Machine Learning of Quasiparticle Energies in Molecules and Clusters

We present a ∆-Machine Learning approach for the prediction of GW quasiparticle energies (∆MLQP) and photoelectron spectra of molecules and clusters, using orbital-sensitive graph-based representations in kernel ridge regression based supervised learning. Coulomb matrix, Bag-of-Bonds, and Bonds-Angles-Torsions representations are made orbital-sensitive by augmenting them with atom-centered orbital charges and Kohn–Sham orbital energies, which are both readily available from baseline calculations on the level of density-functional theory (DFT). We first illustrate the effects of different constructions of the orbital-sensitive representations (OSR) on the prediction of frontier orbital energies of 22K molecules of the QM8 dataset, and show that is is possible to predict the full photoelectron spectrum of molecules within the dataset using a single model with a mean-absolute error below 0.1eV. We further demonstrate that the OSR-based ∆MLQP captures the effects of intra- and intermolecular conformations in application to water monomers and dimers. Finally, we show that the approach can be embedded in multiscale simulation workflows, by studying the solvatochromic shifts of quasiparticle and electron-hole excitation energies of solvated acetone in a setup combining Molecular Dynamics, DFT, the GW approximation and the Bethe–Salpeter Equation. Our findings suggest that the ∆MLQP model allows to predict quasiparticle energies and photoelectron spectra of molecules and clusters with GW accuracy at DFT cost.