Periodic Table vs QM vs Chemistry

Consider the following questions still open after 100 years of debate:

1. Does the Periodic Table PT explain Chemistry?
2. Does Quantum Mechanics QM explain PT?
3. Does QM explain Chemistry?

Eugen Schwarz and Eric Scerri are leading chemists who hesitate to answer the YES of consensus, but still confess to believe in QM as the foundation of Chemistry, at least in principle if not in practice.

But the unanimous consensus is that QM is the canonical mathematical model of atom physics and chemistry in the form of Schrödinger's Equation SE in its original formulation given 100 years ago. The consensus is that physics of atoms is correctly captured by wave functions as solutions to SE, then supported the fact there is no QM prediction in contradiction to observation. The existence of a single contradicting example would shake the consensus. But there is no such thing.

There is a weakness in this argument coming from the exponential computational complexity of wave functions as depending on $3N$ spatial dimensions for a system with $N$ electrons, which make wave functions uncomputable and so impossible to inspect and compare with observation. The lack of contradicting example thus comes from lack of example. 

To make use of QM some form of approximate wave functions as approximate solutions to SE, must be computed. Any contradiction with observation will then be blamed on the approximation and not the exact solution, and so a fiction of no contradiction whatsoever can be maintained: 

• There is no prediction by QM contradicted by observation. 

Critics like Schwarz and Scerri thus focus on the role of PT in chemistry, rather than that of QM, specifically the Aufbau of PT based on periods complemented by Madelung's rule and Hund's rule for filling of electron orbitals, which show many exceptions. 

Despite the criticism of Schwarz and Scerri, physicists can continue to claim that QM explains Chemistry, and chemists that PT/QM explains Chemistry and so keep a facade that everything is in order, despite the criticism.  

The only disturbance to this comfortable status quo is RealQM offering a new form of QM based on non-overlapping one-electron charge densities, which is readily computable, and where atomic/molecule electron configurations are determined as electron packing. 

There is so far limited interest in RealQM as an alternative to the consensus of QM, which is understandable by the monumental investment made to cope with uncomputable aspect of QM, which is unphysical since real physics computes its own evolution.  

Comment by chatGPT

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Thank you for an incisive and thought-provoking piece. You raise three fundamental questions:

1. Does the periodic table explain chemistry?

2. Does quantum mechanics explain the periodic table?

3. Does quantum mechanics explain chemistry?

Your argument that the consensus — that quantum mechanics (QM) via the Schrödinger equation is the foundation of atomic physics and chemistry — rests on the absence of a contradictory prediction is interesting. You point out that because for many-electron systems the wave-functions live in $3N$ dimensions, they are in principle uncomputable and hence untestable in some sense:

“The lack of contradicting example thus comes from lack of example.” claesjohnson.blogspot.com

This is a valuable critique: the fact that we rely on approximations means that when things don’t match experiment, the blame is placed on the approximation rather than on the underlying theory. You also highlight how chemists like Eugen Schwarz and Eric Scerri are uneasy with the notion that quantum mechanics fully explains the periodic table and hence chemistry. claesjohnson.blogspot.com

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What I find persuasive

• Your point about computational intractability is well-taken: in many-electron atomic and molecular systems the practicality of QM is via approximation, and that leaves room for philosophical and foundational questions.

• The distinction between explaining the periodic table structurally (i.e., why the table has its shape) versus explaining chemistry (why substances behave as they do) is well drawn. It’s good to ask whether emergence plays a role here — whether chemistry has “laws” or patterns that go beyond what individual quantum mechanical interactions yield in a straightforward way.

• The invitation to consider alternative or complementary frameworks (you mention “RealQM” and electron packing) is intellectually healthy: science advances by examining assumptions.

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What I’d challenge or ask for further clarification

• While it’s true that exact wave-functions for large $N$ are unattainable, quantum mechanics has been extraordinarily successful in predicting small system behaviour and chemical phenomena (bond energies, spectra, reaction rates) via approximate methods (e.g., Hartree-Fock, DFT, coupled cluster, etc.). It might strengthen the argument to engage more specifically with how far those methods go, where they falter, and to what extent that matters philosophically.

• On the periodic table: the “explanation” of the table via electron shell filling (Aufbau / Madelung / Hund) does have known exceptions (which you note). But one could argue that the table is a compact summary of periodicity arising from quantum structure. The question is: Does summarizing mean “explaining”? Your point that this may leave a gap is compelling—but how might one characterise the gap more precisely? For instance: Are the exceptions merely “edge-cases”, or do they highlight a structural deficiency in the quantum-mechanical explanation of the periodic table itself?

• The idea that QM in practice cannot be directly “inspected and compared with observation” because of dimension explosion: here I’d ask: At what point does this become a genuine theoretical deficiency rather than a practical limitation? If approximate QM works extremely well for the phenomena we test and use, then pragmatically we treat QM as the basis. So is your critique essentially a philosophical one (about understanding) rather than a scientific one (about prediction)? Clarifying this would help.

• The proposed alternative (“RealQM” with non-overlapping one-electron densities and electron-packing) is intriguing. But what empirical or conceptual advantages does it offer over standard QM? What predictions does it make differently (or more simply) that standard QM struggles with? That would make a stronger case for considering it seriously.

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Overall impression

This post is a worthwhile invitation to pause and reflect on the foundations of chemical science. It asks us not to take for granted the hierarchy: QM → periodic table → chemistry. Instead, you suggest that each of those links might have unresolved aspects. That’s valuable.

For someone working in chemistry or physics, you are nudging them to think about explanation not just prediction: Does our theory make sense, does it explain why, not only give numbers that match. And that’s a level of meta-reflection that’s often missing in everyday training.

If I may make a suggestion: it would be helpful to include a few concrete case-studies where QM-based methods fail to explain a chemical phenomenon (or fail to explain it satisfactorily) and show how the periodic table hints at something “more” or “different” than pure QM would suggest. That kind of grounding might make the critique more tangible.

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Thank you again for sharing these thoughts — they contribute to the ongoing dialogue on how we understand the interplay of physics and chemistry.