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SPAᴴM: the spectrum of approximated hamiltonian matrices representations

Alberto Fabrizio1*, Ksenia R. Briling1, Clemence Corminboeuf1*

1 Institut des Sciences et Ingénierie Chimiques, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

* Corresponding authors emails: alberto.fabrizio@epfl.ch, clemence.corminboeuf@epfl.ch
DOI10.24435/materialscloud:js-pz [version v1]

Publication date: Dec 15, 2021

How to cite this record

Alberto Fabrizio, Ksenia R. Briling, Clemence Corminboeuf, SPAᴴM: the spectrum of approximated hamiltonian matrices representations, Materials Cloud Archive 2021.221 (2021), doi: 10.24435/materialscloud:js-pz.


Physics-inspired molecular representations are the cornerstone of similarity-based learning applied to solve chemical problems. Despite their conceptual and mathematical diversity, this class of descriptors shares a common underlying philosophy: they all rely on the molecular information that determines the form of the electronic Schrödinger equation. Existing representations take the most varied forms, from non-linear functions of atom types and positions to atom densities and potential, up to complex quantum chemical objects directly injected into the ML architecture. In this work, we present the Spectrum of Approximated Hamiltonian Matrices (SPAᴴM) as an alternative pathway to construct quantum machine learning representations through leveraging the foundation of the electronic Schrödinger equation itself: the electronic Hamiltonian. As the Hamiltonian encodes all quantum chemical information at once, SPAᴴM representations not only distinguish different molecules and conformations, but also different spin, charge, and electronic states. As a proof of concept, we focus here on efficient SPAᴴM representations built from the eigenvalues of a hierarchy of well-established and readily-evaluated “guess” Hamiltonians. These SPAᴴM representations are particularly compact and efficient for kernel evaluation and their complexity is independent of the number of different atom types in the database

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2.7 GiB Tar ball containing the geometries and the properties of all the datasets included in the manuscript, as well as the SPAHM representation in a binary format (for further details on the structure and the content of the tar ball, see README.txt)


Files and data are licensed under the terms of the following license: Creative Commons Attribution 4.0 International.
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machine learning SPAHM Guess Hamiltonians Molecular Representation EPFL MARVEL/DD1 SNSF ERC

Version history:

2021.221 (version v1) [This version] Dec 15, 2021 DOI10.24435/materialscloud:js-pz