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.
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.
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.
HKstates 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?
Continuing the discussion in the previous post on the possible role of ChatGPT as referee for scientific publication, find below a report (prompt: neutral fact-based) of this article for possible publication in Foundations of Chemistry:
ChatGPT Referee Report
(Foundations of Chemistry – style)
Manuscript:RealQM Chemistry: Introduction Author: Claes Johnson Basis: Manuscript text
The manuscript presents RealQM as an alternative conceptual and mathematical framework for the foundations of chemistry. The central proposal is to model electrons as non-overlapping, spatially extended charge densities in ordinary three-dimensional space, governed by Coulomb interactions and a free-boundary variational principle. The author’s stated aim is to provide both a computationally tractable and ontologically explicit account of atoms and molecules, in contrast to the configuration-space formalism and probabilistic interpretation of standard quantum mechanics.
The paper is ambitious in scope and deliberately interdisciplinary, combining elements of mathematical physics, computational modeling, philosophy of chemistry, and historical reflection. It is clearly written and internally coherent, though it advances claims that will be controversial among both physicists and quantum chemists.
Conceptual Contribution
From the perspective of Foundations of Chemistry, the manuscript’s primary contribution lies in its explicit ontological stance. RealQM assigns physical reality to electron charge densities in three-dimensional space and rejects the wavefunction in configuration space as a foundational object. This addresses a longstanding concern in philosophy of chemistry regarding the lack of clear physical interpretation of quantum-mechanical formalisms when applied to molecules.
The author also emphasizes explanation and intelligibility (“stories”) alongside numerical prediction, aligning the work with broader discussions in the philosophy of chemistry about the explanatory role of models beyond mere calculation.
Relation to Standard Quantum Mechanics
The manuscript positions RealQM as an alternative rather than an extension of Standard Quantum Mechanics. It argues that StdQM functions primarily as a predictive formalism and that its foundational role in chemistry remains unresolved. These claims are stated clearly but largely at a programmatic level. The comparison with StdQM is qualitative rather than systematic, and the manuscript does not attempt a formal reduction, equivalence proof, or controlled benchmark study.
From a philosophical standpoint, the manuscript contributes to ongoing debates about:
reductionism versus autonomy of chemistry,
the explanatory status of quantum-mechanical models,
the legitimacy of alternative ontologies in physical theory.
Mathematical and Computational Aspects
The mathematical formulation of RealQM is presented with sufficient clarity to allow evaluation. The use of variational principles, nonlinear PDEs, and free-boundary conditions situates the work within classical continuum mechanics rather than conventional quantum theory.
The computational implementation is described in outline and supported by references to code repositories. Numerical results are presented for a range of atoms and molecules, with reported agreement to known ground-state energies at a qualitative or semi-quantitative level. However, systematic numerical validation (error estimates, convergence analysis, robustness) is not a central focus of the paper.
Scope and Limitations
The manuscript concentrates primarily on ground-state properties and structural features. Topics such as excited states, spectroscopy, dynamical response, and measurement are only briefly mentioned or deferred. The treatment of spin and the Pauli exclusion principle is intentionally minimal, which may limit the framework’s immediate applicability but is consistent with the author’s foundational objectives.
The extension of the RealQM framework to nuclear structure is presented as exploratory and speculative. While conceptually interesting, this section may be seen as exceeding the core aims of the manuscript.
Style and Presentation
The manuscript is readable and engaging, but occasionally blends technical exposition with polemical or historical commentary. A more neutral tone in some passages would better suit an interdisciplinary readership. References to philosophy of chemistry are appropriate and relevant to the journal.
Recommendation
This manuscript raises substantive questions about the foundations of chemistry and proposes a clearly articulated alternative framework. Regardless of whether one accepts its conclusions, it engages directly with issues central to the remit of Foundations of Chemistry: ontology, explanation, and the relationship between physical theory and chemical practice.
I recommend publication after revision, with revisions aimed at:
clarifying the scope and limits of the proposed framework,
moderating comparative claims regarding Standard Quantum Mechanics,
and distinguishing more clearly between demonstrated results and speculative extensions.
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