Comparing MO Labelling Schemes: LHS vs. RHS

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The discussion centers around two labeling schemes for molecular orbitals (MOs) depicted in a diagram. The left-hand side (LHS) naming scheme is straightforward, as it labels MOs based on the atomic orbitals (AOs) from which they originate, incorporating designations for symmetry (σ/π) and parity (u/g). The right-hand side (RHS) numbering scheme, however, raises questions. It distinguishes orbitals of the same symmetry by numbering them sequentially (1, 2, etc.), which indicates the order of their energy levels or formation. This is exemplified by the first and second σg and σu orbitals, where the symmetry is defined by the σ/π and u/g labels. The clarification provided helps in understanding how these orbitals are organized within their respective symmetry categories.
etotheipi
Two different labelling schemes for MOs are shown on the left and right of this diagram:

1602192168794.png


I understand the LHS naming scheme, since the MOs are simply labelled according to the AOs from which they are derived (along with ##\sigma##/##\pi## and ##u##/##g## for the MO).

I don't understand the numbering scheme on the RHS. The book says that 'orbitals of the same symmetry are distinguished from one another by numbering them 1,2,...'. What does this mean? Thanks.
 
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There is the first sigma_g orbital, the second sigma_g orbital, the first sigma_u orbital, the second sigma_u orbital ... The symmetry is specified here by sigma/pi and the u/g label.
 
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DrDu said:
There is the first sigma_g orbital, the second sigma_g orbital, the first sigma_u orbital, the second sigma_u orbital ... The symmetry is specified here by sigma/pi and the u/g label.

Ah, I see. Thanks!
 

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