The accuracy of molecular bond lengths computed by multireference electronic structure methods

We compare experimental Re values with computed Re values for 20 molecules using three multireference electronic structure methods, MCSCF, MR-SDCI, and MR-AQCC. Three correlation-consistent orbital basis sets are used, along with complete basis set extrapolations, for all of the molecules. These data complement those computed previously with single-reference methods. Several trends are observed. The SCF Re values tend to be shorter than the experimental values, and the MCSCF values tend to be longer than the experimental values. We attribute these trends to the ionic contamination of the SCF wave function and to the corresponding systematic distortion of the potential energy curve. For the individual bonds, the MR-SDCI Re values tend to be shorter than the MR-AQCC values, which in turn tend to be shorter than the MCSCF values. Compared to the previous single-reference results, the MCSCF values are roughly comparable to the MP4 and CCSD methods, which are more accurate than might be expected due to the fact that these MCSCF wave functions include no extra-valence electron correlation effects. This suggests that static valence correlation effects, such as near-degeneracies and the ability to dissociate correctly to neutral fragments, play an important role in determining the shape of the potential energy surface, even near equilibrium structures. The MR-SDCI and MR-AQCC methods predict Re values with an accuracy comparable to, or better than, the best single-reference methods (MP4, CCSD, and CCSD(T)), despite the fact that triple and higher excitations into the extra-valence orbital space are included in the single-reference methods but are absent in the multireference wave functions. The computed Re values using the multireference methods tend to be smooth and monotonic with basis set improvement. The molecular structures are optimized using analytic energy gradients, and the timings for these calculations show the practical advantage of using variational wave functions for which the Hellmann-Feynman theorem can be exploited.