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Boosting Quantum Machine Learning Models with a Multilevel Combination Technique: Pople Diagrams Revisited

  • Peter Zaspel
    Peter Zaspel
    Department of Mathematics and Computer Science, University of Basel, Spiegelgasse 1, 4051 Basel, Switzerland
    More by Peter Zaspel
  • Bing Huang
    Bing Huang
    Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials (MARVEL), Department of Chemistry, University of Basel, Klingelbergstrasse 80, 4056 Basel, Switzerland
    More by Bing Huang
  • Helmut Harbrecht*
    Helmut Harbrecht
    Department of Mathematics and Computer Science, University of Basel, Spiegelgasse 1, 4051 Basel, Switzerland
    *H. Harbrecht. E-mail: [email protected]
  • , and 
  • O. Anatole von Lilienfeld*
    O. Anatole von Lilienfeld
    Institute of Physical Chemistry and National Center for Computational Design and Discovery of Novel Materials (MARVEL), Department of Chemistry, University of Basel, Klingelbergstrasse 80, 4056 Basel, Switzerland
    *O. A. von Lilienfeld. E-mail: [email protected]
Cite this: J. Chem. Theory Comput. 2019, 15, 3, 1546–1559
Publication Date (Web):December 5, 2018
https://doi.org/10.1021/acs.jctc.8b00832
Copyright © 2018 American Chemical Society

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    Abstract

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    Inspired by Pople diagrams popular in quantum chemistry, we introduce a hierarchical scheme, based on the multilevel combination (C) technique, to combine various levels of approximations made when molecular energies are calculated. When combined with quantum machine learning (QML) models, the resulting CQML model is a generalized unified recursive kernel ridge regression that exploits correlations implicitly encoded in training data composed of multiple levels in multiple dimensions. Here, we have investigated up to three dimensions: chemical space, basis set, and electron correlation treatment. Numerical results have been obtained for atomization energies of a set of ∼7000 organic molecules with up to 7 atoms (not counting hydrogens) containing CHONFClS, as well as for ∼6000 constitutional isomers of C7H10O2. CQML learning curves for atomization energies suggest a dramatic reduction in necessary training samples calculated with the most accurate and costly method. In order to generate millisecond estimates of CCSD(T)/cc-pvdz atomization energies with prediction errors reaching chemical accuracy (∼1 kcal/mol), the CQML model requires only ∼100 training instances at CCSD(T)/cc-pvdz level, rather than thousands within conventional QML, while more training molecules are required at lower levels. Our results suggest a possibly favorable trade-off between various hierarchical approximations whose computational cost scales differently with electron number.

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    The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jctc.8b00832.

    • Geometries as xyz files; two types of energy data for each of the three basis sets (sto-3g, 6-31g, and cc-pvdz) [i.e., total energy (E) and effective averaged atomization energies (E*), the latter defined as E – ∑InIeI, where nI is the number of atom I in the molecule and eI is the effective atomic energy of atom I obtained through a linear least-square fit of E = ∑InIeI for all molecules in the data set]; free atom energies for all basis sets and electron methods; energy data for any basis set used (txt format), consisting of three columns representing HF, MP2, and CCSD(T) energies, respectively (ZIP)

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