Low scaling random-phase approximation electron correlation method including exchange interactions using localised orbitals

A random-phase approximation electron correlation method including exchange interactions has been developed which reduces the scaling behaviour of the standard approach by two to four orders of magnitude, effectively leading to a linear scaling performance if the local structures of the underlying quantities are fully exploited in the calculations. This has been achieved by a transformation of the integrals and amplitudes from the canonical orbital basis into a local orbital basis and a subsequent dyadic screening approach. The performance of the method is demonstrated for a range of tripeptide molecules as well as for two conformers of the polyglycine molecule using up to 40 glycine units. While a reasonable agreement with the corresponding canonical method is obtained if long-range Coulomb interactions are not screened by the local method, a significant improvement in the performance is achieved for larger systems beyond 20 glycine units. Furthermore, the control of the Coulomb screening threshold allow...