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SPA(H)M: the spectrum of approximated Hamiltonian matrices representations

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 determ...

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Detalles Bibliográficos
Autores principales: Fabrizio, Alberto, Briling, Ksenia R., Corminboeuf, Clemence
Formato: Online Artículo Texto
Lenguaje:English
Publicado: RSC 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9189859/
https://www.ncbi.nlm.nih.gov/pubmed/35769206
http://dx.doi.org/10.1039/d1dd00050k
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author Fabrizio, Alberto
Briling, Ksenia R.
Corminboeuf, Clemence
author_facet Fabrizio, Alberto
Briling, Ksenia R.
Corminboeuf, Clemence
author_sort Fabrizio, Alberto
collection PubMed
description 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 (SPA(H)M) 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, SPA(H)M 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 SPA(H)M representations built from the eigenvalues of a hierarchy of well-established and readily-evaluated “guess” Hamiltonians. These SPA(H)M 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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spelling pubmed-91898592022-06-27 SPA(H)M: the spectrum of approximated Hamiltonian matrices representations Fabrizio, Alberto Briling, Ksenia R. Corminboeuf, Clemence Digit Discov Chemistry 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 (SPA(H)M) 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, SPA(H)M 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 SPA(H)M representations built from the eigenvalues of a hierarchy of well-established and readily-evaluated “guess” Hamiltonians. These SPA(H)M representations are particularly compact and efficient for kernel evaluation and their complexity is independent of the number of different atom types in the database. RSC 2022-04-04 /pmc/articles/PMC9189859/ /pubmed/35769206 http://dx.doi.org/10.1039/d1dd00050k Text en This journal is © The Royal Society of Chemistry https://creativecommons.org/licenses/by-nc/3.0/
spellingShingle Chemistry
Fabrizio, Alberto
Briling, Ksenia R.
Corminboeuf, Clemence
SPA(H)M: the spectrum of approximated Hamiltonian matrices representations
title SPA(H)M: the spectrum of approximated Hamiltonian matrices representations
title_full SPA(H)M: the spectrum of approximated Hamiltonian matrices representations
title_fullStr SPA(H)M: the spectrum of approximated Hamiltonian matrices representations
title_full_unstemmed SPA(H)M: the spectrum of approximated Hamiltonian matrices representations
title_short SPA(H)M: the spectrum of approximated Hamiltonian matrices representations
title_sort spa(h)m: the spectrum of approximated hamiltonian matrices representations
topic Chemistry
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9189859/
https://www.ncbi.nlm.nih.gov/pubmed/35769206
http://dx.doi.org/10.1039/d1dd00050k
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