The second-order approximate coupled cluster singles and doubles model CC2

An approximate coupled cluster singles and doubles model is presented, denoted CC2. The CC2 total energy is of second-order Mّller-Plesset perturbation theory (MP2) quality. The CC2 linear response function is derived. Unlike MP2, excitation energies and transition moments can be obtained in CC2. A hierarchy of coupled cluster models, CCS, CC2, CCSD, CC3, CCSDT etc., is presented where CC2 and CC3 are approximate coupled cluster models defined by similar approximations. Higher levels give increased accuracy at increased computational effort. The scaling of CCS, CC2, CCSD, CC3 and CCSDT is N4, N5, N6, N7 and N8, respectively where N is th the number of orbitals. Calculations on Be, N2 and C2H4 are performed and results compared with those obtained in the second-order polarization propagator approach SOPPA.