Machine-Learned Energy Functionals for Multiconfigurational Wave Functions

Abstract

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 machinelearned functional of some featurization of the wave function such as its density, ontop density, or both. On a data set of carbene singlet−triplet energy splittings, we show that MC-DDFMs are able to achieve near-benchmark performance on systems not used for training with a robust degree of active-space independence. Beyond demonstrating that the density and on-top density hold the information necessary to correct the singlet−triplet energy splittings of multiconfigurational wave functions, this approach shows great promise for the development of functionals for MC-PDFT because corrections to the classical energy appear to be more transferable to types of molecules not included in the training data than corrections to total energies such as those yielded by CASSCF or NEVPT2.

Dipole Moment Calculations Using Multiconfiguration Pair-Density Functional Theory and Hybrid Multiconfiguration Pair-Density Functional Theory

“…Instead, among the functionals studied here, the tPBE0 is expected to be the most reliable functional for dipole moment evaluations. We speculate that a machine-learned functional, 126 if parametrized using dipole moments, would be able to improve the dipole moments over tPBE0.…”

Large-Scale Benchmarking of Multireference Vertical-Excitation Calculations via Automated Active-Space Selection

“…67 The molecular point group was reduced to the highest available symmetry implemented for the PySCF SA-CASSCF solver: C 2h , C 2v , C s , or D 2h . The APC-rankedorbital active-space-selection scheme 36,59 starts with a set of candidate localized orbitals, ranks them by their approximated orbital entropies, and then eliminates orbitals starting from the lowest-entropy orbitals (those with the highest entropies are considered to be the most important) until the active space size reaches a predetermined maximum number of configuration state functions. We next describe the generation of candidate orbitals, then the ranking scheme, and finally the maximum-size criteria.…”

“…Following previous work, 36 up to 23 lowest-energy virtual orbitals of the Hartree-Fock calculation were selected, and orbitals within this subset were grouped by symmetry and Boys-localized 68 within each symmetry. Likewise, up to 23 highest-energy doubly occupied orbitals were also grouped by symmetry and Boys-localized within each symmetry.…”

“…30,31 Alternatively, quantitative accuracy can be achieved by using a nonclassical-energy functional applied to the the converged wave function in multiconfiguration nonclassical functional theory (MC-NCFT). [32][33][34][35][36] The total energy is then a sum of the classical portion of the CASSCF energy and nonclassical energy from the functional.…”

Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory

“…Our initial generation of machine-learned nonclassical-energy functional theory (ML-NEFT) was trained on the problem of predicting carbene singlet–triplet energy gaps using the recently published QMSpin database, 99 and we obtained mean absolute errors less than 0.05 eV on test data with a robust degree of active space independence. 100 While these results provide a proof of concept, obtaining a broadly useful new functional will require the training and test data to be expanded to a much larger range of data, and we are currently pursuing this direction.…”