= Solution
\b[The labels apply when the <molecule> has an <inversion centre>], as a homonuclear diatomic <molecule> does. The label $g$ means $\psi(-\mathbf r)=\psi(\mathbf r)$, and $u$ means $\psi(-\mathbf r)=-\psi(\mathbf r)$, with the origin at that centre. In a heteronuclear diatomic <molecule>, inversion exchanges different <atomic nuclei> and these are generally not valid symmetry labels.
For the p-derived combinations above,
$$
\boxed{\sigma_g,\qquad\sigma_u^*,\qquad\pi_u,\qquad\pi_g^*.}
$$
Inversion both exchanges the two centres and changes the sign of each individual p <atomic orbital>. Applying both operations to each sum or difference gives these labels. The star denotes <antibonding molecular orbitals>, independently of <parity>: a bonding <molecular orbital> need not always be $g$.
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