What is the molecular orbital diagram for #B_2#?

Before we can draw a molecular orbital diagram for B₂, we must find the in-phase and out-of-phase overlap combinations for boron's atomic orbitals.

Then we rank them in order of increasing energy.

We can ignore the #1s# orbitals, because they do not contain the valence electrons.

Each boron atom has one #2s# and three #2p# valence orbitals.

The #2s# orbitals will overlap to form #2sσ# and #2sσ"*"# orbitals.

The #2p_x# orbitals can overlap end-on to form #2pσ# and #2pσ"*"# orbitals.

The #2p_y# and #2p_z# orbitals can overlap side-on to form degenerate pairs of #2pπ# and #2pπ"*"# orbitals.

The order of energies is #2sσ < 2sσ^✳ < 2pπ < 2pσ < 2pπ^✳ < 2pσ^✳#.

We have three valence electrons from each B atom, so B₂ will have six valence electrons.

We use the Pauli Exclusion Principle and Hund's rule to fill the orbitals in an Aufbau process.

The molecular orbital diagram for B₂ then becomes

The video below describes how to generate molecular orbital diagrams for B₂ and other diatomic molecules from Row 2 elements of the Periodic Table.