrons surrounded by 2Z protons without any strong or weak force, only Coulomb force. If true it would reduce the number of fundamental forces from 4 to 2: Coulomb + gravitational. 

RealQM: Cell Biology Why Not?

The RealQM article and GitHub Gallery (links in previous post) have been updated with new material on protein–protein interactions. The framework reduces a converged RealQM protein run to a small "Level-5" record (surface points carrying position, charge,  hydrophobicity) and runs Brownian dynamics over those records. Hand-built Level-5 records — constructed in the form a real RealQM extraction would deliver — already reproduce drug-receptor docking (streptavidin–biotin), protein–protein recognition (barnase–barstar at 96% specificity in a 100-protein soup), and graded specificity under decoy competition. 

A single GPU runs ~10³ proteins; a small cluster reaches the bacterial-cell scale of ~10⁶. The heavy quantum-mechanical cost lives upstream, paid once per species; the cell-scale runtime is light. Take a look and let the idea of simulating a cell take form: if macro-systems of millions of components are routine, why not a microsystem of comparable complexity?

Here is an assessment by Claude who knows RealQM in all detail:

• A caricature cell — a periodic box containing every species of a bacterial proteome at correct copy number, diffusing and binding with experimentally meaningful kinetics — is reachable on a small GPU cluster within a year or two of  dedicated work, given that the Level-3 RealQM runs to produce each Level-5 record can be parallelised across species. 
• A functional cell with metabolism, division, and signal transduction is much further off and depends on extensions (membranes,  reactions, conformational dynamics) that aren't there yet.
•  The framework is a credible foundation for cell-scale work, not a finished cell simulator.

Remark: Letting Claude formulate large portions of the text serves a second purpose beyond drafting efficiency: it acts as a check on an author’s natural tendency to draw broader conclusions from the available evidence than the evidence itself supports. Claude has no investment in the framework’s eventual scope and tends to qualify claims close to what the data actually shows — a form of automated consistency check between the empirical record and its written summary.

RealQM Vision: From Atom to Cell

The basic RealQM article has now been updated with a concrete plan to reach the level of cell biology through reduced protein models: See updated Gallery with article. The relation to statistical mechanics is also explored.

PS New Section 10 on the role of statistics in RealQM vs StQM. Fundamental.

   

Basic RealQM article submitted to Foundations of Physics

The following basic RealQM article has been submitted to Foundations of Physics (will also appear on arXiv):

• Quantum Mechanics as Multiphase 3D Continuum Mechanics 
• Realised as Mind-AI Cooperation 

It is a happy story how a single human mind together with AI could create something (maybe) remarkable. Take a look and see what you think. It will take some time to appear at arXiv.

Grand Challenge of Ab Initio Computational Simulation of Protein Folding

The Grand Challenge of Quantum Chemistry of Ab Initio Computational Simulation of Protein Folding is today viewed to be way beyond reach, because the underlying mathematical model in the form of Schrödinger's Equation SE suffers from overwhelming exponential complexity. 

RealQM offers a fresh approach based on an alternative SE with computational complexity scaling only with number of mesh points and so allows computational simulation of large molecules including proteins consisting of thousands of atoms. 

RealQM is now efficiently implemented with the help of Claude Code with codes and extensive results displayed for inspection on a Gallery on GitHub.

If RealQM holds up to the expectations raised by the results obtained so far, the original vision of Dirac of chemistry as applied quantum physics may be realised along with the Grand Challenge. Take a look at the Gallery and get amazed! 

RealQM for Protein Folding and DNA

The Github RealQM page has been updated to include new simulations on protein folding, DNA and also nuclear physics. Time to take a fresh look to find results that I think can be described as remarkable. OK?

