Main Question or Discussion Point
Why the moment of inertia of a molecule about the bond axis is small enough to ignore ?
Bystander is correct, the axis you have as your x-axis is one with a non-negligible moment of inertia. There would also be one perpendicular to this and the axis along the bond, which also has a non-negligible moment of inertia, this is why diatomic gases have two rotational degrees of freedom. The bond axis is that which joins the two nuclei.No, that is one of three rotational axes directed at right angles to one another through the center of mass of the molecule; the bond axis is the line connecting the nuclei of the two atoms, and is the one axis of the three that you're interested in for this problem.