Quantum, classical, and hybrid QM/MM calculations in solution: General implementation of the ddCOSMO linear scaling strategy

We present the general theory and implementation of the Conductor-like Screening Model according to the recently developed ddCOSMO paradigm. The various quantities needed to apply ddCOSMO at different levels of theory, including quantum mechanical descriptions, are discussed in detail, with a particular focus on how to compute the integrals needed to evaluate the ddCOSMO solvation energy and its derivatives. The overall computational cost of a ddCOSMO computation is then analyzed and decomposed in the various steps: the different relative weights of such contributions are then discussed for both ddCOSMO and the fastest available alternative discretization to the COSMO equations. Finally, the scaling of the cost of the various steps with respect to the size of the solute is analyzed and discussed, showing how ddCOSMO opens significantly new possibilities when cheap or hybrid molecular mechanics/quantum mechanics methods are used to describe the solute.