Chemistry: The f-block

Anyone into chemistry here, or could you ask your teacher? (university preferable, thanks)

Are the electron configurations in the f-block still under debate, or are these accepted by the scientific community in general?

I'm most interested on the three initial elements of the 5 and 6 periods. Those where the 4f and 5f subshells are said to be 0.

Lanthanum ([Xe] 4f⁰ 5d¹ 6s²
Actinium ([Rn] 5f⁰ 6d¹ 7s²)
Thorium ([Rn] 5f⁰ 6d² 7s²)

What troubles me is the thought of an empty subshell and how this is seemingly violating all we know about the electron configuration theory in quantum chemistry. The other few exceptions to Aufbau or Madelung rules in the periodic table do not go as far as emptying a subshell. Or am I reading this wrong and empty subshells are an accepted possibility?

Orbitals are actually somewhat imaginary so if you have an empty orbital that just means that there are no electrons there. And if an electron is added to an atom then that is where they likely would go. It doesn't seem like a subject of debate.

I have to warn you that I basically asked the internet and my experience with chemistry is quite limited now. Crash Course Chemistry actually did a good job explaining electrons though. https://www.youtube.com/watch?v=rcKilE9CdaA

Well, on these three cases the empty subshell resides on a higher energy level than the valence shell. In the old Bohr model this would be more or less the same as me drawing the nucleus and three rings around it (the inner ring has the highest energy level, the outermost the lowest). Then I'd say that new electrons would go to the middle ring. They can't. Ionic bounds can only be formed on the valence shell. That is, the outermost ring. i.e. the lowest energy level shell (and its subshells) on the atom.

I'm still researching this matter and can't seem to get to a conclusion. Either the data is too dense and I don't have enough knowledge to understand it, or it is being presented in too simplistic ways like the video above (and actually sort of misleading. He keeps saying orbitals, but those are in fact subshells. The s subshell, for instance, has two orbitals each with their own n and m quantum numbers. Both orbitals share the l (that's an L) quantum number). In any case, it seems everyone feels uncomfortable talking about those empty subshells.

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Originally Posted by Mario F.

Well, on these three cases the empty subshell resides on a higher energy level than the valence shell. In the old Bohr model this would be more or less the same as me drawing the nucleus and three rings around it (the inner ring has the highest energy level, the outermost the lowest). Then I'd say that new electrons would go to the middle ring. They can't. Ionic bounds can only be formed on the valence shell. That is, the outermost ring. i.e. the lowest energy level shell (and its subshells) on the atom.

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Is there a new Bohr Atom Model,..or what is being used to explain atomic structure nowadays?
The Bohr Atom model is heavily restricted when it comes to dealing with any relatively large atom,...you might have to consider other atom models for answers.

The letter-ordering of the orbitals only approximately corresponds to relative energy levels. There are some nuclei for which this ordering is not correct. It's not really a big deal, it just means our simplified models are, well, oversimplified.

The "real" rule is that electrons always occupy the lowest energy states first. That rule is never violated.

EDIT: If you mean the complete absence of a subshell which is never filled at all... I'm not an expert in this, but it is probably due to some conflict in quantum number relating to the spin angular momentum.

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Originally Posted by brewbuck

The "real" rule is that electrons always occupy the lowest energy states first. That rule is never violated.

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Well, that's precisely the rule that is violated. The Madelung Rule. The following is the filling order of Lanthanum (I've already included the number of electrons):

[Xe] 6s² 4f⁰ 5d¹

4f, with zero electrons, is on the 4th Principle Energy Level, a lower energy state than 6s (the sixth PEL) and 5d (the 5th PEL). But so far so good. As you well note there are exceptions to what was initially considered a natural filling order based on the energy levels. That's not the only one. 3p->4s->3d is another example. This is what the Mundelung rule states. However, the order obtained by the Madelung rule is important and no electron should have filled 5d without filling 4f first. Lanthanum is a clear violation of this.

In other words, Lanthanum and a few other initial elements on the f-block seemingly violate the most modern knowledge on electron configuration we have.

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EDIT: If you mean the complete absence of a subshell which is never filled at all... I'm not an expert in this, but it is probably due to some conflict in quantum number relating to the spin angular momentum.

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I've read similar answers.... from experts :(
It's particularly troubling considering the fact it doesn't really answer the question, which makes me think they are either embarrassed talking about 4f and 5f or simply don't know the answer.

