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

---

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

---

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.

---

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.

---

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.

---

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

Abstract vs Concrete vs Computational Physics

The science of physics has over time changed nature from concrete/real to abstract/non-real with the pillars of modern physics of Quantum Mechanics QM and General Relativity GR reaching breathtaking levels of abstraction during the first half of the 20th century culminating today as string theory in 11 space dimensions beyond any reality.  

Today with powerful computers available at no cost there is a reverse trend in the form of computation opening new capabilities of using theories of physics for practical purposes. Computation is a concrete process and computational physics starts with a concrete mathematical model and not with an abstraction.

Let us compare Newtonian mechanics in concrete and abstract formulation. 

The concrete form consists of Newton's Law $F=ma$ connecting force $F$ to mass $m$ and acceleration $a=\frac{dv}{dt}$ with $v$ velocity and $t$ time. The evolution over time of any mechanical system (without viscous forces) can be computationally simulated by time-stepping Newton's Law. Concrete and general.

The abstract form states that a mechanical system evolves from $t=0$ to $t=T$ so that:

• The action $L(v)=\int_0^T(T-V)dt$ is stationary,  

where $T=m\frac{v^2}{2}$ is kinetic energy and $V$ is potential energy. The condition for stationarity in differential form then reads $m\frac{dv}{dt}=F$ with $F$ gradient of $V$, which is Newton's Law.

The difference between abstract and concrete is the same as characterising a local minimum of a function $f(x)$ over variation of a real variable $x$ for $x=\bar x$ as $f^\prime (\bar x) =0$ with $f^\prime =\frac{df}{dx}$. Minimisation is abstract in the sense that no computational method is implied other than comparing the value $f(x)$ for all $x$, which can take infinite work. On the other hand, there are many methods for computing a root to the equation $f^\prime (x)=0$. 

We thus see with that the concrete formulation directly opens to computational solution, while the abstract formulation does not. The pendulum thus may swing back from abstract to concrete in a 21st century filled with computation.

But we still live in the era of QM and GR, which are both abstract and uncomputable. QM is based on an abstract multi-dimensional Schrödinger equation without real physical meaning which is uncomputable because of its many dimensions. GR is based on Einstein's equation with a condensed abstract formulation which when written out for computation shows to be uncomputable. 

RealQM is a new form of quantum mechanics based on a concrete computable model. RealQM + Newton offers a unified concrete continuum model covering all scales which is computable. 

Ontology of physics (what is) is concrete, while epistemology of physics (what we can say) can be abstract. Computation can open ontology of physics to inspection and so feed epistemology of physics. Epistemology without ontology is empty.

Physics as Computation at John Chappell's Natural Philosophy

This is an intro to a live video talk I will give on Febr 3 2024 on John Chappell's channel Natural Philosophy: Where Critical Thinking Challenges Theory (directly connecting to the slogan of this blog). If you feel that this must be crackpot science, take a look at my arguments before deciding and remember that established physics can be crackpot science.

Digital computation, with AI (or even AGI) as latest achievement, is today reshaping human conditions and it is natural to ask if also the science of physics as the inner core of existence is transformed.

Classical physics is based on mathematical models in the form of differential equations expressing balance (of forces) in some system, such as Euler’s equations for fluid mechanics and Maxwell’s equations for electro-magnetics, while modern atomic physics is based on Schrödinger’s equation. 

The equations express system forces while solutions of the equations represent evolution in time of systems under given conditions. The task of determining solutions is thus central and here digital computation opens entirely new perspectives with computational complexity or computability as key element. 

Uncomputable systems keep their information hidden to inspection, with prime example Schrödinger’s equation which in its standard multidimensional form is beyond the capacity of any thinkable digital computer. On the other hand, computing solutions to Euler’s equations resolves the enigma of turbulence, as will be shown in the talk.

It is natural to view the evolution in time of a physical system as a form of analog finite precision computation as the action of forces takes the system over small time steps from one state to the next, which can be modeled by finite precision digital computation: 

• Physics as Analog Computation as Digital Computation.

The key elements of computability are (i) finite precision and (ii) stability/wellposedness as a measure of precision required to make computational model output reliable. Forward-in-time evolution then shows to be computable because it is stable, while backward in time evolution is uncomputable because it is unstable, which can be seen to be the essence of the 2nd Law. 

Physics as Computation offers solutions to open problems of (i) turbulence and (ii) atomic physics through new computable forms of Euler's and Schrödinger’s equations, which are the subjects of the talk: 

• Secret of Flight   (Real Euler: Computational Turbulent Incompressible Flow)
• Real Quantum Mechanics

Real here directly connects to computability. A real physical system computes its own evolution forward-in-time and so is analog computable and a mimicing digital computable model can be viewed to be a real model:

• Real models are digital computable because reality is analog computable. 

The standard multidimensional Schrödinger equation is an uncomputable model without real physical meaning (only statistical). RealQM is computable and has a real physical meaning as a collection of non-overlapping interacting charge densities.

Real Euler computes real turbulent flow, and RealQM computes real atoms/molecules, which opens entirely new perspectives on physics: Physics as Computation. 

Real Euler gives an explanation of the 2nd Law (Computational Thermodynamics) as forward-in-time computability and backward-in-time uncomputability. See the book The Clock and the Arrow for a general audience.

There is a connection to Wolfram’s Computational Foundations for the Second Law of Thermodynamics in the sense that computation is central, but the essence is different: For Wolfram it is computational irreducibility, while I favor finite precision+stability.