Coupled-cluster response theory with linear-r12 corrections: The CC2-R12 model for excitation energies

Coupled-cluster response theory for vertical excitation energies within the second-order approximate coupled-cluster singles-and-doubles model CC2, including linear-r₁₂ corrections, is derived and implemented for Ansätze 1 and 2 of R12 theory. An orthonormal auxiliary basis set is used for the resolution-of-the-identity approximation in order to calculate the three- and four-electron integrals needed in R12 theory. The basis set convergence is investigated for a selected set of atoms and small molecules and it is found that in many cases the convergence is not improved. An analysis of the different contributions to excitation energies shows that the present scheme for the construction of the R12 pair functions leads in response theory to an unbalanced description of ground- and excited-state wave functions and needs to be generalized to carry the high accuracy of R12 methods over to response theory.