EDIT: Hmm... That last bit may have sounded a bit chesty of me. I'm no chemist. But trust me it comes out of frustration. I'm currently teaching chemistry to high school students and one did raise this question (a brilliant Angolan student). I didn't know the answer and promised I'd research. But a great deal of the scientific community, whom I do tend to defend eagerly, does still maintain the same arrogant behavior that characterizes it for centuries; A pathological refusal to admit present knowledge may be flawed, or at best to admit they don't know the answer. Naturally this is the message I'll transmit my student. But no thanks to those experts I asked for help, but sadly because I didn't actually get an answer from them.

See http://pdg.web.cern.ch/pdg/2012/revi...nic-struct.pdf for a PDF with the latest opinions on the matter.

To answer your question: yes, empty subshells are an accepted reality/possibility.

They occur very often with excited atoms, but the question here is obviously about the ground state, when the atom is in its lowest energy state, or most "relaxed".

Here are the electron structures copied from above (originally from the NIST database):
Xenon, Xe: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶ 4d¹⁰ 5s² 5p⁶
Radon, Rn: [Xe] 4f¹⁴ 5d¹⁰ 6s² 6p⁶ = 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶ 4d¹⁰ 5s² 5p⁶ 4f¹⁴ 5d¹⁰ 6s² 6p⁶
Lanthanum, La: [Xe] 5d¹ 6s²
Actinium, Ac: [Rn] 6d¹ 7s²
Thorium, Th: [Rn] 6d² 7s²

I've never given any credence to any "rules" in the electron configuration, but then, I'm a physicist, not a chemist. To me, all those rules are just rules of thumb, nothing more. Or, if you want to be a bit more precise, "polynomial approximations to a very complex nonlinear equation" (of bound electron energy levels).

The main reason is that electrons do not stack like legos. They interact, and repel each other. The energy of the state is very complicated to calculate because of this. The more electrons there are, the further away from reality the rules of thumb are.

The higher the subshell, the more complicated the probability density becomes (and the more complex the interaction between electrons), and the larger the effect the quantum numbers besides shell number n have in the energy level of the electron.

The f subshell is notorious for this; it looks more like a group of droplets than a continuous cloud; see here for some examples. Note that they are of the 4f shell, not the higher 5f shell. It should be no surprise that simpler subshells, like 6d and 7s are populated before the complex 5f subshell.

Most physicists find it only interesting that the 5f subshell has that much higher energy orbitals than 6d or even 7s subshells -- even if there is an entire shell between 5f and 7s subshells.

For example, my copy of "Introduction to the Structure of Matter" by John. J. Brehm and William J. Mullin, 1989 (ISBN 0-471-60531-X) states that the order of subshell energies is (page 451)

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Originally Posted by Brehm-Mullin

Let us summarize the solution of the ordering problem by listing the subshells with increasing energy as follows, noting by parentheses the subshells of nearly equal energy:

1s 2s 2p 3s 3p (4s 3d) 4p (5s 4d) 5p (6s 4f 5d) 6p ...

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or, in other words,

• E(4s) ≲ E(3d), but the difference is small
• E(5s) ≲ E(4d), but the difference is small
• E(6s) ≲ E(4f) ≲ E(5d), but the difference is small

which means that e.g. 4s tends to be populated before 3d and so on, except that 3d starts getting populated while 4s is only partially populated, because the energy levels are so close together. (The list on the page does not include 5f; the last subshell listed, with highest energy, is 6p. In other words, E(6p) < E(5f).)

Unfortunately, the table 9-1 which contains the electronic configurations, only goes up to Xenon; it does not have entries for Lanthanum, Actinium, Thorium, or any of the heavier elements.

However, [Xe] 5d¹ 6s² for Lanthanum, [Rn] 6d¹ 7s² for Actinium, and [Rn] 6d² 7s² for Thorium, are in agreement with the text and charts in the chapter, although extrapolation or speculation based on lower shells is required. I'd say these structures were quite accepted or at least acceptable among physicists even in 1989.

Relying on approximations is a sane approach in getting practical results. (I know, I do molecular simulations using classical potential models, which are basically a cross between guesses and models fit to real world results; nowhere near a quantum mechanical worldview!) However, to understand those approximations and rules and their limitations and errors, one has to dig into the quantum mechanical basis.

I hope you found this useful. If you notice any errors (relevant to the discussion here!), please let me know so I can correct them.

Electron to electron interactions did seem to me the most likely (basic) explanation, since they are currently impossible to calculate and thus completely ignored in our present models. But I couldn't find any information that would give any credence to that, and my own knowledge wasn't enough to just state this as a fact to my students.

