How to Teach Atomic Orbitals

[mississippichem]

So I tutor freshmen and sophomore chemistry students as a side job at my university. I've been struggling to explain the concept of atomic orbitals to some of the brighter students who keep asking deeper and deeper questions. A typical conversation goes like this:

 

Me:...so now this model is accepted over the Bohr model I showed you last time.

Student: What's wrong with the Bohr model? It makes more sense.

 

Me:Well the quantum model is more consistent with experiment and it aligns nicely with things like the photoelectric effect, atomic line spectra, the observed structure of molecules (physical and electronic)

Student:Why is that?

 

Me:[quantized energy level rant]...schrodinger equation...uncertainty principle...moving charged particles in fields should radiate...DeBroglie wavelength...

Student:Now I'm more confused than before

 

So what is the best way to go about this and give reasonable insight into the complexity and beauty of the theory without giving students (many of whom are not chemistry or physics majors) the "quantum confusion" that they get from a more rigorous analysis? For the class, the students need to be able to predict electron configurations for atoms and ions, draw MO diagrams for homo-nuclear diatomics, understand orbital hybridization, calculate emission and absorption energies between n-levels, predict electron pair geometries, know the set of quantum numbers (without S, L, J, and spin multiplicity), distinguish between s,p,d, or f-orbitlas, and understand simple HOMO, LUMO, SOMO interactions (without the group theory or much symmetry consideration).

Edited November 16, 2010 by mississippichem

[timo]

As you possibly might know, I am not a chemist. But anyways, here's my advice, assuming your goal is to give a good lecture, and not to teach QM:

 

Don't talk about the Schrödinger equation. Don't talk about uncertainty. Electrons can only be in certain orbits. Period. That explains your atomic line spectra, presumably the structure of molecules (I don't know in detail to what extend which approximations you can make and still get your desired statement, though). And I understood the photoelectric effect as a proof for the QM nature of light, which I don't quite see why you'd need that for your class.

You will always reach the point where a "deeper" question cannot be answered, so don't even start with details that are not required. That is not to discourage people from asking further questions. But build a solid platform of what has to be understood, and what can be considered as "that's just how it is" so that people do not unnecessarily confuse themselves over information they do not need.

 

(somehow, posting this seems like a deja vu, dunno why).

[mississippichem]

As you possibly might know, I am not a chemist. But anyways, here's my advice, assuming your goal is to give a good lecture, and not to teach QM:

 

Don't talk about the Schrödinger equation. Don't talk about uncertainty. Electrons can only be in certain orbits. Period. That explains your atomic line spectra, presumably the structure of molecules (I don't know in detail to what extend which approximations you can make and still get your desired statement, though). And I understood the photoelectric effect as a proof for the QM nature of light, which I don't quite see why you'd need that for your class.

You will always reach the point where a "deeper" question cannot be answered, so don't even start with details that are not required. That is not to discourage people from asking further questions. But build a solid platform of what has to be understood, and what can be considered as "that's just how it is" so that people do not unnecessarily confuse themselves over information they do not need.

 

(somehow, posting this seems like a deja vu, dunno why).

 

Yeah, I don't really go in depth with the Schrodinger, I only mention it in passing. Yeah you are right though, I shouldn't give information that is not pertinent to the class. However, I feel that I'm stuck with a technical explanation when it seems the students can't comprehend what an orbital is. I'm really looking for some simple analogy for an atomic orbital but I'm starting to think one doesn't exist. That's why we have quantum mechanics i guess, because classical mechanics wasn't sufficient. It just hurts my soul to say "that's the way it is, trust me on this". Good advice though, my students thank you for saving them from the uncertainty talk . Thanks

 

-I usually just tell them to go look up the photoelectric effect if they want an interesting read that might help stir their thoughts.

Edited November 16, 2010 by mississippichem

[timo]

Well, there's another thing that goes along the lines of how deep you should dig: I am not sure we both have the same conception of what an orbital is.

For me, it is a very practical lie, in which you assume that the solutions for a many-electron state could be properly tough of as a mere product state of one-electron solutions. Strictly speaking, that is simply wrong (and I don't mean simple things like that you'd have to anti-symmetrize the product state, but the huge problem that your electrons interact). But I admittedly lack any deeper knowledge about the issue.

