Scaled opposite-spin CC2 for ground and excited states with fourth order scaling computational costs

An implementation of scaled opposite-spin CC2 (SOS-CC2) for ground and excited state energies is presented that requires only fourth order scaling computational costs. The SOS-CC2 method yields results with an accuracy comparable to the unscaled method. Furthermore the time-determining fifth order scaling steps in the algorithm can be replaced by only fourth order scaling computational costs using a "resolution of the identity" approximation for the electron repulsion integrals and a Laplace transformation of the orbital energy denominators. This leads to a significant reduction of computational costs especially for large systems. Timings for ground and excited state calculations are shown and the error of the Laplace transformation is investigated. An application to a chlorophyll molecule with 134 atoms results in a speed-up by a factor of five and demonstrates how the new implementation extends the applicability of the method. A SOS variant of the algebraic diagrammatic construction through second order ADC(2), which arises from a simplification of the SOS-CC2 model, is also presented. The SOS-ADC(2) model is a cost-efficient alternative in particular for future extensions to spectral intensities and excited state structure optimizations.