Stacked Ensemble Machine Learning for Range-Separation Parameters

Assessing the accuracy of TD-DFT excited-state geometries through optimal tuning with GW energy levels

We study the accuracy of excited state (ES) geometries using optimally tuned LC-PBE functionals with tuning based on GW quasiparticle energies. We compare the results obtained with the PBE, PBE0, non-tuned, and tuned LC-PBE functionals with available high-level CC reference values as well as experimental data. First, we compare ES geometrical parameters obtained for three different types of systems: molecules composed of a few atoms, 4-(dimethylamino)benzonitrile (DMABN), and conjugated dyes. To this end, we used wave-function results as benchmarks. Next, we evaluate the accuracy of the theoretically simulated spectra as compared to the experimental ones for five large dyes. Our results show that, besides small compact molecules for which tuning LC-PBE does not allow obtaining geometries more accurate than those computed with standard functionals, tuned range-separated functionals are clearly to be favored, not only for ES geometries but also for 0-0 energies, band shapes, and intensities for absorption and emission spectra. In particular, the results indicate that GW-tuned LC-PBE functionals provide improved matching with experimental spectra as compared to conventionally tuned functionals. It is an open question whether TD-DFT with GW-tuned functionals can qualitatively mimic the actual many-body Bethe-Salpeter (BSE/GW) formalism for which analytic ionic gradients remain to be developed.

Accurate Electronic and Optical Properties of Organic Doublet Radicals Using Machine Learned Range-Separated Functionals

Luminescent organic semiconducting doublet-spin radicals are unique and emergent optical materials because their fluorescent quantum yields (Φfl) are not compromised by the spin-flipping intersystem crossing (ISC) into a dark high-spin state. The multiconfigurational nature of these radicals challenges their electronic structure calculations in the framework of single-reference density functional theory (DFT) and introduces room for method improvement. In the present study, we extended our earlier development of ML-ωPBE [J. Phys. Chem. Lett., 2021, 12, 9516-9524], a range-separated hybrid (RSH) exchange-correlation (XC) functional constructed using the stacked ensemble machine learning (SEML) algorithm, from closed-shell organic semiconducting molecules to doublet-spin organic semiconducting radicals. We assessed its performance for a new test set of 64 doublet-spin radicals from five categories while placing all previously compiled 3926 closed-shell molecules in the new training set. Interestingly, ML-ωPBE agrees with the nonempirical OT-ωPBE functional regarding the prediction of the molecule-dependent range-separation parameter (ω), with a small mean absolute error (MAE) of 0.0197 a0-1, but saves the computational cost by 2.46 orders of magnitude. This result demonstrates an outstanding domain adaptation capacity of ML-ωPBE for diverse organic semiconducting species. To further assess the predictive power of ML-ωPBE in experimental observables, we also applied it to evaluate absorption and fluorescence energies (Eabs and Efl) using linear-response time-dependent DFT (TDDFT), and we compared its behavior with nine popular XC functionals. For most radicals, ML-ωPBE reproduces experimental measurements of Eabs and Efl with small MAEs of 0.299 and 0.254 eV, only marginally different from those of OT-ωPBE. Our work illustrates a successful extension of the SEML framework from closed-shell molecules to doublet-spin radicals and will open the venue for calculating optical properties for organic semiconductors using single-reference TDDFT.

Modeling Interfacial Dynamics on Single Atom Electrocatalysts: Explicit Solvation and Potential Dependence

