Geometry optimizations with the coupled-cluster model CC2 using the resolution-of-the-identity approximation

An implementation of the gradient for the second-order coupled-cluster singles-and-doubles model CC2 is reported, which employs the resolution-of-the-identity (RI) approximation for electron repulsion integrals. The performance of the CC2 model for ground state equilibrium geometries and harmonic frequencies is investigated and compared with experiment and other ab initio methods. It is found that CC2 equilibrium geometries have a similar accuracy to those calculated with second-order Møller–Plesset perturbation theory (MP2), but the bond lengths are larger. In particular, double and triple bonds and bonds in electron-rich compounds are elongated by 0.5–1.5 pm. Thereby CC2 slightly outperforms MP2 for single bonds, in particular in electron-rich compounds, but for strong double and triple bonds CC2 is somewhat inferior to MP2. The results for harmonic frequencies go in parallel with the results for equilibrium structures. The error introduced by the RI approximation is found to be negligible compared to the remaining one-electron basis set error, if optimized auxiliary basis sets are used. Typically, the RI error in bond lengths is of the order of $10−3 pm$ and the error in angles $10−3–10−2 deg.$ Applications are reported for the geometry of trans-azobenzene and for the geometry and harmonic frequencies of cis,trans-1,4-difluorobutadiene.