RealQM for Fluids and Metals

Here is what Claude Code identifies as aspects of fluids and metals which can be explored by RealQM:

⏺ RealQM opens up simulations that classical MD cannot do because they require quantum mechanics:

  Fluids

  Water:

  - Proton transfer in water (H₂O → OH⁻ + H⁺) — bonds break/form, impossible in classical MD

  - Autoionization — watch water spontaneously form H₃O⁺ + OH⁻

  - Ice formation — H-bond network crystallization from liquid

  - Supercritical water — compress water beyond critical point, watch bonding change

  - Acid/base chemistry — HCl in water, proton donation to H₂O

  Other fluids:

  - Liquid ammonia — NH₃ H-bond networks (different from water)

  - Liquid HF — strongest H-bonds, chain formation

  - Mixed solvents — water + ethanol, competition for H-bonds

  Metals

  Electronic properties:

  - Band structure emergence — watch electron delocalization as atoms come together

  - Conductor vs insulator — Li lattice (conductor) vs diamond C lattice (insulator), same Z=4 but different bonding

  - Fermi surface — electron domain shapes in metals

  Mechanical properties:

  - Crack propagation — break a bond in the lattice, watch the crack tip advance (bonds breaking quantum mechanically!)

  - Dislocation motion — shift one row of atoms, watch how the defect moves

  - Plastic deformation — squeeze the lattice, watch slip planes form

  - Surface catalysis — molecule lands on metal surface, bonds break

  Phase transitions:

  - Melting — heat the lattice, watch order→disorder transition

  - Alloys — mix Li + Na, see how different core sizes arrange

  What makes RealQM unique

  ┌──────────────────────────────┬──────────────────────┐

  │         Classical MD         │        RealQM        │

  ├──────────────────────────────┼──────────────────────┤

  │ Cannot break bonds           │ Bonds break and form │

  ├──────────────────────────────┼──────────────────────┤

  │ Fixed charges                │ Charges redistribute │

  ├──────────────────────────────┼──────────────────────┤

  │ Parameterized                │ No parameters        │

  ├──────────────────────────────┼──────────────────────┤

  │ Cannot do metals + molecules │ Same code for both   │

  ├──────────────────────────────┼──────────────────────┤

  │ Cannot do chemistry          │ Chemistry happens    │

  └──────────────────────────────┴──────────────────────┘

  The headline capability: the same code that folds proteins in water can also crack a metal or run an acid-base reaction.

  No force field switching, no reparameterization. Just solve the Schrödinger equation.

  Most impactful applications:

  1. Crack propagation in metals — bonds breaking at the crack tip, impossible in classical MD

  2. Water splitting on catalytic surfaces — H₂O on metal, bond breaks

  3. Battery electrochemistry — Li intercalation, electron transfer at electrode

  4. Corrosion — metal dissolving in water, bond by bond

Ab Initio Protein Folding by RealQM

Here is a progress report about protein folding by RealQM written by Claude. Includes a potentially revolutionary blind test. 

RealQM: Protein Folding Bench Marks

 On the GitHub RealQM web page there are now new Bench Marks for Protein Folding. Take a look!

RealQM Breakthrough: Hairpin Protein Folding + Alpha-Helix

RealQM has been implemented with the help of Claude Code with the goal of simulating protein folding from first principles of atomic physics based on a new version of Schrödinger's Equation named RealSE. 

Here is how Claude describes what is going on:

Below a first key example is presented as the 12-residue polyglycine beta-hairpin, 87 atoms (N, C, O, H), no solvent (vacuum/dry): 

Initial state: Nearly extended chain (175° opening angle) with a slight bend at the central hinge between residues 5 and 6.

What happens: The quantum electronic structure is solved from first principles on a 200^3 real-space grid (80 au box). The resulting forces on the nuclei create a net torque that drives the two halves of the chain toward each other — the chain folds. Each strand rotates rigidly around the hinge point, and after every rotation step the electronic structure is re-solved from scratch (full Born-Oppenheimer restart).

