I was given the diagram of $\ce{BF3}$'s LUMO and asked to assess its bonding character as shown below:

Unannotated BF3 HOMO LUMO

Below is the model answer for the annotated version.

I managed to correctly answer the HOMO MO with the same annotations but was confused here slightly.

The LUMO Interaction shows a $\ce{p}$ orbital coming out of the plane, where the B p orbital is out of phase with the $\ce{F3}$ fragmnet orbitals, but the model answer suggests there is a $\ce{\pi}$ type bonding interaction.

This does not make sense to me. Unless mistaken, I thought the p-orbitals from the B and the F atoms (given they are out of phase) show along the bond $\ce{\pi}$ type antibonding properties, rather than $\ce{\pi}$-type bonding interaction.

BF3 HOMO LUMO annotated

Am I correct or not? How is there $\ce{pi}$-type bonding interaction possible along the bond here?


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