# Symmetries and degeneracies of the s,p, and d orbitals

Consider the molecular AB_8 (complex with central atom A and 8 B ligands (coordination number 8), for which I determined the point group D_4d) and determine the symmetries and degeneracies of the s, p, and d orbitals of A.

So I believe the general procedure here is to determine a reducible representation for each s, p, and d orbital of the central atom, but how do I do that? Is the s orbital just A1? Is p just B2 and E1? How do I computer these representations?

• The s orbital is always $A_1$. The others transform the same as their corresponding Cartesian function (e.g. $p_x$ transforms the same as $x$). You can determine how the function transforms under the operations of the group, though this usually given in the the third and fourth columns of the character table. – Tyberius Mar 27 at 20:27
• I was just starting to figure that out! It was much simpler than I was imagining. Thank you for your response! – Kameron Shrum Mar 27 at 20:28