Confusion about the choice of axis for Molecular Orbital Theory

Question

This video from MIT OpenCourseWare says that pi bonds and anti-bonds are for 2px and 2py, i.e., $\pi_{2px}$, $\pi_{2py}$ and $\pi_{2px}^*$, $\pi_{2py}^*$ and sigma bonds and anti-bonds are for 2pz i.e., $\sigma_{2pz}$ and $\sigma_{2pz}^*$.

But in my reference books it says pi bonds and anti-bonds are formed for 2py and 2pz i.e., $\pi_{2py}$, $\pi_{2pz}$ and $\pi_{2py}^*$, $\pi_{2pz}^*$ and sigma bonds and anti-bonds are for 2pz i.e., $\sigma_{2px}$ and $\sigma_{2px}^*$.

Which is actually the right one? Please explain.

Answer 1

Although we could not see what is written in OP's "reference books", the mentioned difference most likely is the result of different choices for the bond axis.

Conventionally, and as it is (implicitly?) done in the MIT video lecture, it is chosen to be the $z$-axis, in which case $\pi$ bonds are indeed formed from $\mathrm{p}_x$ and $\mathrm{p}_y$ orbitals while $\mathrm{p}_z$ can take part in $\sigma$-bonding. If, however, the bond axis is chosen to be the $x$-axis, then $\pi$ bonds are formed from $\mathrm{p}_y$ and $\mathrm{p}_z$ orbitals while $\mathrm{p}_x$ takes part in $\sigma$-bonding.

Answer 2

As other people says x y and z directions are arbitrary, However, the tradition that open courseware uses comes from the diatomic molecules. There the atom-atom axis is assumed to be the z direction and then the y and z, being perpendicular, correspond to the direction of pi bonds. A similar use is to design sigma to the atom-atom direction and pi to the perpendicular ones. This tradition of diatomic molecules is then exported to polliatomic examples. See any good book on molecular spectrocopy (Jeanne L McHale, Molecular Spectroscopy) for instance.