My chemistry knowledge is of a high-school level. In high-school, the properties of atoms were mostly presented as empirical phenomena. We learned some physical principles such as the idea that covalent bonds are based on exchanging electrons and that there are always 8 possible electron "slots" in the outer shell of an atom. But mostly we just had to take as given empirical patterns in the periodic table.

I am wondering whether the chemical properties of the different atoms are currently largely understood as emergent properties of the standard model? Or are these still mostly open questions?

E.g. do we understand in terms of the standard model (using only parameters from the standard model, not additionally empirically observed chemical parameters) why:

  • atoms have 8 electron "slots" in their outer shell

  • why the various periodic properties of the periodic table hold

  • For each individual atom why it has all the particular chemical properties that it has

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    $\begingroup$ Related: physics.stackexchange.com/q/16647/2451 , physics.stackexchange.com/q/129134/2451 and links therein. $\endgroup$
    – Qmechanic
    Commented Apr 15 at 11:24
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    $\begingroup$ @Giorgiop-DoomsdayClockisAt-90 I fear you read the question that way, but the three example questions the OP is asking about are old-fashioned QM questions, where, very arguably, the input parameters like particle masses and charge strength, and effective interaction at about an angstrom might be traceable/connectible to the SM.... If the crucial sizes of the parameter inputs to the relevant Schroedinger eqns are what the OP is asking about, he should strongly emphasize that's at the core of his question. ... $\endgroup$ Commented Apr 15 at 13:58
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    $\begingroup$ ... Particle physics claims that, by being "fundamental", it underlies the explanation of everything, but the "emergence" scenario subverts this reductionism... "Everything" is perhaps in the emergent process involved, not in the input parameters. Imagining that a GUT underlies a tsunami is not really explanatory... $\endgroup$ Commented Apr 15 at 14:04
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    $\begingroup$ An undergraduate "Physical Chemistry" course will cover all these things. $\endgroup$ Commented Apr 15 at 21:51
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    $\begingroup$ See P. Anderson's classic "More is different" paper. I am astonished that no one seems to have mentioned it before. $\endgroup$ Commented Apr 17 at 11:40

8 Answers 8


While the discoveries of the rules of chemistry and some current practical wisdom is empirical, it is better to think of the entire nature of chemistry as dictated by the principles of quantum mechanics. This ranges from the rules you learn in high school such as the 3-D shapes and energies of the hydrogen atom's electron orbitals (which are solutions of the Schrödinger equation) to the number of electrons that can occupy a given orbital, which is a mixture of solving the more complicated Schrödinger equation for atoms and molecules and the Pauli exclusion principle (a key result of relativistic quantum field theory, of which the Standard Model is an example). Bonds are typically described by electrons occupying orbitals found using combinations of functions that look a lot like the hydrogen atom orbitals you would have seen in high school. Also, the octet rule is not a universal rule in chemistry since it only strictly works for elements that have no $d$ orbitals energetically available to mix into their bonds. This is a great approximation for many elements, but it fails as you go deeper into the periodic table, and especially for $d$ and $f$ block elements like the transition metals. In fact, for metals, it is often better to describe the electron states as delocalized over a periodic chunk of material rather than orbitals centered on atoms anyway. This is done in computer codes like VASP. The properties of substances are governed both by these quantum mechanical analyses and the additional rules of thermodynamics and statistical mechanics. For instance, we know that the ground state is the only electron state occupied at room temperature for a hydrogen atom because of the Boltzmann distribution. The prediction of properties for complicated systems like liquids and solids is very much a modern research area in computational chemistry.

All this is to say, it is no secret that chemistry is governed strictly by the rules of quantum mechanics. It is only a matter of how much one must learn and how much work is necessary before it provides any useful information. As Dirac eloquently put it, "The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved."

