Beyond vibrational self-consistent-field methods: Benchmark calculations for the fundamental vibrations of ethylene

A number of different methods for calculation of vibrational energies are reviewed and tested for calculation of the fundamental vibrational frequencies for ethylene. The methods tested for the description of the vibrational states are vibrational self consistent field (VSCF), vibrational configuration interaction (VCI), vibrational M{\o}ller-Plesset theory (VMP), and vibrational coupled cluster (VCC). The convergence of the different methods towards the full vibrational configuration interaction (FVCI) result is discussed for a modest-sized one-mode basis. For larger one-mode basis sets results are presented for selected methods. Different representations of the potential energy surface are compared including full and partial quartic force field as well as expansions using up to sixth derivatives of the potential energy surface. Using MP2 electronic structure theory the electronic structure basis set convergence is tested ​
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