4) Symmetry-adapted linear combinations. (10 pts)
Conjugated \( \pi \) systems in molecules can often be represented primarily as linear combinations of atomic \( p \) orbitals. Naphthalene, shown below, is a prototypical polycyclic aromatic hydrocarbon. Let the molecule lie in the \( x y \) plane, and construct a symmetry adapted basis set consisting only of the \( 2 p_{z} \) orbitals from the carbon atoms. Your final answer should be a vector with the SALCs grouped by irrep.
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