Equivariant representations for molecular Hamiltonians and N-center atomic-scale properties

• URL: http://arxiv.org/abs/2109.12083v1
• Date: Fri, 24 Sep 2021 17:19:57 GMT
• Title: Equivariant representations for molecular Hamiltonians and N-center atomic-scale properties
• Authors: Jigyasa Nigam, Michael Willatt, Michele Ceriotti
• Abstract summary: We discuss a family of structural descriptors that generalize the very successful atom-centered density correlation features to the N-centers case. We show in particular how this construction can be applied to efficiently learn the matrix elements of the (effective) single-particle Hamiltonian written in an atom-centered orbital basis.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Symmetry considerations are at the core of the major frameworks used to provide an effective mathematical representation of atomic configurations, that are then used in machine-learning models to predict the properties associated with each structure. In most cases, the models rely on a description of atom-centered environments, and are suitable to learn atomic properties, or global observables that can be decomposed into atomic contributions. Many quantities that are relevant for quantum mechanical calculations, however -- most notably the Hamiltonian matrix when written in an atomic-orbital basis -- are not associated with a single center, but with two (or more) atoms in the structure. We discuss a family of structural descriptors that generalize the very successful atom-centered density correlation features to the N-centers case, and show in particular how this construction can be applied to efficiently learn the matrix elements of the (effective) single-particle Hamiltonian written in an atom-centered orbital basis. These N-centers features are fully equivariant -- not only in terms of translations and rotations, but also in terms of permutations of the indices associated with the atoms -- and lay the foundations for symmetry-adapted machine-learning models of new classes of properties of molecules and materials.

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