Can it be determined whether a biorthogonalized molecular orbitals is singly occupied just from its shape?

You can see the picture below, describing biorthogonalized molecular orbitals' shapes of $\ce{FeO}$ (Red is Oxygen and the other is Iron) by using Gaussian software (UAFPD functional with 6-311+G(2d,p) basis, quartet spin).

According to the reference of the image$^{1}$:

With this representation, it is clear that the molecule has five singly occupied orbitals consisting of four alpha unpaired electrons localized on the iron atom...

Unfortunately, I have no idea to figure out whether one orbital is singly occupied or not from the picture.

  1. James B. Foresman_ Aeleen Frisch - Exploring Chemistry with Electronic Structure Methods (2015) page 55

FeO Biorthogonalized Molecular Orbitals near Fermi Energy

  • $\begingroup$ 그냥 모양이 비슷한 오비탈을 하나씩 알파스핀이랑 베타스핀에서 찾으면 되지 않을까요? $\endgroup$ Aug 2, 2022 at 9:53
  • $\begingroup$ What's the reference for the image $\endgroup$ Aug 2, 2022 at 14:21
  • $\begingroup$ Thank you for your comment, the reference is James B. Foresman_ Aeleen Frisch - Exploring Chemistry with Electronic Structure Methods (2015) page 55. $\endgroup$ Aug 4, 2022 at 4:58
  • $\begingroup$ 답변 정말 감사합니다. 지금 평행하게 정렬된 알파랑 베타 오비탈이 같은 에너지 레벨입니다.(숫자는 달라도) 물론 가우시안 프로그램에서 전자의 occupancy를 알 수 있긴 한데 오비탈 모양으로 이게 n개의 unpaired 전자가 어느 원자에 속하는지 알 수 있는 게 궁금했습니다. $\endgroup$ Aug 4, 2022 at 5:02
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    $\begingroup$ @SeungHwanKim While there isn't a rule about non-English comments on SE sites unlike for questions/answers, you would likely get more feedback if using English comments. $\endgroup$
    – Tyberius
    Aug 8, 2022 at 20:38

1 Answer 1


They aren't determining the occupation from the shape of the orbital. The orbitals are computed with an unrestricted scheme, meaning $\alpha$ and $\beta$ spin electron are not required to pair up in the same spatial orbital. In other words, all orbitals in this case are either singly occupied or empty.

The five simply comes from the fact that the HOMO and HOMO-n orbitals will be occupied and the LUMO and LUMO+n orbitals will be unoccupied.


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