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I have a concern related to the follwoing question When orbitals are labeled based on their irreps in D2h, how are the orbitals ordered for an N atom? In which the following Answer clearly states that any single atom would have a $K_h$ point group symmetry, which I believe means the single atom is a spherical system. However, the question was referring to the single atom (N atom in that case) to belong to $D_{2h}$ or $D_{\infty_h}$ point groups. What is the convention behind this treatment?

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When choosing the point group, a system with a single nucleus (e.g. a single atom) is considered to be spherically symmetric, so its point group is $K_h$ in Schoenflies notation, in which K stands for the German word Kugel (meaning "ball" or "sphere").

$D_{2h}$ and $D_{\infty h}$ are sub-groups of $K_h$, so they are also valid point groups that can be used to describe the symmetry operations that can be applied to an atom. Most quantum chemistry software packages such as , which is the one that was discussed in the question to which you provided a link, do not contain enough code to fully treat non-Abelian groups such as $D_{\infty h}$ and $K_h$, so they use the largest possible Abelian subgroup, which would be $D_{2h}$ if the system is a single atom.

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    $\begingroup$ +1. An alternative notation for $K_h$ is $O(3)$, the mathematicians' notation for the three-dimensional orthogonal group. For example the BDF program uses the latter notation. Meanwhile many programs (including BDF) can treat finite order non-Abelian groups but not infinite groups, in which case $O(3)$ is typically reduced to a convenient high-order finite group, such as $O_h$. $\endgroup$
    – wzkchem5
    Commented Mar 17 at 13:24

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