Excitation energies of BH, CH 2 and Ne in full configuration interaction and the hierarchy CCS, CC2, CCSD and CC3 of coupled cluster models

Abstract

Excitation energies in the coupled cluster model hierarchy CCS, CC2, CCSD and CC3 have been calculated for Ne, BH and CH 2 and compared with full configuration interaction (FCI) results. Single replacement dominated excitations are improved at each level in this hierarchy, with a decrease in the error compared to FCI of about a factor of three at each level. This decrease is in accordance with the fact that the single replacement dominated excitations in CCS, CC2, CCSD and CC3 are correct through respectively first, second and third order in the fluctuation potential. The improvement from CC2 to CCSD is due to the fact that CCSD gives a full coupled cluster treatment in the singles, doubles space. Double replacement dominated excitations can only be described at the CCSD and CC3 levels, and are correct through first and second order, respectively. The CC3 double replacement dominated excitations have similar quality as the single replacement dominated excitations in CC2. The scaling of CCS, CC2, CCSD and CC3 is N 4, N 5, N 6 and N 7, respectively, where N is the number of orbitals.