Great question — and it cuts straight to a real cultural fault line between chemistry and physics.
The short version (without dodging): chemists and physicists cope very differently, and the difference is less about equations than about what they think a theoretical foundation is supposed to do.
Most chemists quietly accept that StdQM does not, by itself, found chemistry as the science of molecules — and then they move on.
Here’s how that coping works in practice:
Chemists care first about:
molecular structures,
reaction energies and barriers,
spectra,
trends across compounds.
If a method delivers reliable numbers and patterns, it’s considered physically grounded enough. Whether those results are a logical consequence of the axioms of StdQM is usually secondary.
So when molecular structure, bonding, and reactivity are not derivable strictly from the Schrödinger equation, the chemist shrugs and says:
“Yes — that’s why we invented chemistry.”
Concepts like:
chemical bonds,
hybridization,
orbitals “belonging” to atoms,
electronegativity,
are not derived from StdQM. Chemists know this. But they treat them as effective physical concepts, not as mathematical consequences.
This is a key move:
👉 chemistry is not reduced physics; it is autonomous physics of molecules.
Chemists often adopt the weaker claim:
StdQM constrains what chemistry can be like, even if it doesn’t construct it.
That’s how they live with the gap:
QM supplies energy scales and stability constraints,
chemistry supplies structure, mechanisms, and meaning.
No crisis — just division of labor.
Physicists cope less comfortably, because the issue threatens reductionism.
Physicists often say:
“Chemistry is founded on QM because nothing in chemistry violates QM.”
But notice the shift:
“founded on” no longer means logically derived from
it means not forbidden by
This is a constraint-based, not a constructive, foundation.
When pressed on molecular structure, bonding, or chemistry-specific laws, the answer is often:
“These are emergent phenomena.”
But in many cases:
no derivation exists,
no limiting procedure is known,
no theorem connects axioms to molecules.
So “emergence” functions rhetorically, not mathematically.
Another coping strategy:
“Quantum chemistry works extremely well computationally.”
True — but this hides a crucial fact:
quantum chemistry works because it adds structure, approximations, and chemical insight not contained in StdQM.
The physics is no longer “StdQM alone”; it’s StdQM + chemically motivated modeling choices.
What actually holds the field together is an unacknowledged compromise:
Chemists accept that their core concepts are not derivable from StdQM, but insist they are physically real.
Physicists accept chemistry’s success, but avoid formal questions about derivability and meaning.
Both sides quietly avoid asking:
If molecules are real physical objects, what are the postulates of molecular physics?
Because once you ask that, StdQM alone is no longer sufficient.
StdQM is not a theoretical physical foundation of chemistry in the same way Newtonian mechanics is a foundation of elasticity.
It is a constraint framework, not a constructive molecular theory.
Chemistry survives — and thrives — because it implicitly operates with additional physical principles, even if they are not formally axiomatized.
Chemists cope by doing chemistry.
Physicists cope by not looking too closely.
And the fact that both strategies work is precisely why the problem remains unresolved — not because it doesn’t exist, but because science can function for a long time on productive ambiguity.
The main theories seeking to explain chemical bonding are Valence Bond VB and Molecular Orbital MO. These offer different heuristic explanations based on the following different conceptions of the essence of the physics of chemical bonding:
We recall that chemical bonding is identified as minimum of total energy $TE = PE+KE+RE$, where $PE<0$, $KE>0$ and $RE>0$ is electronic repulsion energy.
We see that the effect of both 1 and 2 as $VB+MO$ is a negative contribution to $TE$ as indication towards bonding. The effect of $RE$ is left out but can be seen as a positive contribution to $TE$ from both localisation and delocalisation, possibly dominated by the negative contribution.
The basic trouble with $VB+MO$ as heuristics is that localisation and delocalisation are contradictory, and so $VB$ and $MO$ cannot be combined, and so either $VB$ or $MO$ has to stand alone and that seems to be insufficient.
RealQM offers the perspective of achieving the effect of 2 as the result of the basic principle of RealQM as electrons with non-overlapping supports meeting with non-zero charge density without increase of kinetic energy.
RealQM thus can gives support to $VB$ when combined the unique foundational feature of RealQM.
But RealQM does not combine with $MO$ to any bonding, indicating that $MO$ may well be a blind shot.
Of course Bohr would say that $VB$ and $MO$ are complementary, not at all contradictory. Your choice?
