Machine-Learned Energy Functionals for Strongly Correlated Systems

30 June 2021, Version 3
This content is a preprint and has not undergone peer review at the time of posting.


We introduce multiconfiguration data-driven functional theory (MC-DDFT) as a new approach to multiconfiguration nonclassical functional theory (MC-NCFT), in which the classical energy of a multiconfigurational wave function is combined with a machine-learned functional for the nonclassical exchange-correlation energy. We also present results obtained by a related approach, multiconfiguration energy-correcting functional theory (MC-ECFT), in which the total energy of a wave function method (e.g. CASSCF or NEVPT2) is corrected with a machine-learned functional. On a dataset of carbene singlet-triplet energy splittings, we demonstrate that these new multiconfiguration data-driven functional methods (MC-DDFMs) are able to achieve near-benchmark performance on systems not used for training while being less active-space dependent than multiconfiguration pair-density functional theory using currently available translated functionals.


Machine Learning
Pair-Density Functional Theory
Strongly Correlated
We introduce multiconfiguration data-driven functional methods (MC-DDFMs)
a group of methods which aim to correct the total or classical energy of a qualitatively accurate multiconfigurational wave function using a machine-learned functional of some featurization of the wave function
such as the density or on-top density. On a dataset of carbene singlet-triplet energy splittings
we demonstrate that MC-DDFMs are able to achieve near-benchmark performance on systems not used for training with a ro- bust degree of active space independence. This data-driven approach holds particular promise for the development of new functionals for multiconfigurational pair-density functional theory (MC-PDFT)
because corrections to the CASSCF classical energy appear to be more transferable to types of molecules not included in the training data than corrections to total energies yielded by wave function methods such as CASSCF or NEVPT2.

Supplementary materials

Supporting Information
Names of the carbenes included in the training, validation, test, and test subsets. Histograms showing systematic errors in reference methods. Basis set dependence of MC-DDFMs. Performance and active space and basis set dependence of MC-DDFMs trained solely on density features or solely on on-top density features. Individual performances on benzene, cyclobutadiene, and 1,3-bis(methylene)-cyclobutadiene.


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