I was watching an MIT OpenCourseWare lecture on MO theory which mentioned that $\sigma$ orbitals are "cylindrically symmetrical." I was a bit confused, because I was under the assumption that the cross section of a $\sigma$ orbital is an ellipse, such that a $\sigma$ orbital is an ellipse that has undergone a full revolution around an axis. This is somewhat of a topology/nomenclature question, but seeing as the context is Chemistry, I though I'd post here first. Could anyone clear up the definition of cylindrical symmetry?
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$\begingroup$ You're right. A $\sigma$ bond would be more like an ellipsoid than a spherocylinder (capsule) and even less like a cylinder. All three of these would have a rotational axis. $\endgroup$ – MaxW Apr 17 '20 at 0:25
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$\begingroup$ They just mean that, like a cylinder, there is an axis of infinite rotational symmetry $C_\infty$ $\endgroup$ – Andrew Apr 17 '20 at 11:11
