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We propose a scheme to construct predictive models for Hamiltonian matricesin atomic orbital representation from ab initio data as a function of atomicand bond environments. The scheme goes beyond conventional tight bindingdescriptions as it represents the ab initio model to full order, rather than intwo-centre or three-centre approximations. We achieve this by introducing anextension to the Atomic Cluster Expansion (ACE) descriptor that representsHamiltonian matrix blocks that transform equivariantly with respect to the fullrotation group. The approach produces analytical linear models for theHamiltonian and overlap matrices. Through an application to aluminium, wedemonstrate that it is possible to train models from a handful of structurescomputed with density functional theory, and apply them to produce accuratepredictions for the electronic structure. The model generalises well and isable to predict defects accurately from only bulk training data.

Equivariant analytical mapping of first principles Hamiltonians to accurate and transferable materials models