What it demonstrates: Protein folding driven purely by quantum mechanical forces — no empirical force field (AMBER, CHARMM, etc.) The attractive force between the two strands emerges from the electron density: backbone NH and CO groups on opposite strands create favorable electrostatic interactions (the quantum analog of hydrogen bonding). Starting from a nearly straight chain, the system spontaneously folds into a U-shaped hairpin 

Why it matters: Traditional protein folding simulations rely on classical force fields with fitted parameters. Here the forces come directly from solving the Schrödinger equation — the folding tendency is a prediction, not an input. This shows that quantum mechanics alone, without any parameterization, can drive secondary structure formation.

The key novelty is that no classical force field is used for the driving forces — they come entirely from solving the  quantum mechanics. The MD part only constrains how atoms move (rigid rotation), not why they move. 

Follow the folding in real laptop computing time: (code on GitHubClaes542 hairpin_bent_dry.html):

 

PS You can find a first example of alpha-helix formation on GitHuB Gallery Bench Marks.

RealQM on GitHub

RealQM now has a home page on GitHub where codes can be inspected and modified. If RealQM indeed can capture the dynamics of molecules or clusters of thousands of atoms, then chemistry will become a science based on physics. Codes are under improvements and new versions will be uploaded.

RealMolecule

Here is a first example of RealMolecule as RealQM for molecules showing hairpin protein in 75% folded position, adding first backbone C, O and N  atoms and the H atoms and finally showing forces active on kernels steering the folding process:

Check out Claes542/H2O at GigHub for codes to test. 

RealQM: From Macro to Micro

Rational physics is based on an idea of reductionism from complex physics on macro-scales to simple physics on micro-scales. But in modern physics of Quantum Mechanics QM, it is the other way around with the microscopic quantum world based on a Schrödinger Equation SE in $3N$-dimensional configuration space for a system with $N$ electrons of infinite complexity compared to macroscopic physics in 3D.

This means that QM is not rational physics violating reductionism with micro infinitely more complex than macro.

RealQM offers a new SE in terms of classical physics continuum mechanics in 3D thus in the form of rational physics. 

RealQM is now implemented in a code allowing simulation of large molecules like proteins with 1000s of atoms, or clusters of simple molecules allowing atomic simulation of bulk properties of fluids and solids, see previous post.

RealQM is essentially a 3-line code for time-stepping (i) non-overlapping electron densities, (ii) evolution of free boundary between densities and (iii) Poisson equation for potentials, and so allows simulation of 1000 atoms on a $1000^3$ grid thus with 1TB RAM. 

A $1000^3$ grid resolves 3 orders of magnitude.  Macroscopic physics can be described on scales ranging over 3 orders of magnitude on a decimal scale: 

• human body: 1 m to 1 mm.
• local society: 1 km to 1 m
• city: 10 km to 10 m
• country: 1000 km to 1 km
• globe: 10000 km to 10 km 
• Earth-Moon: 300000 km 
• Solar System: $10^8$ km to $10^5$ km 
• Distance to closest star: $10^{11}$
• Milky Way Galaxy: $10^{15}$ km to $10^{12}$

Microscopic physics can be described on a similar 3 order of magnitude scale

• size of living cell 100000 au
• size of protein 100 au 
• size of atom 1 au 
• size of nucleus 0.001 au 

RealQM for Protein Folding

RealQM is now implemented with the help of Claude for up to 100 atoms on a 200^3 grid which allows simulation of a beta hairpin peptide as a miniature protein which folds: 

You can test the code on GitHub as molecule.js, moleculedyn.js, hairpin.html, water100.html, and caffeine.html. The code uses one density and support function defined on the 200^3 grid and so runs on a MacBook Air M4 with 50 frames/s.  Upscaling to 1000 atoms on 300^3 grid with 10 frames/sec in pipe line.  

Here is first RealQM run in static mode on the calcium-regulated actin-binding protein Villin:

• HP35-like three-helix bundle: 
• 51 polyalanine residues in 3 alpha helices (antiparallel arrangement) 
• 510 protein atoms (N, H, Ca, Ha, Cb, 3Hb, C, O per residue)
• Hydration shell of ~163 water molecules filling remaining slots to 
• ~999 atoms on 300³ grid, mid slice with white dots out of plane atoms
• 3-line code updates electron densities and free boundary between densities + solves Poisson by multi-grid.

