Explicitly-correlated ring-coupled-cluster-doubles theory: Including exchange for computations on closed-shell systems

- Ring-coupled-cluster-doubles approach now implemented with exchange terms.
- Ring-coupled-cluster-doubles approach now implemented with F12 functions.
- Szabo-Ostlund scheme (SO2) implemented for use in SAPT.
- Fast convergence to the limit of a complete basis.
- Implementation in the TURBOMOLE program system.

Random-phase-approximation (RPA) methods have proven to be powerful tools in electronic-structure theory, being non-empirical, computationally efficient and broadly applicable to a variety of molecular systems including small-gap systems, transition-metal compounds and dispersion-dominated complexes. Applications are however hindered due to the slow basis-set convergence of the electron-correlation energy with the one-electron basis. As a remedy, we present approximate explicitly-correlated RPA approaches based on the ring-coupled-cluster-doubles formulation including exchange contributions. Test calculations demonstrate that the basis-set convergence of correlation energies is drastically accelerated through the explicitly-correlated approach, reaching 99% of the basis-set limit with triple-zeta basis sets. When implemented in close analogy to early work by Szabo and Ostlund [36], the new explicitly-correlated ring-coupled-cluster-doubles approach including exchange has the perspective to become a valuable tool in the framework of symmetry-adapted perturbation theory (SAPT) for the computation of dispersion energies of molecular complexes of weakly interacting closed-shell systems.