Exploiting both C_3v symmetry and sparsity in vibrational calculations for methanelike molecules

Vibrational spectroscopy calculations for five-atom systems were performed to exploit full G₁₂ symmetry. The first step was the derivation of a Hamiltonian matrix representation which exactly satisfies the desired symmetry. The second step was to develop an explicit numerical recipe for performing efficient matrix-vector products that also satisfies the desired symmetry. Very enhanced numerical efficiency was achieved.