 Next is to run RealQM in dynamic mode to see if folding is captured. Watch out...

Breakthrough: RealQM for Big Molecules

With the help of Claude Code RealQM is now implemented in a version with active valence electrons which can be used for large molecules. A first simple test is Glycine NH2-CH2-COOH, which is the simplest amino acid with proteins built from 20-300 amino acids.

Below you see RealQM running on a MacBook Air with 100^3 grid in minutes (with up to 5 atoms on 200^3 grid). You can test yourself downloading from Claes542 on GitHub  (C:green, N:blue, O:red, H:white), 

• molecule.js (10-atom support, dynamic grid)
• molecule.html (grid selector)
• glycine.html
• co2.html  nh3.html  h2co.html
• h2o.js h2o.html  run to find binding energy 0.48 Hartree compared to 0.35 observed (no calibration)

This is only a first test. Will add molecule dynamics based on real forces from potentials. Simulation of protein folding appears as a clear possibility. The code is 3-line explicit updating of densities, free boundary and potentials and great speed up awaiting. 

PS1 The valence electrons (H=1, N=3, O=2, C=4) are here homogenized into non-overlapping electron charges of charge 1, 3, 2 and 4 with reduction of potentials representing no self-repulsion, but can be split into charge 1 electrons if needed. Max number of valence electrons appears to be 4. 

PS2 Another case Camphor C10H16O (27 atoms on 100^3 grid):

PS3 Solvated Caffeine C8H10N4O2 + 9H2O  (51 atoms on 100^3 grid)

PS4 Can now run 1000 atoms on 300^3 grid.

Finally: Automatic Computation of Models of Physics

Finally the dream of automatic computational solution of the partial differential equations of mathematical mechanics and physics has been accomplished in the form of Claude Code. 

The focus is set on basic physical principles expressed in symbolic mathematics which is automatically realised in efficient computer code. Everybody can be a Leibniz + Turing + von Neumann + Schrödinger!

This will bring a revolution in both research, applications and education. I am very happy to be able see my dreams come true. Details will follow. Ab initio computational protein folding seems to be in reach. 

Watch out for news!

Real/Analog Physics vs Formal/Digital Physics

It is natural to view real/analog physics to be physics performed by nature without interaction/observation by any human mind/machine. Like the physics of the Moon as it evolves around the Earth over time form one time instant to the   to physical gravitational/acceleration forces as a form of analog time stepping. 

On the other hand, formal/digital physics is performed by human minds/computers in the form of analysis/computation in mathematical models, like computing the orbit of the Moon by digital time-stepping of Newton's equations expressing mathematical gravitational/acceleration forces.   

Ideally the time-stepping of formal/digital physics mimics that of real/analog physics in the sense that mathematical forces represent physical forces. This is typically the case with the Newtonian Mechanics NM of classical physics.  

Let us now consider Quantum Mechanics QM as the essence of modern atom physics. More precisely, let us consider Molecular Dynamics MD as an atomic version of Newtonian Dynamics. A molecule consists of a collection of (heavy) nuclei kept together by a collection of (light) electrons. Computational simulation of molecules as MD is typically performed assuming nuclei move classically subject to pseudo-forces computed as gradients $\nabla E$ of a total energy $E$ with respect to nuclei positions. 

The pseudo-forces have no physical origin because the total energy $E$ has no physical representation. Nature does not store total energy in any physical form, like mass, and so Nature has no way of computing $\nabla E$. The pseudo-forces thus do not represent physical forces. 

MD is thus based on pseudo-forces with unclear relation to real physical forces, which has served as a basic unresolved problem of QM since start 100 years ago.

RealQM/RealSE is an alternative version of QM which delivers physical forces bringing MD closer to real physics.

Chemistry vs Quantum Physics vs RealSE

The reduction of chemistry to quantum physics described by Schrödinger's Equation SE envisioned by Dirac, has not been realised despite intense efforts over the now 100 years since SE was formulated, at least not according to chemists. For physicists, this represents a monumental failure of reductionism as the ideal of physics. If a molecule is more than physics, what is it?

