Ab initio effective one‐electron potential operators: Applications for charge‐transfer energy in effective fragment potentials

• Published in: Journal of computational chemistry 2021-03, Vol.42 (6), p.398-411
• Main Authors: Błasiak, Bartosz, Bednarska, Joanna D., Chołuj, Marta, Góra, Robert W., Bartkowiak, Wojciech
• Format: Article
• Language: English
• Subjects: ab initio force field; Charge transfer; Computing costs; effective fragment; electron repulsion integral; Electronic structure; Electrons; Molecular structure; Multipoles; one‐electron potential; Operators (mathematics); Perturbation theory; Wave functions
• ISSN: 0192-8651; 1096-987X
• DOI: 10.1002/jcc.26462

The concept of effective one‐electron potentials (EOPs) 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 is presented, that is tuned toward 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 (DF) 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 noninteracting 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. Effective one‐electron operators can be systematically used to convert fragment‐based methods into effective fragment potentials. As an example, we developed an efficient charge transfer energy method, which can be used in ab initio force fields such as EFP2, with less computational effort and maintaining accuracy.