  Quantum-chemical fragmentation methods offer an efficient approach for the
treatment of large proteins, in particular if local target quantities such as
protein--ligand interaction energies, enzymatic reaction energies, or
spectroscopic properties of embedded chromophores are sought. However, the
accuracy that is achievable for such local target quantities intricately
depends on how the protein is partitioned into smaller fragments. While the
commonly employed na\"ive approach of using fragments with a fixed size is
widely used, it can result in large and unpredictable errors when varying the
fragment size. Here, we present a systematic partitioning scheme that aims at
minimizing the fragmentation error of a local target quantity for a given
maximum fragment size.
  To this end, we construct a weighted graph representation of the protein, in
which the amino acids constitute the nodes. These nodes are connected by edges
weighted with an estimate for the fragmentation error that is expected when
cutting this edge. This allows us to employ graph partitioning algorithms
provided by computer science to determine near-optimal partitions of the
protein. We apply this scheme to a test set of six proteins representing
various prototypical applications of quantum-chemical fragmentation methods
using a simplified molecular fractionation with conjugate caps (MFCC) approach
with hydrogen caps. We show that our graph-based scheme consistently improves
upon the na\"ive approach.