ConspectusSingle atom electrocatalysts, with noble metal-free composition, maximal atom efficiency, and exceptional reactivity toward various energy and environmental applications, have become a research hot spot in the recent decade. Their simplicity and the isolated nature of the atomic structure of their active site have also made them an ideal model catalyst system for studying reaction mechanisms and activity trends. However, the state of the single atom active sites during electrochemical reactions may not be as simple as is usually assumed. To the contrary, the single atom electrocatalysts have been reported to be under greater influence from interfacial dynamics, with solvent and electrolyte ions perpetually interacting with the electrified active center under an applied electrode potential. These complexities render the activity trends and reaction mechanisms derived from simplistic models dubious.In this Account, with a few popular single atom electrocatalysis systems, we show how the change in electrochemical potential induces nontrivial variation in the free energy profile of elemental electrochemical reaction steps, demonstrate how the active centers with different electronic structure features can induce different solvation structures at the interface even for the same reaction intermediate of the simplest electrochemical reaction, and discuss the implication of the complexities on the kinetics and thermodynamics of the reaction system to better address the activity and selectivity trends. We also venture into more intriguing interfacial phenomena, such as alternative reaction pathways and intermediates that are favored and stabilized by solvation and polarization effects, long-range interfacial dynamics across the region far beyond the contact layer, and the dynamic activation or deactivation of single atom sites under operation conditions. We show the necessity of including realistic aspects (explicit solvent, electrolyte, and electrode potential) into the model to correctly capture the physics and chemistry at the electrochemical interface and to understand the reaction mechanisms and reactivity trends. We also demonstrate how the popular simplistic design principles fail and how they can be revised by including the kinetics and interfacial factors in the model. All of these rich dynamics and chemistry would remain hidden or overlooked otherwise. We believe that the complexity at an electrochemical interface is not a curse but a blessing in that it enables deeper understanding and finer control of the potential-dependent free energy landscape of electrochemical reactions, which opens up new dimensions for further design and optimization of single atom electrocatalysts and beyond. Limitations of current methods and challenges faced by the theoretical and experimental communities are discussed, along with the possible solutions awaiting development in the future.

Accurate prediction of global-density-dependent range-separation parameters based on machine learning

In this work, we develop an accurate and efficient XGBoost machine learning model for predicting the global-density-dependent range-separation parameter, ωGDD, for long-range corrected functional (LRC)-ωPBE. This ωGDDML model has been built using a wide range of systems (11 466 complexes, ten different elements, and up to 139 heavy atoms) with fingerprints for the local atomic environment and histograms of distances for the long-range atomic correlation for mapping the quantum mechanical range-separation values. The promising performance on the testing set with 7046 complexes shows a mean absolute error of 0.001 117 a0-1 and only five systems (0.07%) with an absolute error larger than 0.01 a0-1, which indicates the good transferability of our ωGDDML model. In addition, the only required input to obtain ωGDDML is the Cartesian coordinates without electronic structure calculations, thereby enabling rapid predictions. LRC-ωPBE(ωGDDML) is used to predict polarizabilities for a series of oligomers, where polarizabilities are sensitive to the asymptotic density decay and are crucial in a variety of applications, including the calculations of dispersion corrections and refractive index, and surpasses the performance of all other popular density functionals except for the non-tuned LRC-ωPBE. Finally, LRC-ωPBE (ωGDDML) combined with (extended) symmetry-adapted perturbation theory is used in calculating noncovalent interactions to further show that the traditional ab initio system-specific tuning procedure can be bypassed. The present study not only provides an accurate and efficient way to determine the range-separation parameter for LRC-ωPBE but also shows the synergistic benefits of fusing the power of physically inspired density functional LRC-ωPBE and the data-driven ωGDDML model.

Enhanced Predictions for the Experimental Photophysical Data Using the Featurized Schnet-Bondstep Approach

An assessment of modifying the SchNET model for the predictions of experimental molecular photophysical properties, including absorption energy (ΔE_abs), emission energy (ΔE_emi), and photoluminescence quantum yield (PLQY), was reported. The solution environment was properly introduced outside the interaction layers of SchNET for not overly amplifying the solute-solvent interactions, particularly being supported by the changes of prediction errors between the presence and absence of the solvent effect. Two featurization schemes under the framework of the Schnet-bondstep approach, with featuring the concepts of reduced-atomic-number and reduced-atomic-neighbor, were demonstrated. These featurized models can consequently provide fine predictions for ΔE_abs and ΔE_emi with errors less than 0.1 eV. The corresponding predictions of PLQY were shown to be comparable to the previous graph convolution network model.

One-Shot Approach for Enforcing Piecewise Linearity on Hybrid Functionals: Application to Band Gap Predictions

We present an efficient procedure for constructing nonempirical hybrid functionals to accurately predict band gaps of extended systems. We determine mixing parameters by enforcing the generalized Koopmans' condition on localized electron states, which are achieved by inserting an optimized potential probe. Application of this scheme to a large set of materials yields band gaps with a mean error of 0.30 eV with respect to experiment. Next, we consider a perturbative one-shot approach in which the single-particle eigenvalues are calculated with the wave functions obtained at the semilocal level. In this way, the computational cost is reduced by ∼85% without loss of accuracy. The scheme is found to be robust upon consideration of different defect species and functional forms.