Since my metal complex has the spin state as doublet, its MO diagram (in Gaussview, picture attached) has both alpha and beta orbitals. For calculating the energy gap between HOMO and LUMO of the molecule, which orbitals should be considered? alpha LUMO and alpha HOMO or beta LUMO and beta HOMO?
Premkumar G. You need to take into account both the alpha and beta orbitals independently when computing the energy difference between the HOMO and LUMO orbitals in a doublet spin state.
Specifically, the energy gap between the HOMO and LUMO in a doublet spin state would be the difference between the energy of the lowest unoccupied alpha molecular orbital (alpha LUMO) and the highest occupied alpha molecular orbital (alpha HOMO). Alternatively, you could also calculate the energy gap using the beta orbitals by taking the difference between the energy of the lowest unoccupied beta molecular orbital (beta LUMO) and the highest occupied beta molecular orbital (beta HOMO).
If you consider the spin orbit coupling the energy gap between the alpha and beta may vary but in most of the cases the difference is small, and you can take either the alpha or beta orbital alone while calculating the HOMO-LUMO gap.
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