---
res:
  bibo_abstract:
  - Qualitative and quantitative orbital properties such as bonding/antibonding character,
    localization, and orbital energies are critical to how chemists understand reactivity,
    catalysis, and excited-state behavior. Despite this, representations of orbitals
    in deep learning models have been very underdeveloped relative to representations
    of molecular geometries and Hamiltonians. Here, we apply state-of-the-art equivariant
    deep learning architectures to the task of assigning global labels to orbitals,
    namely energies characterizations, given the molecular coefficients from Hartree–Fock
    or density functional theory. The architecture we have developed, the Cartesian
    Equivariant Orbital Network (CEONET), shows how molecular orbital coefficients
    are readily featurized as equivariant node features common to all graph-based
    machine-learned potentials. We find that CEONET performs well at predicting difficult
    quantitative labels such as the orbital energy and orbital entropy. Furthermore,
    we find that the CEONET representation provides an intuitive latent space for
    differentiating orbital character for the qualitative assignment of e.g. bonding
    or antibonding character. In addition to providing a useful representation for
    further integrating deep learning with electronic structure theory, we expect
    CEONET to be useful for automatizing and interpreting the results of advanced
    electronic structure methods such as complete active space self-consistent field
    theory. In particular, the ability of CEONET to infer multireference character
    via the orbital entropy paves the way toward the machine-learned selection of
    active spaces.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Daniel S.
      foaf_name: King, Daniel S.
      foaf_surname: King
  - foaf_Person:
      foaf_givenName: Daniel
      foaf_name: Grzenda, Daniel
      foaf_surname: Grzenda
  - foaf_Person:
      foaf_givenName: Ray
      foaf_name: Zhu, Ray
      foaf_surname: Zhu
  - foaf_Person:
      foaf_givenName: Nathaniel
      foaf_name: Hudson, Nathaniel
      foaf_surname: Hudson
  - foaf_Person:
      foaf_givenName: Ian
      foaf_name: Foster, Ian
      foaf_surname: Foster
  - foaf_Person:
      foaf_givenName: Bingqing
      foaf_name: Cheng, Bingqing
      foaf_surname: Cheng
      foaf_workInfoHomepage: http://www.librecat.org/personId=cbe3cda4-d82c-11eb-8dc7-8ff94289fcc9
    orcid: 0000-0002-3584-9632
  - foaf_Person:
      foaf_givenName: Laura
      foaf_name: Gagliardi, Laura
      foaf_surname: Gagliardi
  bibo_doi: 10.1073/pnas.2510235122
  bibo_issue: '48'
  bibo_volume: 122
  dct_date: 2025^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/1091-6490
  dct_language: eng
  dct_publisher: National Academy of Sciences@
  dct_title: Cartesian equivariant representations for learning and understanding
    molecular orbitals@
  fabio_hasPubmedId: '41269783'
...