Simulated evolution of fluorophores for light emitting diodes

Deep Learning-Based Chemical Similarity for Accelerated Organic Light-Emitting Diode Materials Discovery

Thermally activated delayed fluorescence (TADF) material has attracted great attention as a promising metal-free organic light-emitting diode material with a high theoretical efficiency. To accelerate the discovery of novel TADF materials, computer-aided material design strategies have been developed. However, they have clear limitations due to the accessibility of only a few computationally tractable properties. Here, we propose TADF-likeness, a quantitative score to evaluate the TADF potential of molecules based on a data-driven concept of chemical similarity to existing TADF molecules. We used a deep autoencoder to characterize the common features of existing TADF molecules with common chemical descriptors. The score was highly correlated with the four essential electronic properties of TADF molecules and had a high success rate in large-scale virtual screening of millions of molecules to identify promising candidates at almost no cost, validating its feasibility for accelerating TADF discovery. The concept of TADF-likeness can be extended to other fields of materials discovery.

Conjugated Polymer Process Ontology and Experimental Data Repository for Organic Field-Effect Transistors

Polymer-based semiconductors and organic electronics encapsulate a significant research thrust for informatics-driven materials development. However, device measurements are described by a complex array of design and parameter choices, many of which are sparsely reported. For example, the mobility of a polymer-based organic field-effect transistor (OFET) may vary by several orders of magnitude for a given polymer as a plethora of parameters related to solution processing, interface design/surface treatment, thin-film deposition, postprocessing, and measurement settings have a profound effect on the value of the final measurement. Incomplete contextual, experimental details hamper the availability of reusable data applicable for data-driven optimization, modeling (e.g., machine learning), and analysis of new organic devices. To curate organic device databases that contain reproducible and findable, accessible, interoperable, and reusable (FAIR) experimental data records, data ontologies that fully describe sample provenance and process history are required. However, standards for generating such process ontologies are not widely adopted for experimental materials domains. In this work, we design and implement an object-relational database for storing experimental records of OFETs. A data structure is generated by drawing on an international standard for batch process control (ISA-88) to facilitate the design. We then mobilize these representative data records, curated from the literature and laboratory experiments, to enable data-driven learning of process-structure-property relationships. The work presented herein opens the door for the broader adoption of data management practices and design standards for both the organic electronics and the wider materials community.

Parametrically Managed Activation Function for Fitting a Neural Network Potential with Physical Behavior Enforced by a Low-Dimensional Potential

Machine-learned representations of potential energy surfaces generated in the output layer of a feedforward neural network are becoming increasingly popular. One difficulty with neural network output is that it is often unreliable in regions where training data is missing or sparse. Human-designed potentials often build in proper extrapolation behavior by choice of functional form. Because machine learning is very efficient, it is desirable to learn how to add human intelligence to machine-learned potentials in a convenient way. One example is the well-understood feature of interaction potentials that they vanish when subsystems are too far separated to interact. In this article, we present a way to add a new kind of activation function to a neural network to enforce low-dimensional constraints. In particular, the activation function depends parametrically on all of the input variables. We illustrate the use of this step by showing how it can force an interaction potential to go to zero at large subsystem separations without either inputting a specific functional form for the potential or adding data to the training set in the asymptotic region of geometries where the subsystems are separated. In the process of illustrating this, we present an improved set of potential energy surfaces for the 14 lowest ³A' states of O₃. The method is more general than this example, and it may be used to add other low-dimensional knowledge or lower-level knowledge to machine-learned potentials. In addition to the O₃ example, we present a greater-generality method called parametrically managed diabatization by deep neural network (PM-DDNN) that is an improvement on our previously presented permutationally restrained diabatization by deep neural network (PR-DDNN).

Benchmarking DFT Functionals for Excited-State Calculations of Donor-Acceptor TADF Emitters: Insights on the Key Parameters Determining Reverse Inter-System Crossing

The importance of intermediate triplet states and the nature of excited states has gained interest in recent years for the thermally activated delayed fluorescence (TADF) mechanism. It is widely accepted that simple conversion between charge transfer (CT) triplet and singlet excited states is too crude, and a more complex route involving higher-lying locally excited triplet excited states has to be invoked to witness the magnitude of the rate of reverse inter-system crossing (RISC) rates. The increased complexity has challenged the reliability of computational methods to accurately predict the relative energy between excited states as well as their nature. Here, we compare the results of widely used density functional theory (DFT) functionals, CAM-B3LYP, LC-ωPBE, LC-ω*PBE, LC-ω*HPBE, B3LYP, PBE0, and M06-2X, against a wavefunction-based reference method, Spin-Component Scaling second-order approximate Coupled Cluster (SCS-CC2), in 14 known TADF emitters possessing a diversity of chemical structures. Overall, the use of the Tamm-Dancoff Approximation (TDA) together with CAM-B3LYP, M06-2X, and the two ω-tuned range-separated functionals LC-ω*PBE and LC-ω*HPBE demonstrated the best agreement with SCS-CC2 calculations in predicting the absolute energy of the singlet S₁, and triplet T₁ and T₂ excited states and their energy differences. However, consistently across the series and irrespective of the functional or the use of TDA, the nature of T₁ and T₂ is not as accurately captured as compared to S₁. We also investigated the impact of the optimization of S₁ and T₁ excited states on ΔE_ST and the nature of these states for three different functionals (PBE0, CAM-B3LYP, and M06-2X). We observed large changes in ΔE_ST using CAM-B3LYP and PBE0 functionals associated with a large stabilization of T₁ with CAM-B3LYP and a large stabilization of S₁ with PBE0, while ΔE_ST is much less affected considering the M06-2X functional. The nature of the S₁ state barely evolves after geometry optimization essentially because this state is CT by nature for the three functionals tested. However, the prediction of the T₁ nature is more problematic since these functionals for some compounds interpret the nature of T₁ very differently. SCS-CC2 calculations on top of the TDA-DFT optimized geometries lead to a large variation in terms of ΔE_ST and the excited-state nature depending on the chosen functionals, further stressing the large dependence of the excited-state features on the excited-state geometries. The presented work highlights that despite good agreement of energies, the description of the exact nature of the triplet states should be undertaken with caution.

