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Direct Determination of Optimal Real-Space Orbitals for Correlated Electronic Structure of Molecules

  • Edward F. Valeev*
    Edward F. Valeev
    Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
    *E-mail: [email protected]
  • Robert J. Harrison
    Robert J. Harrison
    Department of Applied Mathematics & Statistics, Stony Brook University, Stony Brook, New York 11794, United States
  • Adam A. Holmes
    Adam A. Holmes
    Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
  • Charles C. Peterson
    Charles C. Peterson
    Office of Advanced Research Computing, University of California, Los Angeles, Los Angeles, California 90095, United States
  • , and 
  • Deborah A. Penchoff
    Deborah A. Penchoff
    UT Innovative Computing Laboratory, University of Tennessee, Knoxville, Tennessee 37996, United States
Cite this: J. Chem. Theory Comput. 2023, 19, 20, 7230–7241
Publication Date (Web):October 4, 2023
https://doi.org/10.1021/acs.jctc.3c00732
Copyright © 2023 American Chemical Society

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    Abstract

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    We demonstrate how to determine numerically nearly exact orthonormal orbitals that are optimal for the evaluation of the energy of arbitrary (correlated) states of atoms and molecules by minimization of the energy Lagrangian. Orbitals are expressed in real space using a multiresolution spectral element basis that is refined adaptively to achieve the user-specified target precision while avoiding the ill-conditioning issues that plague AO basis set expansions traditionally used for correlated models of molecular electronic structure. For light atoms, the orbital solver, in conjunction with a variational electronic structure model [selected Configuration Interaction (CI)] provides energies of comparable precision to a state-of-the-art atomic CI solver. The computed electronic energies of atoms and molecules are significantly more accurate than the counterparts obtained with the orbital sets of the same rank expanded in Gaussian AO bases, and can be determined even when linear dependence issues preclude the use of the AO bases. It is feasible to optimize more than 100 fully correlated numerical orbitals on a single computer node, and significant room exists for additional improvement. These findings suggest that real-space orbital representations might be the preferred alternative to AO representations for high-end models of correlated electronic states of molecules and materials.

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