We have applied a proposed higher-order random phase approximation (RPA) to the simple model system of two pi electrons in the double bond of ethylene. The higher-order RPA removes some difficulties involved in the usual RPA, but retains the form of the RPA equations. To derive the higher RPA we retain all terms linear in the ground state correlation coefficients in the equations of motion for the excitation energy and in the equation determining the ground state. These equations are solved self-consistently and are simpler to handle than a configuration interaction solution in a realistic example. We do not use the quasiboson approximation