Seen from the bottom-up view of a physicist, the issue is pretty simple: we cannot solve the many-electron problem analytically, and even numerical procedures like DFT have to make approximations to solve anything beyond perhaps 3-4 electrons and still be reliable (whatever reliable might mean - I am far from an expert in this, as I said). So obviously, the whole orbital idea can just be a guess. On the other side of the spectrum, there is no doubt that chemistry is quite successful with their orbital view, so at least for me that is a completely convincing reason to take it as "that's how it works" and use it.

 

I am not sure if something in the line of "ad-hoc extension of the Hydrogen solutions" is what you have in mind when thinking about what an orbital "really is". I doubt it for two reasons, though: first, from my experience, only theoretical physicists and perhaps mathematicians tend to take the stance that what they are working with is just a model, that happens to be as good as the model happens to be. When I talk to say experimentalists, chemists, or people from medical sciences, I often get the impression that they feel like the model they are being taught is "how it really is", in the sense of actually being reality and not just a tool that is adequate for the purpose at hand. The second reason is a bit more profane: I happen to own exactly one chemistry book: Atkins, "Physical Chemisty". Sure, it's an undergrad text, but the fact that it says relatively little about it (Chapter 13.4 in my version) seems like an indicator to me, that it might in fact not be standard knowledge of every chemist, that the whole orbital idea is not necessarily the full story.

[mississippichem]

Well, there's another thing that goes along the lines of how deep you should dig: I am not sure we both have the same conception of what an orbital is.

For me, it is a very practical lie, in which you assume that the solutions for a many-electron state could be properly tough of as a mere product state of one-electron solutions.

 

I agree there, it is a practical lie, just more practical than the Bohr Model. I don't need to go into Dirac or DFT approximations as much as I would like to.

 

I am not sure if something in the line of "ad-hoc extension of the Hydrogen solutions" is what you have in mind when thinking about what an orbital "really is".

 

Yeah it actually is. I 'm talking about "good-ole" spheres dumb-bells and flowers; nothing complicated The students just need to know the order of filling in the orbitlals and be able to draw and identify them. All this is standard knowledge for the run-of-the-mill chemists. Physical chemists, which is what I hope to be in about a year, would be a little more hip to the electron-electron interactions, vibronic coupling, most definitely DFT, and some more of the finer points (one could say less relevant but who cares) of QM.

[pioneer]

The orbitals are the result of interaction between the protons of the nucleus and the electrons. Each orbital represents a lowest energy shape that results from the EM addition of the movement of electrons and protons. Electrons are particles and waves. This is where the wave nature of electrons come in. Electrons are not just a negative charge, but a charge in motion. The result is electrons give off both electrostatic and magnetic waves. Opposite spin electrons attract, since they will develop a magnetic attraction that can overcome the expected electrostatic repulsion. When all is said and done the energy of the atom is minimized when electrons circulate in the orbital shapes we see. Since these shapes are repeatable and stack in a repeatable order with respect to atomic number, this indirectly tells us that the protons of the nucleus may also have orbital configurations also due to similar wave addition, in the context of the electrons.

 

An interesting effect is magnetism where all the electrons are not in the lowest energy orbitals. In this case, the magnetic does not cancel the electrostatic repulsion, and we notice the extra magnetic output. Since this is stable for some atoms, one would expect a tweak in the nuclear proton orbitals may also occur. If the nuclear proton electrostatic potential was higher it could compensate for the higher electrostatic charge of the electrons. This would allow the proton to detach some of its own magnetic field, so it can add with the electron magnetic field, while still allowing a semi-stable magnetic atom.

 

The magnetic iron in the center of the earth exists at temperatures that normally denature magnetic properties. One way to overcome that is via induced stability in the slighter higher energy proton orbital configuration, which then stabilizes the electrons.

Edited November 16, 2010 by pioneer

[swansont]

The orbitals are the result of interaction between the protons of the nucleus and the electrons. Each orbital represents a lowest energy shape that results from the EM addition of the movement of electrons and protons. Electrons are particles and waves. This is where the wave nature of electrons come in. Electrons are not just a negative charge, but a charge in motion. The result is electrons give off both electrostatic and magnetic waves. Opposite spin electrons attract, since they will develop a magnetic attraction that can overcome the expected electrostatic repulsion. When all is said and done the energy of the atom is minimized when electrons circulate in the orbital shapes we see. Since these shapes are repeatable and stack in a repeatable order with respect to atomic number, this indirectly tells us that the protons of the nucleus may also have orbital configurations also due to similar wave addition, in the context of the electrons.

