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According to this question/answer, isolated atoms are spherical – and don't have, for example, p-orbital lobes sticking out. The reason is that each complete set of p-, d- and f-orbitals taken together is spherically symmetrical – and the overall wavefunction will be a superposition of all possible states. That superposition will be spherically symmetric, so the atom will be, too. (Sorry for paraphrasing, simplifying etc!).

So my question is: apart from the orbitals involved in making e.g. sigma and pi bonds, is 'the rest' of the atom spherically symmetrical? I have done this rough picture. Image shows formation of molecular orbitals in four molecules

You will notice that down the left, the p-orbitals are shown (even though in an isolated atom they would not exist like that – I've kept them so they can show potential 'bonding sites'). But on the right, in the 'finished' molecules, all but the orbitals involved in bonding disappear, into a spherically symmetric shape as before.

I realise there are several to many simplifications here, but this is for a general audience, and I just want to give a sense of molecular orbitals without getting anything horribly wrong. (In every artwork I find online, people only seem to focus on the orbitals involved, as if they are separate from the rest of their respective atoms.)

I'd really appreciate any help and thoughts. Thank you.

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  • $\begingroup$ Electrons interact, so of course if one orbital is not symmetric (e.g. if it's bonding to another atom), this will to some extent also break the symmetry of all other orbitals. And I'm not sure if I follow the logic of this "isolated atoms are spherical", firstly because I don't see how you can prove this statement. $\endgroup$
    – Karl
    Commented Nov 26, 2017 at 12:05
  • $\begingroup$ Good point. Darn. Do you look at my illustration and balk? Or do you think it's at least useful and acceptable, for a general audience, as I say? Thanks for your answer. $\endgroup$
    – Jack
    Commented Nov 27, 2017 at 10:37
  • $\begingroup$ Who exactly is your audience? $\endgroup$
    – Karl
    Commented Nov 27, 2017 at 14:26
  • $\begingroup$ Well ... it's a general audience, from teenage up, with little prior experience but hopefully an interest – and I will have built up to this, of course, via a general introduction to quantum mechanics and atomic orbitals etc. Thanks again. $\endgroup$
    – Jack
    Commented Nov 29, 2017 at 9:24

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Given an external electromagnetic field, the orbitals do split and even an otherwise isolated atom is no longer spherically symmetrical. For a mostly magnetic field, this is called the Zeeman effect, and for an essentially electrostatic field it is the Stark effect.

Of course, this begs the definition of an "isolated" atom. As @Karl mentions, how do you measure the shape without interacting with the atom? Any incident photon, for example, would be "letting the cat out of the box."

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  • $\begingroup$ Thanks. Yes, in reality, I suppose there is no such thing as a truly isolated atom! I'm just keen to show the molecular orbitals in context, i.e. with the rest of the atom also present, for a general audience. Do you think the illustration is at least useful? $\endgroup$
    – Jack
    Commented Nov 27, 2017 at 10:39
  • $\begingroup$ The illustration is quite useful! If used in a presentation, I would split it into multiple frames, because it presents so many important concepts. Best wishes with what should be an edifying presentation. $\endgroup$
    – DrMoishe Pippik
    Commented Nov 27, 2017 at 17:39

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