Response functions in the CC3 iterative triple excitation model

The derivation of response functions for coupled cluster models is discussed in a context where approximations can be introduced in the coupled cluster equations. The linear response function is derived for the approximate coupled cluster singles, doubles, and triples model CC3. The linear response functions for the approximate triples models, CCSDT-1a and CCSDT-1b, are obtained as simplifications to the CC3 linear response function. The consequences of these simplifications are discussed for the evaluation of molecular properties, in particular, for excitation energies. Excitation energies obtained from the linear response eigenvalue equation are analyzed in orders of the fluctuation potential. Double replacement dominated excitations are correct through second order in all the triples models mentioned, whereas they are only correct to first order in the coupled cluster singles and doubles model (CCSD). Single replacement dominated excitation energies are correct through third order in CC3, while in CCSDT-1a, CCSDT-1b, and CCSD they are only correct through second order. Calculations of excitation energies are reported for CH+, N2, and C2H4 to illustrate the accuracy that can be obtained in the various triples models. The CH+ results are compared to full configuration interaction results, the C2H4 results are compared with complete active space second order perturbation theory (CASPT2) and experiment, and the N2 results are compared to experiment. Double replacement dominated excitations are improved significantly relative to CCSD in all the triples models mentioned, and is of the same quality in CC3 and CCSDT-1a. The single replacement dominated excitation are close to full configuration interaction results for the CC3 model and significantly improved relative to CCSD. The CCSDT-1 results for the single replacement dominated excitations are not improved compared to CCSD.