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Introduction

I have been trying to use computational software to gain more insight into how molecular orbitals are formed, as well as their shapes and sizes in accordance with Molecular Orbital Theory.

What I know so far

The molecule I examined was allyl bromide. allyl bromideWhat I knew theoretically was that, contrary to VBT, all of the orbitals interact with each other, generating more complex hybrid orbitals. This makes sense, given the fact that GaussView generated 60 molecular orbitals.

Here is a snapshot of the LUMO for this molecule: LUMO

Questions

My question is what accounts for the shape of these orbitals?

According to my textbook (which offers a simplified representation for this orbital), the LUMO should behave like an arithmetic combination between the π* orbital of the C-C bond and the σ* orbital of the C-Br bond. But this approach seems localized, as if the influence of other orbitals would be negligible. Since MOT states that all of the orbitals interact to some extent, isn't this approach wrong?

lumo2

So, how is this LUMO actually supposed to look like? What is the mathematical mechanism behind orbital structure and energy? To what extent is it wrong to just add orbitals together to try and predict their behaviour?

References

Jonathan Clayden, Nick Greeves, Stuart Warren, Peter Wothers - Organic Chemistry-Oxford University Press, USA (2000)

TheRelentlessNucleophile
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  • What C-O bond? Do you mean C-Br? – Buck Thorn Mar 12 '21 at 12:44
  • Apologies, I was referring specifically to an SN2' mechanism. That makes use of both the bonds I was talking about. – TheRelentlessNucleophile Mar 12 '21 at 12:45
  • OK but there is no "O" if by that you mean oxygen. – Buck Thorn Mar 12 '21 at 12:48
  • I edited it. Looking back, I understand why that paragraph seemed like nonsense. Bonds broken: C1=C2 and C-Br. Bonds formed: C2=C3 and C-Nu (random nucleophile). – TheRelentlessNucleophile Mar 12 '21 at 12:51
  • Another question successfully ignored... :( – TheRelentlessNucleophile Mar 12 '21 at 18:36
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    You have a lot of questions in your post and it's a bit hard to unwrap it (know where to start explaining). What you see in your textbook is evidently a simplificaction, a schematic, that highlights the most important aspects of the electronic structure for the purpose of explaining the particular mechanism in question. MOs are LCAOs. The coefficients in the expansion determine AO contributions. The important point is that $H\psi=E\psi$ be satisfied, provided $\psi \psi*=1$ for a one electron spin-orbital, since the Schr. equation is linear the coefficients can be any real number 0<c<1. – Buck Thorn Mar 13 '21 at 08:42
  • @BuckThorn, thank you for your response! Can you recommend a textbook or any source that covers AOs and essentially MOT? All of the sources I find either offer extremely simplified descriptions (such as my textbooks, and those simplifications work just fine in those contexts) or stuff that involves a lot of complicated maths that I cannot grasp since I'm a HS Junior. Anything in the middle would be highly appreciated. – TheRelentlessNucleophile Mar 13 '21 at 09:20
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    You may want to look through https://chemistry.stackexchange.com/questions/37303/resources-for-learning-chemistry My best suggestion is a physical chemistry textbook. An old favorite of mine is Miessler and Tarr which covers MO theory and is not too mathy but might be too advanced for HS. – Buck Thorn Mar 13 '21 at 09:44
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    An alternative is an orgo textbook that introduces MO theory. – Buck Thorn Mar 13 '21 at 09:47
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    BTW How did you get hold of Gaussview as a HS Junior? – Buck Thorn Mar 13 '21 at 09:48
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    Haha, from a friend of mine who studies Chemistry at EPFL, in Switzerland. – TheRelentlessNucleophile Mar 13 '21 at 09:49
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    Also, some chem SE questions may be useful intros eg: https://chemistry.stackexchange.com/questions/19365/the-rules-for-lcaos-in-molecular-orbital-theory?rq=1 I'm going to vote to close your post since I think that one answers your question. – Buck Thorn Mar 13 '21 at 09:50
  • Let us continue this discussion in chat. – TheRelentlessNucleophile Mar 13 '21 at 15:18

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