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    $\begingroup$ My problem with understanding your answer lies in this sentence: "it is better to think of the entire nature of chemistry as dictated by the principles of quantum mechanics". There is a difference between 1. "chemistry follows in principle from quantum mechanics" and 2. "humans in 2024 can in practice explain all the chemical properties of the elements that chemists care about from quantum mechanics". To me 1 is obvious, and my question is to what extent 2 is true. But I am not sure which you are answering. $\endgroup$
    – user56834
    Commented Apr 15 at 11:46
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    $\begingroup$ The pure elements are essentially fully understood from the principles of quantum mechanics. The reasons why are fairly obvious; if we are capable of modeling piezoelectric, modeling solid titanium shouldn't be too hard! But as you go to more complicated materials that have more complex interactions, especially in the condensed phase, the task of modeling these substances gets exponentially more complex. Often the question is not whether it is possible, but whether there is a practical reason to do it (and if you have the resources to do it). $\endgroup$ Commented Apr 15 at 13:47
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    $\begingroup$ I would argue that the emergence of chemistry from QM is not completely understood even on the level of a single molecule. We know how to find equilibrium bond lengths and bond angles in the Born-Oppenheimer framework (by finding the minima of the PES), and these values are usually in nice agreement with experiment, but extracting the same information from the fully quantum, non-adiabatic treatment (no BO approximation, nuclei treated explicitly) is highly non-trivial, not just computationally but conceptually as well. (See e.g. the works of Woolley and Sutcliffe.) $\endgroup$ Commented Apr 15 at 15:11
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    $\begingroup$ @dennismoore94 That is completely fair. I was definitely thinking of the "trivial" problem of treating the quantum mechanical properties of matter using non-relativistic quantum mechanics that does not account for the full complexity of standard model effects like nuclear binding forces or even the quantum nature of the nuclei. But it still seems perfectly reasonable to say that since we can reproduce the key features of chemistry using this simplified framework, chemistry is really emergent from quantum theory. It is just extremely hard to account for everything at once! $\endgroup$ Commented Apr 15 at 18:31
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    $\begingroup$ This is a very direct answer to the question, but I think it helps to understand that historically, chemistry and physics were considered to be entirely separate fields and that it was only relatively recently that science started treating chemistry as a branch of physics. It seems to me a lot of people are still unaware of this. $\endgroup$
    – JimmyJames
    Commented Apr 15 at 19:46
  • atoms have 8 electron "slots" in their outer shell

The shape of the periodic table is one of the great successes of non-relativistic quantum mechanics. If we approximate that we're considering independent electrons orbiting infinitely massive nuclei, the rules are:

  1. Orbital angular momentum comes in lumps. You can have orbital quantum number $\ell\in\{0,1,2,\cdots\}$.
  2. The projection of $\ell$ onto your favorite axis also comes in lumps. The projection quantum number may be any integer $|m| \leq \ell$. This means, for example, that an $\ell=2$ electron may have one of five different $m$.
  3. An electron may occupy one of two spin states, $m_s=±\frac12$.
  4. Each electron with the same quantum numbers $\ell, m, m_s$ must have a different energy. The energies are also quantized, so we label them with a quantum number $n$. This is usually called the "principal quantum number," but it makes more sense for me to put it last, rather than first.

If the chemical properties of an element are related to the orbital angular momentum $\ell$ of its most-recently-added electron, these rules suggest chemical properties should be periodic in groups that are twice an odd number. The actual periodic table has two columns on the left; six (twice three) columns on the right; ten (twice five) columns in the middle; and fourteen (twice seven) columns that are also in the middle, but they don't really fit on a standard sheet of paper, so most people put them along the bottom. The order in which the orbitals get filled is dictated by the aufbau principle.

  • for each individual atom, why it has all the particular chemical properties that it has

This is the subject of "physical chemistry." Electrons in a multi-electron atom are not really independent of each other, and an approximation that neglects the electron-electron interactions is not very good. In heavy atoms, the non-relativistic approximation fails when describing electron motion very close to the nucleus of the atom.

For the modern state of prediction of bulk chemical properties, you might enter the literature at the superheavy elements such as tennessine, which is probably a metallic halogen. Not that there will ever be enough room-temperature tennessine in one place to demonstrate bulk properties, since its millisecond-scale radioactive decay would interfere with millisecond-scale bulk processes like the transmission of sound waves. But that's one place that a physical chemist can go to make predictions about a material without the prediction biases that come with already knowing the properties of the material.


"Do we understand chemistry from particle physics?"

I suggest that the answer is 'no', but some people believe on a theoretical basis that we should be able to understand chemistry from physics or particle physics.

In support of the answer 'no', it should be enough to point out a number of important chemical phenomena, such as the binding of proteins to specific binding partners.

If the answer to the question were truly 'yes', then what should exist now should include actual derivations of such chemical binding properties in individual complex cases, derivations that start in fundamental physics. If somebody would produce evidence of such derivations, then -- to the extent that the derivations are generalisable to other specific cases -- then I would agree that we are at least some way down a road to producing a positive answer to this question, but otherwise, not.


No. The problem with understanding chemistry from particle physics is the quantum solutions of anything more than H₂ simply don't exist as analytic solutions. We can grind through particle physics on simulation through a few of the simplest compounds before everything falls apart due to accumulated error and computational overflow.

Chemistry is understood by the classical model well supported by direct observation, and quantum and relativistic corrections are applied as needed. It's almost always easier to actually measure that binding energy than try to compute it. If QM were never discovered at all; organic chemistry would be at a very small loss. We can make it work without ever bothering. Benzene might never have been solved but the kludge 1.5 bond ring would have worked good enough.

