Ab Initio Effective One-Electron Potential Operators:Applications for Charge-Transfer Energy in Effective Fragment Potentials

The concept of effective one-electron potentials (EOP) has proven to be extremely useful in efficient description of electronic structure of chemical systems, especially extended molecular aggregates such as<br>interacting molecules in condensed phases. Here, a general method for EOP-based elimination of electron<br>repulsion integrals (ERIs) is presented, that is tuned towards the fragment-based calculation methodologies<br>such as the second generation of the effective fragment potentials (EFP2) method. Two general types of the<br>EOP operator matrix elements are distinguished and treated either via the distributed multipole expansion or<br>the extended density fitting schemes developed in this work. The EOP technique is then applied to reduce<br>the high computational costs of the effective fragment charge-transfer (CT) terms being the bottleneck of<br>EFP2 potentials. The alternative EOP-based CT energy model is proposed, derived within the framework of<br>intermolecular perturbation theory with Hartree–Fock non-interacting reference wavefunctions, compatible<br>with the original EFP2 formulation. It is found that the computational cost of the EFP2 total interaction<br>energy calculation can be reduced by up to 38 times when using the EOP-based formulation of CT energy,<br>as compared to the original EFP2 scheme, without compromising the accuracy for a wide range of weakly<br>interacting neutral and ionic molecular fragments. The proposed model can thus be used routinely within<br>the EFP2 framework.