Improving upon the accuracy for doubly excited states within the coupled cluster singles and doubles theory

An alternative strategy of computations for double character excited states has been examined. The basic idea is to employ the reference function specific to the excited state of interest, as opposed to the traditionally used reference function, usually corresponding to the ground state, specific to the entire spectrum of a molecule. The procedure is used within the framework of the coupled cluster singles and doubles (CCSD) method. The conventional spin-conserving CC approach as well as its spin-flip (SF) extension has been analyzed. For the latter, two variants are considered, changing the S(z) value of the reference function by one [equation-of-motion (EOM)-SF] and two (EOM-2SF). The accuracy of the methods is benchmarked for the C(2) and C(4) molecules and referred to the full configuration interaction (FCI) or CC singles, doubles, and triples results. The vertical and adiabatic excitation energies, equilibrium geometries, and harmonic frequencies are studied. A significant improvement is demonstrated for the excitation energies of doubly excited states. Comparing these values with the FCI method, the errors of the conventional EOM CCSD method of about 1.7-2.2 eV are reduced to about 0.0-0.4 eV for the SF method. An improvement is also shown for the equilibrium geometries and harmonic frequencies.