This is amazing and precisely what I was looking for. I can't thank you enough for all the work you had to put up this post! To summarize, it is accepted by the scientific community in general and it may have to do with very close or possibly even overlapping energy levels between orbits of different subshells. This also helps tremendously in understanding the remaining exceptions to Aufbau/Madelung's, which don't go as far as emptying a subshell, but are still filled "strangely". e.g. cooper and gold, among others.

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Originally Posted by Mario F.

Electron to electron interactions did seem to me the most likely (basic) explanation, since they are currently impossible to calculate and thus completely ignored in our present models.

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Impossible algrebraically, but not numerically, I think.

We can model the electron configuration, including electron-electron interactions, numerically; even if the electrons are spread over a probability distribution the Coulomb interaction (F = (q₁ q₂ r) / (4 π ε₀ ε r²)) between them still applies (although for heavier elements, the relativistic effects become noticeable, and ε depends on the overall electron density (including other nearby atoms)), it's just very difficult to calculate. The thing with numerical calculations and iterations is, you only need to prove you have a way that always gets closer to the correct solution (never further away), however slowly, and you don't need to worry about being exactly right. Just iterate enough times to get as close you need.

It's not easy, and I don't know if it has been done without severe approximations for heavy elements (in other words, using "pure" theoretical models without simplifications). You have to start with pretty close to the structure you end up with, or the excess energy is enough to ionize the atom, shooting off one or more electrons! And you need a way to make sure you obtain the ground state -- by somehow bleeding off excess energy from the electrons, for example -- or you end up just getting an excited state instead. So, not "impossible" numerically, I think; just very, very hard.

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Originally Posted by Mario F.

But I couldn't find any information that would give any credence to that, and my own knowledge wasn't enough to just state this as a fact to my students.

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The Brehm-Mullin book is dense -- I remember how I really had to struggle to comprehend the then-alien concepts --, but it does explain why and how; it does not just state how the authors think things are. It's pretty good; I'd recommend taking a look just in case it helps.

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Originally Posted by Mario F.

To summarize, it is accepted by the scientific community in general and it may have to do with very close or possibly even overlapping energy levels between orbits of different subshells.

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Exactly.

(And, because I bet you get asked why they overlap: the energy levels are that way because at higher subshells, the orbitals get more and more complicated due to those electron-electron interactions. The Brehm-Mullin book does show the exact algebraic expressions for all orbitals (for a single-electron atom, i.e. excluding electron-electron interactions and relativistic effects), and how they are derived from the models.

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Originally Posted by Mario F.

copper

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This is completely off-topic, but my very first molecular dynamics simulation was of Morse copper. I joined a solid lattice of copper and a molten chunk of liquid copper together, but miscalculated the distance between the two; there were atoms much too close to each other at the join. The end result was the entire system rang like a bell: I got acoustic waves that were much, much larger than my system, which I only realized after running my simulation for many thousands of time steps and visualizing the atom locations.. I also tried melting a solid piece of Morse copper, but got a small superheated droplet inside the solid instead; it took about 20000 time steps for the heat from the droplet to start expanding to the rest of the simulated piece; after which it only took a couple of hundred time steps for the entire system to melt. I speculated the situation was similar to water on a hot plate: the "steam" (very fast atoms) "insulated" the droplet from the perfect lattice. Fun stuff!

Currently, I'm quite interested in clathrates, especially methane clathrates in shallow northern seas and in swamps near permafrost. There is enough methane tied in clathrates in Siberia to dwarf any kind of global warming we've currently seen. Way scary.
But the interesting thing about methane clathrate is how basically liquid water molecules surround basically a gaseous methane molecule, and form a solid very similar to ice. (The Wikipedia page shows several small chunks burning. It looks like burning ice.)
It does not form a molecule or salt (no covalent or ionic bonds), its much weaker than that: a rigorous stirring will break it up. (This is the fear; stirring the melting permafrost and swamps will release the methane stored in the clathrates. According to reports, it's already started in Siberia.)

The weak-but-strong-enough interactions are very closely related to the shapes of the electron densities of these molecules, and how they interact at "long" distances (relatively speaking, of course).

The world is full of wonders, and it's just such a small piece of the larger universe.. (Just think of all the weird nuclear processes that occur in stars, for example.)

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Originally Posted by Mario F.

gold

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The golden glow gold has is actually a relativistic phenomenon!