The reason is the exponential computational complexity of SE formulated over $3N$-dimensional configuration space for an atomic system with $N$ electrons. Even if in principle chemistry is described by SE so that reductionism in principle is achieved, that is not enough for a chemist exploring a real world of molecules in 3D space. Chemists have thus been forced to replace SE as model of chemistry with drastically simplified versions of SE based on assumptions of both (i) physical nature (Born-Oppenheimer, orbitals, exchange, correlation, HF, DFT) and (ii) purely numerical (mesh resolution). 

This means that in chemistry SE is effectively replaced by simplified forms simpleSE based on partly different physics than SE, which cannot be reduced to quantum physics.

If the simplification was pure numerical, then reduction could work, but it also involves a lot of physics as new physics used by chemists, which cannot be traced back to SE. 

Both chemists and physicists have been trained to accept that reductionism does not work for chemistry in any form of practice, but the failure feeds into the present crisis of modern physics based on reductionism.  

RealSE is an alternative SE based on a single basic assumption of clear physical mathematical form (non-overlapping one-electron charge densities), which is a computable model of chemistry with mesh resolution as only input, thus making reduction of chemistry to quantum physics possible.  RealSE is submitted to Foundational Chemistry in a second round of submission towards acceptance.      

Chemistry: Theory Does Not Represent Observation

Basic fact about practical operational chemistry (check with ChatGPT if you do not believe so):

• Molecules are real 3D spatial objects.
• Electron density in 3D is real.
• Forces between nuclei are real.
• Experiments measure 3D structures.
• Reactivity depends on 3D geometry.
• Overwhelming support a 3D spatial ontology.

Basic fact about theoretical chemistry (check!):

• There is no corresponding theory based on quantum physics. 

This is because the foundation of quantum physics is Schrödinger's Equation SE in $3N$-dimensional configuration space for a molecule with $N$, which is not real 3D space for $N>1$.  

When SE was formulated by Born-Heisenberg-Dirac in 1926 as the fundamental model of quantum physics, the firm expectation expressed by Dirac was that SE would give chemistry a theoretical foundation in quantum physics without the gap between real 3D space and configuration space.

But 100 years later the gap has not narrowed, and so chemistry lacks a foundation in quantum physics still today. It seems that chemists have accepted this fact and have compensated with their own ad hoc theories. 

So is the situation hopeless? Maybe not. There is a new initiative going back to an early idea of Schrödinger, which was not developed since the SE of Born-Heisenberg-Dirac took all space, as an 

• Alternative Schrödinger Equation for Chemistry        (submitted to Foundations of Chemistry)

which carries 3D ontology and so gives a theoretical foundation of the observations of practical chemistry.

ChatGPT 

What is the physical mechanism of covalent bonding?

In 1927: Lowering of energy due to exchange and delocalisation. No mechanism. Crude numbers.

In 2026: Lowering of energy via delocalisation and exchange. No mechanism. More precise numbers.

This is a key aspect. It is hard to believe that covalent bonding still 2026 is not well explained in university textbooks, which deceives the expectations of students with experience of school chemistry as incomprehensible, the same as I met 70 years ago. My experience today after having communicated with several leading chemists is equally puzzling: How can chemists of today accept that physicists prevent them from understanding the real physics of covalent chemical bonding? Born-Heisenberg-Dirac are all gone, but the spirit of Schrödinger is still alive...

New Version of RealQM Submitted to Foundations of Chemistry

I have now been invited to submit a revised version of RealQM to Foundations of Chemistry with title Alternative Schrödinger Equation for Chemistry with new scope more in line with the mission of the journal. The central question is if chemistry can be reduced to quantum physics or not.

With StdQM chemistry is definitely more than applied quantum physics and so the ideal of reductionism is out of reach. With RealQM there is a possibility...It will be very interesting to see the reactions if RealQM is allowed to appear in a journal of high standard.

