Equivariant representations for molecular Hamiltonians

The application of machine learning to the modeling of materials and molecules has proven to be extremely successful in accelerating the understanding, design, and characterization of materials. A major factor in this success has been the development of representations of atomic structures that reflect physics-based symmetries of the underlying interactions. Most of the descriptions of atomic properties or even global observables rely on decompositions into atomic contributions that are subsequently learnt in an atom-centered framework. However, many quantities associated with quantum mechanical calculations, such as the single-particle Hamiltonian matrices written in an atomic-orbital basis, are associated with multiple atom-centers. Following the introduction of equivariant N-center structural descriptors, in the reference below, that generalize the very successful atom-centered density correlation features to the problem of learning properties indexed by N atoms, we present benchmarks showing how the construction can be applied to efficiently learn the matrix elements of the (effective) single-particle Hamiltonian in an atom-centered orbital basis. In this record, we include the dataset comprising the Fock and overlap matrices in the def2-SVP of 1000 distorted water molecules, up to 4500 ethanol structures, and a subset of QM7-CHNO molecules. We also provide scripts to generate the two-center representations and fit linear and sparse kernel models for the Hamiltonians.