Application of the RPA and Higher RPA to the V and T States of Ethylene

We have applied our proposed higher random‐phase approximation (HRPA) to the $T$ and $V$ states of ethylene. In the HRPA, unlike the RPA, one solves for the excitation frequencies and the ground‐state correlations self‐consistently. We also develop a simplified scheme (SHRPA) for solving the equations of the HRPA, using only molecular integrals sufficient for the usual RPA calculations. The HRPA removes the triplet instability which often occurs in the RPA. The excitation energy for the $\mathrm{N\hspace{0.17em}\to \hspace{0.17em}T}$ transition is now in good agreement with experiment. The $\mathrm{N\hspace{0.17em}\to \hspace{0.17em}V}$ transition energy increases by 15% over its RPA Value. The $\mathrm{N\hspace{0.17em}\to \hspace{0.17em}V}$ oscillator strength changes only very slightly. These results are also useful in explaining the appearance and ordering of states obtained in recent direct open‐shell SCF calculations.