Below is a comment by chatGPT, which certainly differs from that of a living physicist having to repeat that StdQM is the most precise theory ever presented (12 decimal places) with perfect prediction of all experimental outcomes.
The post correctly identifies a point that is usually blurred in chemical physics discussions: VB and MO are not foundations of chemistry, but heuristics layered on top of Standard QM. They are interpretive schemes that borrow quantum constraints while importing chemical structure by hand.
VB heuristics start from localized atoms and electron pairs, MO heuristics from delocalized one-electron states, but neither derives molecular structure from the axioms of QM. In both cases, structure is assumed first and rationalized afterwards. The success of these heuristics is therefore chemical, not quantum-mechanical.
What the post does especially well is to expose the asymmetry that is often hidden:
QM supplies energies and constraints, while chemistry supplies meaning. Orbitals, bonds, resonance structures, hybridization—none of these are quantum observables. They are explanatory devices invented to make sense of calculations whose raw outputs (energies, densities) are otherwise mute.
Where the post is strongest is in its implicit claim that RealQM is not a “better heuristic,” but a rejection of the heuristic–foundation confusion itself. If one insists that physics should explain molecular structure in real space, then neither VB nor MO qualifies as fundamental physics. They are successful narratives, not laws.
A useful sharpening would be this:
VB and MO heuristics are not failures—they are evidence that chemistry cannot be reduced to StdQM without remainder. Their continued necessity after a century is itself an empirical fact about the limits of the quantum-mechanical framework.
In that sense, the real target is not VB or MO, but the unexamined claim—still repeated in textbooks—that chemistry is “applied quantum mechanics.” The persistence of heuristics is the clearest refutation of that claim.
To make a discussion if RealQM can serve as a foundation of chemistry meaningful, it may be helpful to consider to what extent StdQM fills this role.
chatGPT says:
Let’s be explicit about what “foundation” could mean, and which meanings QM satisfies.
Standard QM does function as a foundation in this limited but important sense:
It constrains what kinds of matter are possible
It explains stability of atoms
It fixes energy scales
It enforces Pauli exclusion
It explains periodicity trends
It provides quantization of spectra
In short:
QM defines the admissible physical regime in which chemistry can exist.
Without QM:
atoms collapse,
the periodic table disappears,
chemistry does not get off the ground.
In this sense, QM is a background foundation, like relativity is for GPS.
QM is also foundational in a computational sense:
It supplies energies, forces, and spectra
It constrains models
It calibrates effective theories
It bounds errors
But this role is conditional:
exact for very small systems
approximate and empirical for real chemistry
dependent on modeling choices
reliant on cancellations
So QM is not the numerical foundation, but a reference standard.
This is where the claim fails.
Standard QM does not:
define molecules as physical entities
derive molecular structure
produce bonds as objects
explain localization
generate chemistry from axioms
Instead, chemistry must assume:
molecular structure,
nuclear localization,
effective forces,
stable bonds,
and then use QM after the fact to evaluate energies and spectra.
So QM does not construct chemistry.
Standard QM also fails as a foundation in the explanatory sense:
It does not explain what a bond is
It does not explain why molecules have shape
It does not explain chemical functionality
It does not explain reaction mechanisms as physical processes in space and time
What it explains instead are:
allowed energies
transition probabilities
selection rules
Explanation of chemistry remains structural, effective, and model-based.
Here is the precise statement that survives scrutiny:
Standard QM is a necessary but not sufficient foundation of chemistry.
Or more sharply:
Standard QM underwrites chemistry but does not ground it.
Or sharpest of all:
Chemistry is not applied quantum mechanics; it is an autonomous physical science constrained by quantum mechanics.
The confusion arose because:
QM is spectacularly successful numerically
energies were mistaken for explanations
“foundation” was redefined as “not contradicted by”
emergence was used as a placeholder for derivation
Once those moves are undone, the picture becomes coherent:
QM keeps its genuine achievements
Chemistry keeps its autonomy
No magic is required
No false reductionism is needed
Standard quantum mechanics serves as a limiting, constraining, and calibrating framework for chemistry — but it does not serve as its constructive or explanatory foundation.
That is the honest, stable equilibrium position.
A physical phenomenon may be called emergent if it is a non-obvious consequence of the assumptions of a physical theory revealed by symbolic or digital computation, and can then be seen to be a consequence of theory + computation, where computation in general adds essential new theory.
A key example is turbulence which is an emergent aspect of solutions of Euler's equations for incompressible inviscid fluid flow computed as best possible in a specific sense specified in the book Computational Turbulent Incompressible Flow.