 

The magnetic interaction can overcome the electrostatic repulsion? Can I see a calculation of when that occurs? That would imply electron-electron bound states.

 

Electrons in bound states don't give off "electrostatic and magnetic waves" except to change to another level, and cannot do so in the ground state. That's the whole point behind the Bohr atom and then QM — to explain why this doesn't occur!

 

An interesting effect is magnetism where all the electrons are not in the lowest energy orbitals. In this case, the magnetic does not cancel the electrostatic repulsion, and we notice the extra magnetic output. Since this is stable for some atoms, one would expect a tweak in the nuclear proton orbitals may also occur. If the nuclear proton electrostatic potential was higher it could compensate for the higher electrostatic charge of the electrons. This would allow the proton to detach some of its own magnetic field, so it can add with the electron magnetic field, while still allowing a semi-stable magnetic atom.

 

What? It sounds like you are saying magnetic materials are not in their ground state.

 

The magnetic iron in the center of the earth exists at temperatures that normally denature magnetic properties. One way to overcome that is via induced stability in the slighter higher energy proton orbital configuration, which then stabilizes the electrons.

 

Again, what?

 

Musings on your own version of atomic theory belong in speculations.

[mississippichem]

An interesting effect is magnetism where all the electrons are not in the lowest energy orbitals. In this case, the magnetic does not cancel the electrostatic repulsion, and we notice the extra magnetic output. Since this is stable for some atoms, one would expect a tweak in the nuclear proton orbitals may also occur. If the nuclear proton electrostatic potential was higher it could compensate for the higher electrostatic charge of the electrons. This would allow the proton to detach some of its own magnetic field, so it can add with the electron magnetic field, while still allowing a semi-stable magnetic atom.

 

Are you referring to high spin complexes? These are in the electronic ground state but that ground state just happens to be paramagnetic. It a phenomenon of orbital splitting than can be approximated with crystal field theory and described very well with ligand field theory/Tanabe-Sugano diagrams (that account for paramagnetic electron-electron repulsion). Yes there are some species that are only paramagnetic in excited states, but these transitions are often spin-forbidden (spin-multiplicity isn't conserved) and therefore unlikely and difficult to observe as far as I know.

 

The magnetic interaction can overcome the electrostatic repulsion? Can I see a calculation of when that occurs? That would imply electron-electron bound states.

 

I wouldn't wait too long on those numbers

 

Electrons in bound states don't give off "electrostatic and magnetic waves" except to change to another level, and cannot do so in the ground state. That's the whole point behind the Bohr atom and then QM — to explain why this doesn't occur!

 

 

Yes, thanks for saving me the debunk. Swansont, any advice on my OP? You seem to be adept at explaining these things in the "common tongue".

[swansont]

 

Yes, thanks for saving me the debunk. Swansont, any advice on my OP? You seem to be adept at explaining these things in the "common tongue".

 

Sorry, I meant to address that but got interrupted.

 

I think it depends on the question you are trying to answer. "What's wrong with the Bohr model?" is different from "Why do we use QM?"

 

Since they are chemists, you could ask why don't we use earth, air, fire, water as a basis for explaining things anymore. It worked for the Greeks. Then, after you get an answer (and you let the students establish that "it's wrong/has shortcomings" is an acceptable answer), you can tell them some of the problems with the Bohr model — angular momentum is wrong, doesn't explain observed spectra, etc. Then you can get into why QM is right. But I think you have to wean them from "the Bohr model makes sense" first, because you're dealing with something that is not intuitive. "Making sense" based on classical thinking is no longer a criterion. That's a tough barrier to break down.

[timo]

A slightly unrelated remark that just occurred to me when reading "making sense [...] is no longer a criterion". Historically (not sure if it was meant that way), I'm not convinced it's ever been. I'd think that historically, the stance that things must be like <that> because it makes sense really was a driving force. What happens is that we are very good at actively making sense of how things are. I don't find it a completely ridiculous idea that in some future, people will see QM as the obvious way how it is, similarly to a role that the existence of atoms and elements plays in our society. And from that perspective, the idea to apply classical mechanics to subatomic structures might seem as strange as the elements fire, water, ... as a basis of chemistry seem to us today.

