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

Abstract

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.

An effective potential for Frenkel excitons

“…In this section, we derive the approximation of the TI/CIS model that is completely free from ERIs. This is possible due to effective elimination of ERIs according to the general prescription: 32 X…”

“…All the other components of the model involve ERIs between the HOMO and LUMO of monomers A and B. These can be grouped into the following three categories: 32 1. Integrals of type (…”

“…In this work, the CAMM method is used to generate the distributed multipole moments from such density matrices, as discussed in ref. 32.…”

“…Matrix elements needed to evaluate EET coupling due to electron and hole transfer processes involve overlap-like ERIs. These shall be treated by the extended density fitting (EDF) technique, 32 i.e., (…”

“…In this paper we introduce a new efficient method to calculate the electronic EET couplings within the TI approach that is valid in both the long-and short-range regimes and is based on the recently introduced effective one-electron potential (EOP) operators technique to eliminate ERIs from fragment-based models. 32 Although we focus here on the singlet-singlet (SS) EET, extension to the triplet-triplet (TT) EET can be readily achieved from the corresponding TI model.…”