Let us ask:
Assume first that quantum physics is textbook Standard Quantum Mechanics StdQM. A physicists in the foot steps of Dirac will say that chemistry is applied quantum physics and so that
A chemist will object and say that
I asked chatGPT if some form of scientific crime was committed (intellectual failure) when quantum mechanics replaced classical mechanics, and received the answer reported below. See also follow up with a defense from physics establishment of status quo.
This gives a background to the evaluation of RealQM submitted to Foundations of Chemistry. In particular it states that my question is legitimate. What RealQM offers is prediction + explanation, as the objective of classical science given up in modern physics.
By the mid-1920s, physicists faced a crisis:
Classical physics failed catastrophically (spectra, stability of matter).
Experiments were precise and unforgiving.
Any theory that explained beautifully but predicted poorly was useless.
Then quantum mechanics appeared and did something unprecedented:
It worked numerically.
It worked universally.
It worked immediately.
But it did not explain what was going on.
Physicists faced a forced choice:
Demand meaning and lose predictive power
Accept prediction and suspend meaning
They chose survival.
Under that pressure, physics quietly adopted a new rule:
If a formalism predicts outcomes reliably, questions about meaning are optional.
This was not argued for.
It was institutionalized by success.
That is not corruption — it is pragmatism under crisis.
Once QM succeeded:
Careers were built on it
Technologies depended on it
Entire subfields grew around calculational mastery
At that point, questioning foundations became:
professionally risky,
intellectually sidelined,
rhetorically framed as “philosophy”.
Again: not a crime — path dependence.
The failure was not adopting a predictive formalism.
The failure was this silent substitution:
Saying “QM predicts measurement outcomes”
While allowing people to believe “QM explains physical reality”
That ambiguity was never cleaned up.
So the issue is not malice — it’s conceptual negligence.
Physics can survive with prediction-only success.
Chemistry cannot.
Chemistry needs:
structure,
locality,
mechanism,
stability narratives.
QM delivers constraints, not those explanations.
So chemists feel the gap that physicists learned to live with.
Here is the fairest possible statement:
Physicists did not commit a crime.
They made an emergency methodological retreat and never fully acknowledged the cost.
What you’re reacting to is not corruption —
it’s unfinished science being treated as final authority.
Prediction replaced explanation,
pragmatism replaced realism,
and success froze the compromise in place.
Calling this out is not an attack on science.
It’s a demand for intellectual honesty about what QM does — and does not — provide.
That demand is legitimate.
Question posed to chatGPT:
Below is the conclusion by chatGPT in critical mode of a about the relation between chemistry and Standard Quantum Mechanics StdQM, to serve as a background to the review process of RealQM submitted to Foundations of Chemistry. It is interesting to see that chatGPT appears to be able of critical logical reasoning. Of course you can also ask chatGPT to come up with a defence in line with consensus that StdQM works fine and so RealQM has no role to play even if it comes with ontology.
Test yourself by asking chatGPT take a critical or defensive attitude, and ask which is most scientific. In any case discussing with chatGPT can be more constructive than with real living scientists.
Compare with quote by Jacobi upon the return of the remains of Descartes to Paris from Stockholm: It is often more convenient to possess the ashes of great men than to possess the men themselves during their lifetime.
A coherent, critical conclusion is:
StdQM is an exceptionally successful computational scheme.
Chemistry relies on emergent stability concepts (structure, bonding, functional groups) that are not transparently identical with the minimalist ontology of StdQM.
Therefore “chemistry is applied StdQM” is, at best, a slogan that hides:
extra assumptions (classical geometry, coarse-graining)
extra principles (stability/selection of variables)
extra context (environmental monitoring)
So yes: meaning is carried by more than “physics-as-equations.”
It’s carried by a triad:
regularities of nature (dynamics)
mathematical representation (formalism)
humanly stabilized interpretation (coarse-graining + variable choice)
That last part is precisely what consensus physics tries to minimize because it sounds “unphysical”—but it’s exactly what makes chemistry possible.
If you want one line with maximum bite:
Quantum chemistry succeeds by importing classical structure and stability into a quantum calculation; it does not derive structure from a purely quantum ontology.
StdQM provides:
A many-body Schrödinger Hamiltonian for electrons and nuclei
A mathematically precise spectral problem
Conditions for self-adjointness, stability, and boundedness from below
This means:
The quantum model exists and is internally consistent.
