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To identify IR and Raman active, symmetry of p- and d-orbitals are used.

If we start since making ${D_{3h}}$ character table, how to match between symmetry of p- and d-orbitals and Mulliken symbol? because when I tried to find out, symmetry after doing symmetry operation isn't similar with any symmetry (Mulliken symbols).

For example, considering ${AsCl_5}$ symmetry operation of p_x of AsCl5

compared with ${D_{3h}}$ character table D3h character table

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    $\begingroup$ The p orbitals can be considered to be unit vectors along their respective axes. Thus they transform as displacements in $x,\; y$ and $z$, hence transform as $E'$ for $x$ and $y$ and $A_2''$ for $z$. $\endgroup$ – porphyrin Dec 10 '18 at 8:36

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