Selected Machine Learning of HOMO-LUMO gaps with Improved Data-Efficiency

Abstract

Quantum Machine Learning (QML) models of molecular HOMO-LUMO-gaps often struggle to achieve satisfying data-efficiency as measured by decreasing prediction errors for increasing training set sizes. Partitioning training sets of organic molecules (QM7 and QM9-data-sets) into three classes [systems containing either aromatic rings and carbonyl groups, or single unsaturated bonds, or saturated bonds] prior to training results in independently trained QML models with improved learning rates. The selected QML models of band-gaps (at GW, B3LYP, and ZINDO level of theory) reach mean absolute prediction errors of ∼0.1 eV for up to an order of magnitude fewer training molecules than for conventionally trained models. Direct comparison to ∆-QML models of bandgaps suggest that selected QML possesses substantially more data-efficiency. The findings suggest that selected QML, e.g. based on simple classifications prior to training, could help to successfully tackle challenging quantum property screening tasks of large libraries with high fidelity and low computational burden.

An orbital-based representation for accurate Quantum Machine Learning

“…In this work, we used intrinsic bond orbitals 34 as they provide a straightforward path to analyzing a Slater determinant in terms of chemically intuitive concepts, which have been shown to be very useful for HOMO and LUMO energy predictions. 35 We denote a coefficient φ A i with respect to an atomic orbital as C A,i kln , where k is the index of the atom on which the atomic orbital is centered (k = 1, . .…”

Orbital Mixer: Using Atomic Orbital Features for Basis Dependent Prediction of Molecular Wavefunctions

“…An explosion of interest has surrounded applying machine learning (ML) methods to quantum chemistry with a plethora of interesting application areas such as learning interatomic potentials (Behler & Parrinello, 2007;Unke et al, 2021c;Bartók et al, 2010;Smith et al, 2017;Chmiela et al, 2017;2018;Schütt et al, 2018;Unke & Meuwly, 2019;Unke et al, 2021b;Batzner et al, 2021;Klicpera et al, 2020;Liu et al, 2021a;Schütt et al, 2021), constructing density functionals (Snyder et al, 2012;Brockherde et al, 2017;Ryczko et al, 2019;Kalita et al, 2021;Li et al, 2021), predicting spectroscopic properties (Gastegger et al, 2017;Westermayr & Marquetand, 2020), optoelectronic properties (Lee et al, 2021;Mazouin et al, 2021;Lu et al, 2020;Gladkikh et al, 2020), activation energies (Lewis-Atwell et al, 2021;Grambow et al, 2020), and a variety of physical properties throughout chemical compound space (Montavon et al, 2013;De et al, 2016;von Lilienfeld et al, 2020;Keith et al, 2021;Liu et al, 2021b;Tielker et al, 2021;Bratholm et al, 2021). Quantum chemistry workflows can obtain such chemical and physical information by modelling the electronic Schrodinger equation in a chosen basis set of localized atomic orbitals that is then used to derive the ground-state molecular wavefunction.…”

Computational Workflow for Accelerated Molecular Design Using Quantum Chemical Simulations and Deep Learning Models

“…This so-called "HOMO-LUMO" gap often correlates very well with the lowest-energy, and hence most accessible, excited state that a molecule typically adopts upon energy intake due to the absorption of photons. Thus, HOMO-LUMO gaps have recently become the target of AI-based approached to photoactive molecules [10,12,13]. However, as mentioned above, this approach is only a reasonable shortcut, since for the inverse design of molecular structures with desirable photo-optical properties the entire absorption and/or emission spectrum over the energy range of visible light is required [10].…”