Automatic Molecule Fragmentation for Density Matrix Embedding Theory

In quantum chemical calculations, the computational cost of highly accurate ground-state energy calculations for large-scale molecules is exceedingly high. To reduce the computational cost while sustaining high accuracy, quantum embedding methods, such as the density matrix embedding theory (DMET) and bootstrap embedding (BE), have been developed. In DMET, we need to manually determine how to fragment a target molecule, and both the accuracy and computational cost strongly depend on it. This issue hinders the easy application of DMET to practical molecules. On the other hand, BE can be easily applied to any molecules because it automatically constructs fragments based on the structure of a target molecule. In this work, we propose a graph-based automatic molecule fragmentation (GAF) technique to enable the easy application of DMET and evaluate the accuracy and wall-clock time of DMET applying the proposed technique (GAF-DMET) and the atom-based BE (ABE) for a wide variety of molecules on a cluster system. GAF represents a molecular structure with an undirected graph where edge weights represent interatomic interactions and determines an accurate fragmentation pattern by solving a graph partitioning problem that minimizes the total weight of edges cut. For GAF, we present two metrics to accurately represent interatomic interactions in different basis sets and the automatic adjustment of the number of fragments. The evaluation for 14 small molecules shows that (1) GAF successfully selects accurate fragmentation patterns, and (2) GAF-DMET can achieve higher or comparable accuracy than ABE in shorter wall-clock times. Moreover, we demonstrate that GAF-DMET is more accurate than ABE in two use cases: binding energy calculations between middle and small molecules, and an S_N2 reaction.