 

So what I am trying say is that this barrier that Tom speaks of isn't necessarily inherent to QM, but moreso to leaving the grounds of common knowledge, where education has giving you the illusion that things are "logical" or intuitive (because you never really were in the situation to be seriously confronted with an alternative). Not exactly related to the thread, though, but I found the though interesting (and found an excuse to procrastinate preparing my talk tomorrow ).

 

EDIT: err ... ohh ... I meant "... was not a driving force." above . Point is: one is very tempted to see that things were easier before (even I know that there's a correlation between rats and the spreading of the Plague, so it cannot be so hard to figure out!) and only now we've hit the point where research is completely counter-intuitive and hard to understand. In first approximation, there is no reason to assume that is actually true.

Edited November 16, 2010 by timo

[swansont]

A slightly unrelated remark that just occurred to me when reading "making sense [...] is no longer a criterion". Historically (not sure if it was meant that way), I'm not convinced it's ever been. I'd think that historically, the stance that things must be like <that> because it makes sense really was a driving force. What happens is that we are very good at actively making sense of how things are. I don't find it a completely ridiculous idea that in some future, people will see QM as the obvious way how it is, similarly to a role that the existence of atoms and elements plays in our society. And from that perspective, the idea to apply classical mechanics to subatomic structures might seem as strange as the elements fire, water, ... as a basis of chemistry seem to us today.

 

So what I am trying say is that this barrier that Tom speaks of isn't necessarily inherent to QM, but moreso to leaving the grounds of common knowledge, where education has giving you the illusion that things are "logical" or intuitive (because you never really were in the situation to be seriously confronted with an alternative). Not exactly related to the thread, though, but I found the though interesting (and found an excuse to procrastinate preparing my talk tomorrow ).

 

I'm sure it shows up elsewhere. It's just that my experience is going to lean heavily into physics, and there was the comment in the OP as well as a whole lot of "alternative" physics we get here that appeals to logic as justification. I agree, anything out of the common experience is prone to this. My personal experience has been that QM becomes logical and reasonable over time. It's just a matter of continued exposure.

[Mr Skeptic]

I think Aristotle had plenty of good examples of how things "making sense" didn't necessarily conform to reality. His idea for gravity, for example (things wanting to reach their level). There's a few flaws in the Bhor model that could be pointed out. As described, the electrons ought to be emitting radiation and spiraling into the nucleus (due to maxwell's equations), and I don't think there's anything that quantizes their energies. My way to transition from the Bhor model was using the idea of wavelengths of the electrons. Just draw the same orbitals as waves, and show that if the length was not a whole number of wavelengths they'd interfere. How to transition to p orbitals I don't know, maybe just tell them that they can do the calculations themselves (eg point out a web page that explains it) so they know how it is derived or just take your word for it.

[magicalprimate]

I would say to first explain the concept of the "probability density function", which if they are in the level you describe, they should at least be able to understand the concept of.

 

Then discuss how the position of the electron around a nucleus is dictated by a probability density function which in turn is dictated by things such as certain quantum numbers, energies, etc.

[Dave World]

This is perfectly sensible advise, pointing out a semantically satisfying response that is respectful in nature, non-condescending, and accurate. Say to those with questions that your role is to help them get successfully through the course while, at the same time, leaving room in their heads and time in their schedules for other demands. - dw

 

As you possibly might know, I am not a chemist. But anyways, here's my advice, assuming your goal is to give a good lecture, and not to teach QM:

 

Don't talk about the Schrödinger equation. Don't talk about uncertainty. Electrons can only be in certain orbits. Period. That explains your atomic line spectra, presumably the structure of molecules (I don't know in detail to what extend which approximations you can make and still get your desired statement, though). And I understood the photoelectric effect as a proof for the QM nature of light, which I don't quite see why you'd need that for your class.

You will always reach the point where a "deeper" question cannot be answered, so don't even start with details that are not required. That is not to discourage people from asking further questions. But build a solid platform of what has to be understood, and what can be considered as "that's just how it is" so that people do not unnecessarily confuse themselves over information they do not need.

 

(somehow, posting this seems like a deja vu, dunno why).

Edited September 3, 2011 by Dave World

[MigL]

From your answer to the OP, swansont, I would guess that you've taught in the past, or even currently. Have you ??