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When classifying the molecules in symmetry point groups some non-principal rotation axes $C_2$ and some reflection planes $\sigma_v$ and $\sigma_d$ are primed or double primed, like $\sigma_v'$, $\sigma_v''$, $C_2'$ or $C_2''$. What determines which is the unprimed, primed or double primed $C_2$-axis/$\sigma_v$-plane, or is it arbitrary?

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    $\begingroup$ Search for Mulliken Symbols, there is a table here mathworld.wolfram.com/MullikenSymbols.html $\endgroup$ – porphyrin May 3 '17 at 10:16
  • $\begingroup$ Sure the Mulliken symbols of irreducible representations also have primes given in the table you linked, but this is not what I am asking about (i think). I ask bout the primes in the symmetry elements themselves, like the $\sigma_v'$ plane, or the $C_2''$ axis. $\endgroup$ – Jonatan Öström May 4 '17 at 11:34
  • $\begingroup$ I misunderstood; they are just to identify between similar operations, say, the three different $C_2$ axes in $D_6h$. Some tables use $C_2(x), C_2(y)$ etc. rather than $C_2'$ etc. and $\sigma (xy)$ instead of $\sigma '$. $\endgroup$ – porphyrin May 4 '17 at 11:53
  • $\begingroup$ OK, now that makes sense. So whether the plane of the water molecule is called $\sigma_v'$ or $\sigma_v''$ may differ in different books, for example? $\endgroup$ – Jonatan Öström May 4 '17 at 13:07
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    $\begingroup$ yes or even $\sigma (xz)$ and $\sigma(yz), which I prefer, as different authors use different axes orientations, for example, all the atoms in water may be chosen to lie on the zx plane or on the zy plane, z being the principal axis. So its often necessary to check what is being used and convert to your preferred orientation if needed. $\endgroup$ – porphyrin May 4 '17 at 13:21

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