When I went to school; we could not derive the periodic table from particle physics. Crunching through the numbers spat out a table, but the observed table didn't match. In several places (mostly transition metals), the number of electrons in the outermost shells was simply wrong. In addition, boron's predicted chemistry didn't match the actual. The most striking example of this is in fact gold. A classical QM calculation yields the wrong answer by a lot. Due to relativistic effects, gold does not oxidize.

The fact of the matter is the attack sequence in computer modeling is to refine the model until it spits out the correct values for simple cases you know the answer for, then try to use it for the cases you want to solve. This works in that it yields the best possible answer but it used up all your ability test its output and so we can't actually say how good the answer is. (If we didn't use all of our ability and kept some in reserve we could compute an error bar for the computational solution, but then the answer's worse.)

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    $\begingroup$ Understanding something, in physics, rarely means having an "analytic solution"—we only get that for exceptionally simple systems, like the hydrogen atom. It normally involves a combination of carefully chosen approximations (like the Born-Oppenheimer framework mentioned in this comment) and qualitative pictures backed up by approximations (like the discussion of the periodic table in this answer). $\endgroup$
    – Vectornaut
    Commented Apr 16 at 7:42
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    $\begingroup$ @MattHanson: I watched the attempts at computers to build up usable approximations to complicated electron shells as seen in covalent bonds in the '90s. It simply didn't yield good solutions until this century and the methodology still appears to be iterate until you come upon the known solution, and therefore can't attack a problem that's not yet solved. $\endgroup$
    – Joshua
    Commented Apr 16 at 13:48
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    $\begingroup$ I recall this old technique existing that could calculate a reasonable approximation of the binding energy of a new compound. By the '60s, every individual bond energy could be looked up in the tables; but second order corrections were needed as bonds interacted with other bonds. $\endgroup$
    – Joshua
    Commented Apr 16 at 14:02
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    $\begingroup$ @MattHanson: When you can run variational theorem with the SR version of QM for a chlorophyll molecule let me know. $\endgroup$
    – Joshua
    Commented Apr 16 at 18:05
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    $\begingroup$ @MattHanson You say there's no theory to that at all. Nonsense, there is an elaborate web of models linking the empirical measurements. Of course, particle physics is the same. The only difference is the conceit of particle physicists that their web is more "fundamental" than the chemists' web. But no theory is fundamental to science: the empirical measurements are. $\endgroup$
    – John Doty
    Commented Apr 17 at 21:21

We can build much of chemistry from non-relativistic quantum mechanics (NRQM). However, the "Standard Model" is relativistic quantum field theory (RQFT); and a direct derivation would ideally be a proof that the familiar non-relativistic atoms and the like approximate proven states in the relativistic quantum field theory.

The problem with this is that relativistic quantum field theories are - really - incomplete, and in fact what they are not complete for is precisely the type of situation you'd need to fully prove that chemistry is contained within the theory. That is to say, a state where all elements are in continuous interaction with regard to each other. The electrons and nuclei both interact with the EM field, so that's at least 3 fields in interaction. Yet, RQFT is only fully described mathematically for the case of non-interacting fields.

And when you have interacting fields, there are pretty much only two well-defined mathematical options for treatment of them so far: either you only consider scattering processes, which bound atoms are emphatically not, or else you throw out Lorentz invariance by doing your QFT on a lattice ... that is to say, discretizing space, which in effect means you are really just doing a "distorted" non-relativistic QM and so one can argue the extent to which derivations of this type truly "understand" it from particle physics.

Hence, there is so far no fully rigorous derivation, because there is no fully rigorous theory on which to build it to begin with. The closest I believe you could come is a tight-spacing lattice theory and then try to somehow use a combination of intense computational and formal mathematical arguments to prove that under the appropriate circumstances both a bound state must exist and that its non-relativistic limit, i.e. where $c \rightarrow \infty$ faster than the lattice spacing goes to 0, is the regular hydrogen atom (say).


Chemistry has a theoretical basis drawn from quantum mechanics, but relies on experimentation to confirm it's findings. Chemists reason about chemical properties (e.g. reactivity, oxidation states, why elements in group 1 of periodical table have similar properties) using electron configurations.

Electron orbitals have a theoretical basis drawn from quantum mechanics (e.g. exact solutions of the Schroedinger equation for hydrogen - then extrapolated for other atoms).

[can] humans in 2024 in practice explain all the chemical properties of the elements that chemists care about from quantum mechanics?

We can use quantum theory to model exact chemical properties for hydrogen, and that's it. The exact solution to the Schroedinger equations exist for hydrogen (1 proton, 1 electron) - but beyond that, approximations must be used to derive further solutions.

But we chemists don't let that stop us from building up theoretical and computational models from quantum principles. Approximations are used to give us "close enough" solutions (e.g. what would the heat of enthalpy be of this compound?) - and then experiments in the laboratory confirm or deny if our approximation was close enough.

