I have seen some books indicated sigma bond has C2 symmetry. I understand pi and delta bond change their signs about C2 and C4 rotation about bond axis, but I don't understand why sigma bond has C2 symmetry not C∞ about its bond axis. The example of the sigma bond came from two 1s orbitals.
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1$\begingroup$ I have seen books about two-headed people living beyond the ocean. Somehow, this does not bother me one bit. A sigma bond is $C_\infty$-symmetric all right. $\endgroup$– Ivan NeretinCommented Feb 11, 2020 at 18:10
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2$\begingroup$ Possibly they meant C2 around an axis perpendicular to the bond, especially since 1s orbital bonding is H2, which is symmetric. $\endgroup$– AndrewCommented Feb 11, 2020 at 19:10
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2$\begingroup$ Technically speaking a $\sigma$ bond fits in the $C_{2}$ point group since $C_{2}\subset C_{\infty}$. $\endgroup$– ZheCommented Feb 11, 2020 at 23:21
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$\begingroup$ @Andrew the book indicates the rotation axis with the bond axis. $\endgroup$– skwonCommented Feb 12, 2020 at 2:25
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