Machine Learning of Quasiparticle Energies in Molecules and Clusters

Abstract

We present a Δ-machine learning approach for the prediction of GW quasiparticle energies (ΔMLQP) and photoelectron spectra of molecules and clusters, using orbital-sensitive representations (OSRs) based on molecular Cartesian coordinates in kernel ridge regression-based supervised learning. Coulomb matrix, bag-of-bond, and bond-angle-torsion representations are made orbital-sensitive by augmenting them with atom-centered orbital charges and Kohn–Sham orbital energies, both of which are readily available from baseline calculations at the level of density functional theory (DFT). We first illustrate the effects of different constructions of the OSRs on the prediction of frontier orbital energies of 22k molecules of the QM8 data set and show that it is possible to predict the full photoelectron spectrum of molecules within the data set using a single model with a mean absolute error below 0.1 eV. We further demonstrate that the OSR-based ΔMLQP 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 ΔMLQP model allows us to predict quasiparticle energies and photoelectron spectra of molecules and clusters with GW accuracy at DFT cost.

The resolution-vs.-accuracy dilemma in machine learning modeling of electronic excitation spectra

“…[18][19][20] For atomization or bonding energies, their prediction uncertainties are comparable to that of hybrid density functional theory (DFT) approximations. 14,[21][22][23][24][25][26] They have also successfully modeled non-adiabatic molecular dynamics, 27 vibrational spectra, 28,29 electronic coupling elements, 30 excitons, 31 electronic densities, 32 excited states in diverse chemical spaces, [33][34][35] as well as excited-state potential energy surfaces (PES). 34,[36][37][38][39] A key difference in the performance of ML in the latter two application domains is that ambiguities due to atomic indices and size-extensivity that affect the quality of structural representations for chemical space explorations 40,41 do not arise in PES modeling or dipole surface modeling [42][43][44] resulting in better learning rates.…”

“…This limitation becomes evident from the modest performances of ML models of excitation energies, 33,34 and their zero-order approximations, the frontier molecular orbital (MO) energies. 22,35,50,51 In this study, we: (i) present a high-quality chemical space dataset, bigQM7u, containing ground-state properties and electronic spectra of 12 880 molecules containing up to 7 CONF atoms modeled at the uB97XD level with different basis sets. (ii) Demonstrate the resolution-vs.-accuracy dilemma in modeling spectroscopic intensities.…”

“…This limitation becomes evident from the modest performances of ML models of excitation energies, 33,34 and their zero-order approximations, the frontier molecular orbital (MO) energies. 22,35,50,51…”

Data-Driven Modeling of S0 -> S1 Excitation Energy in the BODIPY Chemical Space: High-Throughput Computation, Quantum Machine Learning, and Inverse Design

“…For excited state properties, in general, the error rates in QML have been noted to be inferior compared to that of ground state properties [61][62][63][64]. Yet, QML methods continue to find applications in excited state modeling in chemical space datasets [50,[65][66][67] as well as in potential surface manifolds [68][69][70][71][72][73]. Keeping abreast with the progress in QML, materials/molecules inverse-design protocols have also advanced since the earliest implementation nearly twenty years ago [74].…”

Resolution-vs.-Accuracy Dilemma in Machine Learning Modeling of Electronic Excitation Spectra

“…Past studies have focused on excited-state modeling across the chemical space [28,29,32] as well as in potential energy surfaces (PESs) [27,29,[33][34][35]. A key difference in QML performances in these two application domains is that ambiguities due to atomic indices and size-extensivity that affect the quality of structural representations for chemical space explorations [36,37] do not arise in PES or dipole surface modeling [38][39][40], resulting in better learning rates.…”