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    $\begingroup$ I would rather explain it as QM explains Chemistry, not that Chemistry draws from QM to do its thing. $\endgroup$
    – T. Sar
    Commented Apr 16 at 19:25

As you can see from the wide range of answers, the answer to your question is rather philosophical, so even practicing chemists and physics do not necessarily agree on it.

We believe that all chemical properties (outside of extreme conditions where the term "chemical" starts to lose its meaning) could in principle be derived from the Standard Model with enough computational power, as Dirac said. We believe this very strongly. In fact, we believe that in most cases (with a few exceptions), chemical properties could in principle be derived from non-relativistic theories of quantum mechanics that are much simpler than the Standard Model.

But we can't prove this claim, because we don't have enough computational power. So in practice, almost all useful "laws" of chemistry are semi-empirical and/or derived from somewhat hand-wavy simplifications of quantum theory, e.g. by neglecting certain correlation effects of quantum entanglement.

It is logically conceivable, although very very unlikely, that we might one day:

  1. develop enough computational or analytical capability to extract chemistry-scale empirical predictions with very low uncertainties directly from the Standard Model,
  2. compare those predictions to the results of chemistry experiments and find disagreements well outside of the simulations' uncertainties, and therefore
  3. discover new physics beyond the Standard Model (e.g. novel many-body effects) from chemistry experiments.

In other words, it's conceivable that the empirical laws of chemistry in fact do not arise from the Standard Model. But it's difficult to overstate just how high the burden of proof would be on these simulations for claiming a discovery of new fundamental physics. (We know that the predictions of the Standard Model do deviate from experiment in certain regimes, e.g. at extremely high energies and/or where gravity is important. But the regime of chemistry is not where we expect to see such deviations.)

  • $\begingroup$ "It is logically conceivable, although very very unlikely". Even with quantum computers? $\endgroup$
    – user56834
    Commented Apr 18 at 4:21
  • $\begingroup$ @user56834 Yes, even then. Even if quantum computers enable us to achieve condition #1 - which I doubt - the challenge is condition #2, which IMO is even more unlikely and is completely out of our control. I think it's very likely that all chemistry-regime behavior is (in principle) fully described by the Standard Model. $\endgroup$
    – tparker
    Commented Apr 18 at 13:28

GILBERT LEWIS model of the atomic structure and a few unusual suggestions

Niels Bohr: „Thus LEWIS, who in several respects independently came to the same conclusions as Kossel, suggested that the number 8 characterizing the first groups of the periodic system might indicate a constitution of the outer atomic groups where the electrons within each group formed a configuration like the corners of a cube.“(1) (p.112) . . . (Valence theory from Gilbert N. Lewis)

On the basis of the first two periods, Bohr assumes the formula $2n^2$ for all orbitals. This leads to this orbital division:

enter image description here

Langmuir's shell model with 2, 8, 8, 18, 18, ... electrons per shell follows the empirically established periodic table of the elements.
Bohr's shell model according to the formula with 2, 8, 18, 32, ... electrons is not comprehensible.

And Bohr continues: „It is to be remarked, however, that such a “static” model of electronic configuration will not be possible if we assume the forces within the atom to be due exclusively to the electric charges of the particles.“(1) (p.112)

If we assume for a moment that when electrons are captured in the atom, the electric field of the electrons is reduced by the emission of EM radiation, we could follow Lewis. The magnetic dipole properties of the electron would be the starting point for the arrangement of the electrons in the shells. All we need is the willingness to think about it,

  • that we have only ever measured the standar charge of the electron for free electrons
  • that the emission of EM radiation could be fed by the fields of the electron (and proton)
  • that the Pauli exclusion principle has its cause precisely in the pairwise interaction of the magnetic dipoles of the electrons.

LANGMUIR, who has attempted … to account not only for the occurrence of the first octaves, but also for the longer periods of the periodic system, supposes therefore the structure of the atoms to be governed by forces whose nature is unknown to us.“ (1) (p.112-113)

The magnetic moment (electrons are magnetic dipoles, which is all too often regarded as unimportant) is precisely the force that was not yet known in Langmuir's time or was later regarded as unworthy of consideration.

He conceives the atom to possess a “cellular structure,” so that each electron is in advance assigned a place in a cell and these cells are arranged in shells in such a manner, that the various shells from the nucleus of the atom outward contain exactly the same number of places as the periods in the periodic system proceeding in the direction of increasing atomic number.“ (1) (p.113)

For me, the best argument in favor of Lewis's model is the phenomenon of $sp^3$ hybridization, for the explanation of which QM has to stand on its head, although this arises quite naturally in the cubic atomic model.
And if there has to be a calculation based on the spherical harmonics, then please do not assume a Carthean symmetry as the basis, but rather one based on the thetrahedron with $l=3, m=2, l-m=1$.

(1) The Theory of Spectra and Atomic Constitution


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