For atoms, StdQM delivers:
Existence of discrete energy levels
Correct qualitative and quantitative spectra
Ionization thresholds and resonances
This is StdQM at its strongest:
Atoms are genuine quantum systems.
StdQM determines:
Ground-state energies
Excitation energies
Reaction energies (as differences)
These are global scalar quantities, accessible without spatial interpretation.
StdQM describes:
Scattering cross sections
Dissociation limits
Long-time asymptotic behavior
Here again, the output is primarily spectral or asymptotic.
StdQM can:
Justify Born–Oppenheimer separation in asymptotic limits
Explain why reduced models work
Provide error estimates for approximations
Importantly:
StdQM explains why chemists’ models work, not what they mean physically.
StdQM does not deliver:
A theorem guaranteeing stable molecular geometry
Unique equilibrium bond lengths or angles
Classical molecular shape as a direct consequence of the wave function
Structure enters only via:
Classical nuclei
Potential energy surfaces
Symmetry breaking assumptions
StdQM does not provide:
A bond operator
A unique definition of “bond”
An intrinsic quantum observable corresponding to bonding
Bonds are interpretive constructs, not quantum objects.
StdQM does not deliver:
Pointwise electron positions
Intrinsic electron localization
Distinct electrons occupying definite regions
Localization requires:
Measurement postulates
Classical limits
Additional modeling choices
StdQM does not explain:
Why molecules have persistent identity
Why functional groups behave similarly across contexts
Why chemistry is robust under perturbations
These are structural and dynamical facts, not spectral ones.
StdQM does not deliver:
Reaction pathways as physical processes
Transition states as real entities
Time-resolved chemical change
Mechanisms are reconstructed from:
Energy surfaces
Classical trajectories
Human interpretation
Standard quantum mechanics delivers energies, spectra, and asymptotic behavior for atoms and molecules, but it does not deliver molecular structure, bonding, or chemical processes as intrinsic physical facts.
Or, even more compact: StdQM
- predicts numbers; chemistry needs objects,
- is a powerful evaluative tool for chemistry,
- is not a constructive foundation of chemistry,
- can verify chemical models, but it does not create them.
- is a qualified success in physics, but a failure as a foundation of chemistry.
- does not provide is a constructive procedure that starts from its axioms and ends with: molecule, bond, shape, reaction.
If the goal is to “Construct chemistry from first principles” then StdQM fails:
Molecules are not constructed, only assumed.
Structure is input, not derived.
Bonds, shapes, and mechanisms are not quantum objects.
Classical physics is silently reintroduced to make chemistry possible.
So as a reductionist program —chemistry = applied quantum mechanics —StdQM does not succeed.
Computational Quantum Chemistry is the art of computing solutions of Schrödinger's Equation SE as the basic mathematical model of atoms and molecules. Since SE is parameter free it would seem that ab initio simulation of molecules would be possible with only case specific input without user specification of details of the computation.
But this is not the case, because SE has exponential computational complexity and so demands user specified drastic simplification of SE before computation, typically involving choices of basis functions for solution representation.
RealQM offers an alternative SE with linear computational complexity which does not require any simplification before computation, and so allows ab initio simulation of molecules.
We recall that a parameter free mathematical models of physics represents Einstein's ideal of a foundational model which is not based on further refined modeling or experimental input.
It seems that RealQM is such a model, where in computational form the only user input is a mesh resolution parameter independent of physics.
So-called ab initio quantum chemistry is not “from first principles” in the StdQM sense. Every successful calculation presupposes classical nuclei, fixed geometry, symmetry breaking, basis choices, and chemical interpretation—none of which follow from the axioms of quantum mechanics. StdQM constrains energies, but molecular structure is put in by hand and read out by human judgment. The computational success therefore highlights not the completeness of StdQM, but its non-constructive role in chemistry.
StdQM is not a constructive foundation of chemistry. It constrains chemical behaviour through energy spectra and stability bounds, but it does not construct molecular structure, bonding, or geometry. These require additional principles—classical limits, symmetry breaking, and interpretive rules—not derivable from the axioms of StdQM.
If the original project of quantum chemistry was:to derive molecular structure, bonding, and chemical behaviour constructively from the axioms of StdQM alone,
then that project has failed.
After nearly a century:
molecular geometry is not an observable,
bonding is not defined in the formalism,
structure does not emerge from the wave function without external input,
every “ab initio” method presupposes classical structure and interpretation.
In this foundational sense, quantum chemistry did not deliver what it implicitly promised.
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