Comprehensive Comparison of Molecular Fragmentation Schemes for Proteins

Conventional quantum chemical (QC) methods exhibit a steep computational scaling with respect to the number of atoms in the investigated system. Hence, working with larger systems like peptides or even proteins becomes computationally unfeasible with traditional QC methods. One way to overcome this challenge is through molecular fragmentation methods. Many different flavours of molecular fragmentation schemes based on different partitionings have been suggested in the literature, but have hardly been compared numerically. Our group has recently reported a common formalism for molecular fragmentation schemes, which enables a consistent benchmark of different approaches. Here, we assess the performance of the molecular fractionation with hydrogen caps (MFHC), the pair-pair approximation to the generalized many-body expansion (pp-GMBE), the molecules-in-molecules (MIM) approach, and the kernel energy method (KEM) within this general framework. Our benchmark includes single- and multilevel schemes as well as an electrostatic embedding of the fragments in point charges of the whole system. The energies and computational demand of a chosen set of proteins are evaluated with the different methods within the framework. This enables a rare numerical comparison between the different schemes. Of the compared methods, our implementation of pp-GMBE yields the best agreement with supermolecular QC reference calculations, while MFHC with additional pair couplings offers a good cost-accuracy ratio.