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