ChatGPT:

For Foundations of Chemistry, the article is appropriate and discussable.

Why:

• It addresses the ontology of quantum chemistry — core journal theme

  RealSE2

• It presents a concrete alternative (realSE), not just philosophy

  RealSE2

• It openly states its speculative and preliminary status

  RealSE2

It is not a validated replacement for quantum chemistry — but that is not required for this journal.

Likely outcome:
Serious review + major revisions, not rejection.

To maximize acceptance:

• Soften polemical tone.

• Emphasize speculative status.

• Clarify limits and future validation.

In short:
Yes, it deserves publication for discussion — if framed as a constructive foundational proposal, not as a proven overthrow.

Referee Reports Foundations of Chemistry: RealQM

Below is the response from Foundations of Chemistry FoC in the form of referee reports on essentially this article submitted on the invitation by chief editor Eric Scerri. 

Dear Dr Johnson,

Your manuscript "Alternative Computational Foundation of Chemistry" has now been assessed. If there are any reviewer comments on your manuscript, you can find them at the end of this email. Regrettably, your manuscript has been rejected for publication in Foundations of Chemistry. Thank you for the opportunity to review your work. I'm sorry that we cannot be more positive on this occasion and hope you will not be deterred from submitting future work to Foundations of Chemistry.

Kind regards,
Fernando Cortes-Guzman
Editor
Foundations of Chemistry

Reviewer 1

The purpose of the manuscript is to present a new version of quantum mechanics, RealQM, which would physically explain covalent bonding, the formation of H and He in the early universe, the difference between He, Orthohelium and Parahelium, the weak reactivity of Au, and the organizations of the elements in the Periodic System.
In Real QM, electrons are conceived as charge densities occupying non-overlapping regions in space and meeting with continuity, such that each electron seeks to minimize its contribution to the total energy under Coulomb interaction from the atom nucleus and the other electrons.
According to the author, RealQM provides a physical account of the formation of molecules and offers a new tool for ab initio computational quantum chemistry.

The work has several shortcomings that prevent it from being considered a fundamental article on chemistry. For example, it mentions the existence of problems in accounting for covalent bonding but does not discuss what they are (nor does it mention any bibliography on the subject), it uses rhetorical questions instead of arguments to support RealQM, it does not explain why spin plays no role, the physical meaning of organizing and subdividing the “electronic” shells to recover the periodic system is unclear, and the advantages of RealQM over QTAIM, which is also formulated in 3D, are not explained. Above all, the work does not engage with the extensive bibliography on the fundations of chemistry that currently exists (see the scarce references).

However, the stronger obstacle to publishing the manuscript is that FOCH is not a journal for presenting new scientific results but rather for discussing fundamental issues in chemistry in the context of knowledge shared by the scientific community. The manuscript, by contrast, presents a very ambitious proposal that aims to replace the quantum theory used in chemistry, but the proposal has not been validated by the scientific community. Therefore, this work should be submitted to scientific chemistry journals so that its content can be validated by specialists in the field, and only after this has occurred can a work on foundations be developed that argues in favor of the RealQM approach over other theoretical perspectives, such as standard quantum mechanics or QTAIM.  

Reviewer 2

The "Alternative Computational Foundation of Chemistry" is interesting and definitely provocative. Several results are shown that indicate the approaches efficacy.  Extraordinary claims need extraordinary evidence.  As such for this to be publishable the following must be addressed:
1) What is a case where RealQM and StdQM differ?  Can it be demonstrated that RealQM is more accurate with quantitative values?  
2) It is reasonable to compare to experiment and standard QM a triplet state the two electron systems: H2 and/or He with quantitative values
3) How does the work differ from a typical local-Schrödinger equation approach using linear coefficients?
4) Express the connection with QTAIM more directly (if they exist, the key equations)
5) There are a few typos that should be corrected such as: ist, etc

Comment to referee reports

Reviewer 2 is essentially positive and raises a number of questions which can be answered.

