Question

What orbitals are used in the sigma bond of `"O"_2`?

Answer 1

The `2p_z` orbital, i.e. the `2p` orbital pointing directly along the internuclear (`z`) axis.

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The `bbsigma`/sigma bond is always made along the internuclear axis, overlapping the orbitals head-on. By convention, for linear molecules, that is the `z` axis.

On the other hand, the one `pi` bond in `"O"_2` is made using either a `2p_x` or `2p_y` orbital (arbitrary). For `"O"_2`, there does NOT have to be hybridization, either.

See here for "when" to hybridize.