Abstract We investigate the correlation energy in the ground state of 4He due to all 2ℏω excitations. An effective residual interaction derived from the Hamada-Johnston potential is used. Contributions from 2ℏω excitations are treated to all orders by diagonalization. These constributions are found to be relatively small (≈0.6 MeV particle ). It is found that the calculation is extremely sensitive to the presence of states with spurious center-of-mass motion. The spectrum of negative-parity 1ℏω states is calculated with the same interaction. The calculated spectrum is in only qualitative agreement with experiment.