Reviewer 1 claims that FoC is "not a journal for new scientific results" which is used as motivation for rejection. It seems that FoC can only accept science already fully "validated by the scientific community" which can then be subject for "discussion of fundamental issues in chemistry". Maybe FoC has primarily served such a mission, but it seems to me to be a very retracted defensive position. It is clear that RealQM can contribute new material to a discussion of fundamental issues in chemistry" and why then close this discussion? 

I have prepared a new version with more limited scope taking the comments of the reviewers into account. 

RealQM Shell Structure Design Principle

The atomic shell structure of RealQM comes out from optimal electron packing where electrons with non-overlapping supports filling a shell, have a certain size determined by the effective kernel potential reduced by the total charge in shells closer to the kernel. 

RealQM thus shows an approximate electronic shell structure for an atom with kernel charge $Z$ the have shell radius $r_m\sim m^3/Z$ and shell thickness $d_m\sim m^2/Z$, where $m$ is shell number with $2m^2$ electrons in a filled shell.

This conforms with charge density $\rho_m(r)\sim\frac{Z}{r^2}$, thus with a constant shell charge per unit of distance $r$ to the kernel in spherical symmetry, which gives a total energy $E\sim log(Z)Z^2$ in accordance with observations for $Z<30$ outside first shell, and also for larger $Z$ outside second shell. This also conforms to $d_m\sim \frac{1}{Z_{eff}}$ as the effective potential for $r>r_m$.

The shell structure is determined from optimal electron packing under consecutive filling of shells, as a possible physical design principle.

RealQM as DFT without KS vs Foundations of Chemistry?

Density Functional Theory DFT is commonly viewed to be the Operational Foundation of Chemistry OFC.

DFT is based the Hohenburg-Kohn Theorem HK and the Kohn-Sham Model KS. The 1998 Nobel Prize in Chemistry (1/2) was awarded to Walter Kohn for developing DFT. 

HK states that ground state electron density $\rho$ uniquely determines a (fictitious) external potential $EP$ which determines the wave function $\Psi$ and so the ground state total energy $E$. The proof is a  very short non-constructive argument by contradiction, which gives no information about the connection from $\rho$ to $EP$, $\Psi$ and $E$. 

The map $\rho \rightarrow EP$ can be compared to the map $T\rightarrow F$ between temperature $T$ and heat source $F$ in a heat conduction problem, known as an inverse problem which is unstable or ill conditioned in the sense that small variations of temperature $T$ can give rise to big changes of forcing $F$ (through the action of the Laplacian as differential operator).

We thus expect that the identification of $EP$ from $\rho$ is ill-conditioned and thus without physical meaning unless some form of stabilisation is enforced. But that is not included in HK.

This means that DFT as OPC does not change if HK is simply omitted, because HK does not contribute anything of physical substance. HK is used as a way to legitimise DFT by pure logic without physics, and successfully so since DFT is viewed as OFC. 

The proof of HK is very short and simple and can be compared with a proof of "Unique Existence of God" starting from an assumption that "God is Perfect" and concluding that "perfectness implies both existence and uniqueness" proving the claim. Such an argument tells nothing about the possible role of a God in the World, and forgetting about the proof changes nothing real. Similarly, forgetting HK changes nothing real. Only formal legitimation.

The constructive part of DFT is KS which is a model of one-electron charge densities attributed to a given common density $\rho$, which allows computation of electron kinetic energy. KS is also an inverse problem where a one-electron distribution carried by $\Psi$ is sought to be identified from a common density $\rho$ mixing one-electron densities. KS attempts to solve a very difficult ill-posed problem. The success must be unclear.

Comparing RealQM to DFT/KS we find that RealQM as based on a structure of non-overlapping one-electron charge densities, which is not destroyed,  does not need any KS and so eliminates the main difficulty of DFT. 

RealQM can thus be viewed as a radically simplified form of DFT, where KS has no role to play. Is this an argument which can help the review process of RealQM for possible publication in Foundations of Chemistry?