Size-consistency-corrected multireference configuration interaction provides highly accurate molecular excitation energies

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Abstract
Accurate reference data for electronically excited states are essential for assessing multireference electronic-structure methods. We benchmark state-averaged completeactive-space self-consistent field (SA-CASSCF), exchange-scaled CASSCF (XS-CASSCF), fully uncontracted multireference configuration interaction with single and double excitations (MR-CISD), and four a posteriori size-consistency corrections against the theoretical best estimates of QUESTDB. The dataset comprises 262 valence excitations of 41 small and medium-sized molecules, including singlet and triplet n*, *, and doubly excited states. All calculations used a consistent COLUMBUS protocol with molecule-specific active spaces and the aug-cc-pVDZ basis set. For the 232 safe transitions, SA-CASSCF and MR-CISD yield mean absolute errors of 0.57 and 0.31 eV, respectively, with predominantly positive biases. The Davidson–Silver/Siegbahn (+DV3) and Pople (+P) corrections reduce the mean absolute errors to 0.10 and 0.11 eV and the root-mean-square errors to 0.13 eV. They also provide a more balanced description across spin multiplicities and excitation characters. Both XSCASSCF improve singlet * states, particularly those with pronounced ionic character, but degrade n* states and do not improve the overall statistics relative to SA-CASSCF. For 36 selected unsafe or doubly excited transitions, MR-CISD+DV3 and MR-CISD+P retain mean absolute errors of 0.16 eV. Their agreement with exFCI-based reference values and discrepancies from several CASPT3- and PC-NEVPT2-based estimates identify states whose current best estimates merit independent re-examination. Overall, size-consistencycorrected MR-CISD provides highly accurate and broadly balanced valence excitation energies.