Where can I find chemistry experiments that are accurately described with the Dirac equation?

[jonjacson]

TL;DR Summary

I am looking for real experiments where I can compare the solutions of the Dirac equation with the data, and see that both coincide.

Let's say we can solve the Dirac equation numerically with a powerful computer. What experiments do you recommend to take a look at to compare the result of the simulations with the real data.

Maybe chemical reactions?

 

[jonjacson]

Let's say we can solve the Dirac equation numerically with a powerful computer. What experiments do you recommend to take a look at to compare the result of the simulations with the real data.

 

[Borek]

As far as I am aware chemistry in which relativistic effects matter is not that common. Wikipedia says that the Dirac equation was validated by accounting for the fine structure of the hydrogen spectrum in a completely rigorous way, I feel like doing the same numerically should be reasonably easy with today's processing power.

Two things that are typically explained by the presence of relativistic effects are color of gold and fact that mercury is liquid at STP, so these sound like candidates for your experiment as well. But they can be numerically challenging compared to hydrogen.

 

[Demystifier]

Not exactly what you asked for, but still: https://en.wikipedia.org/wiki/Precision_tests_of_QED

 

[Vanadium 50]

Why chemistry? Why not, e.g. spectroscopy?

 

[jonjacson]

Not exactly what you asked for, but still: https://en.wikipedia.org/wiki/Precision_tests_of_QED

Nice, yes, something like that would be nice.

Why chemistry? Why not, e.g. spectroscopy?

That would also be interesting for sure, but chemical reactions were the phenomenon that I was most interested in.

 

[Vanadium 50]

but chemical reactions were the phenomenon that I was most interested in.

I get that. I don't get why. That's why I asked you why. So why?

 

[jonjacson]

I get that. I don't get why. That's why I asked you why. So why?

Because I am made of atoms and molecules and chemical reactions are happening right now inside of my body by the millions.

 

[Vanadium 50]

I expected a serious answer. My mistake. Good luck.

 

[TeethWhitener]

If you include instances where spin is treated as emergent, rather than in an ad hoc fashion, then the Dirac equation is fundamental to pretty much every process in chemistry.

If you include the prediction of the positron, the same argument can be made for the prediction of holes in solid state physics, which has lots and lots of applications in chemistry, particularly in heterogeneous photocatalysis.

In the limit of massless fermions, the Dirac equation reduces to the Weyl equation, which is a good approximate solution to the electronic structure of graphene near the Fermi energy. This is useful for chemical sensing, as the valence and conduction bands form “Dirac cones” at the Fermi energy, where the density of states drops to zero at a single doping level, and in principle this level can be tuned via interaction with analytes of interest.

 

[Vanadium 50]

All true, but none of this is a chemistry experiment to verify the Dirac equation.

The OP has pooh-poohed spectroscopy. These examples are even farther away than the original questions.

 

[jonjacson]

If you include instances where spin is treated as emergent, rather than in an ad hoc fashion, then the Dirac equation is fundamental to pretty much every process in chemistry.

If you include the prediction of the positron, the same argument can be made for the prediction of holes in solid state physics, which has lots and lots of applications in chemistry, particularly in heterogeneous photocatalysis.

In the limit of massless fermions, the Dirac equation reduces to the Weyl equation, which is a good approximate solution to the electronic structure of graphene near the Fermi energy. This is useful for chemical sensing, as the valence and conduction bands form “Dirac cones” at the Fermi energy, where the density of states drops to zero at a single doping level, and in principle this level can be tuned via interaction with analytes of interest.

Do you know papers or books that show solutions of the Dirac equation for chemical reactions?

 

[weirdoguy]

I would say there are none, because:
- chemical reactions are way to complicated to use Dirac equation directly
- relativistic effects have (FAPP) none implications for chemical reactions

So why bother?

 

[Frabjous]

You might enjoy this
https://www.degruyter.com/document/doi/10.1515/cti-2023-0043/html?lang=en

 

[jonjacson]

I would say there are none, because:
- chemical reactions are way to complicated to use Dirac equation directly
- relativistic effects have (FAPP) none implications for chemical reactions

So why bother?

How do you compute a chemical reaction? if it is possible

You might enjoy this
https://www.degruyter.com/document/doi/10.1515/cti-2023-0043/html?lang=en

Thanks, interesting.

 

[weirdoguy]

How do you compute a chemical reaction?

What exactly do you mean by that? Also, what do you think Dirac (or even Schrodinger) equation represents? What does it tell you? What does that mean in the context of chemical reactions? Actually these are the question you should be asked at the very beginning.

 

[Vanadium 50]

Actually these are the question you should be asked at the very beginning.

Which is where the "why not spectroscopy" came from. Unfortunately, the response was less than serious.

 

[DrDu]

There are some quantum chemistry programs which treat atoms relativistically, e.g. 'paragauss'. Relativistic effects are important in all heavier elements. E.g. the stange chemistry of gold and mercury is due to the relativistic contraction of the s orbitals. Pekka Pykkö was a pioneer on the topic and has written some very readable reviews.

 

[Vanadium 50]

Relativistic effects are important in all heavier elements.

Sort of. They are more important to the inner electrons than the outer ones. That's partly why I asked about spectroscopy, where the effects are easier to observe. But he seems not to be interested in spectroscopy.

 

[DrDu]

That's partly true, but you have to take into account that the outer orbitals are orthogonal to the inner ones. So while the 1s orbital is most influenced by relativistic effects, this change will propagate to the outer s orbitals as well. For example, in mercury this leads to a considerable stabilization of the valence s orbital, which renders mercury into a quasi-noble metal and also explains its low melting point. https://onlinelibrary.wiley.com/doi/full/10.1002/anie.201302742
See also
https://en.wikipedia.org/wiki/Relativistic_quantum_chemistry