Machine learning of atomic force microscopy images of organic solar cells

The bulk heterojunction structures of organic photovoltaics (OPVs) have been overlooked in their machine learning (ML) approach despite their presumably significant impact on power conversion efficiency (PCE). In this study, we examined the use of atomic force microscopy (AFM) images to construct an ML model for predicting the PCE of polymer : non-fullerene molecular acceptor OPVs. We manually collected experimentally observed AFM images from the literature, applied data curing and performed image analyses (fast Fourier transform, FFT; gray-level co-occurrence matrix, GLCM; histogram analysis, HA) and ML linear regression. The accuracy of the model did not considerably improve even by including AFM data in addition to the chemical structure fingerprints, material properties and process parameters. However, we found that a specific spatial wavelength of FFT (40-65 nm) significantly affects PCE. The GLCM and HA methods, such as homogeneity, correlation and skewness expand the scope of image analysis and artificial intelligence in materials science research fields.

Insights into the deviation from piecewise linearity in transition metal complexes from supervised machine learning models

Virtual high-throughput screening (VHTS) and machine learning (ML) with density functional theory (DFT) suffer from inaccuracies from the underlying density functional approximation (DFA). Many of these inaccuracies can be traced to the lack of derivative discontinuity that leads to a curvature in the energy with electron addition or removal. Over a dataset of nearly one thousand transition metal complexes typical of VHTS applications, we computed and analyzed the average curvature (i.e., deviation from piecewise linearity) for 23 density functional approximations spanning multiple rungs of "Jacob's ladder". While we observe the expected dependence of the curvatures on Hartree-Fock exchange, we note limited correlation of curvature values between different rungs of "Jacob's ladder". We train ML models (i.e., artificial neural networks or ANNs) to predict the curvature and the associated frontier orbital energies for each of these 23 functionals and then interpret differences in curvature among the different DFAs through analysis of the ML models. Notably, we observe spin to play a much more important role in determining the curvature of range-separated and double hybrids in comparison to semi-local functionals, explaining why curvature values are weakly correlated between these and other families of functionals. Over a space of 187.2k hypothetical compounds, we use our ANNs to pinpoint DFAs for which representative transition metal complexes have near-zero curvature with low uncertainty, demonstrating an approach to accelerate screening of complexes with targeted optical gaps.

Active Learning Exploration of Transition-Metal Complexes to Discover Method-Insensitive and Synthetically Accessible Chromophores

Transition-metal chromophores with earth-abundant transition metals are an important design target for their applications in lighting and nontoxic bioimaging, but their design is challenged by the scarcity of complexes that simultaneously have well-defined ground states and optimal target absorption energies in the visible region. Machine learning (ML) accelerated discovery could overcome such challenges by enabling the screening of a larger space but is limited by the fidelity of the data used in ML model training, which is typically from a single approximate density functional. To address this limitation, we search for consensus in predictions among 23 density functional approximations across multiple rungs of "Jacob's ladder". To accelerate the discovery of complexes with absorption energies in the visible region while minimizing the effect of low-lying excited states, we use two-dimensional (2D)efficient global optimization to sample candidate low-spin chromophores from multimillion complex spaces. Despite the scarcity (i.e., ∼0.01%) of potential chromophores in this large chemical space, we identify candidates with high likelihood (i.e., >10%) of computational validation as the ML models improve during active learning, representing a 1000-fold acceleration in discovery. Absorption spectra of promising chromophores from time-dependent density functional theory verify that 2/3 of candidates have the desired excited-state properties. The observation that constituent ligands from our leads have demonstrated interesting optical properties in the literature exemplifies the effectiveness of our construction of a realistic design space and active learning approach.

Exploiting Ligand Additivity for Transferable Machine Learning of Multireference Character across Known Transition Metal Complex Ligands

Accurate virtual high-throughput screening (VHTS) of transition metal complexes (TMCs) remains challenging due to the possibility of high multireference (MR) character that complicates property evaluation. We compute MR diagnostics for over 5,000 ligands present in previously synthesized octahedral mononuclear transition metal complexes in the Cambridge Structural Database (CSD). To accomplish this task, we introduce an iterative approach for consistent ligand charge assignment for ligands in the CSD. Across this set, we observe that the MR character correlates linearly with the inverse value of the averaged bond order over all bonds in the molecule. We then demonstrate that ligand additivity of the MR character holds in TMCs, which suggests that the TMC MR character can be inferred from the sum of the MR character of the ligands. Encouraged by this observation, we leverage ligand additivity and develop a ligand-derived machine learning representation to train neural networks to predict the MR character of TMCs from properties of the constituent ligands. This approach yields models with excellent performance and superior transferability to unseen ligand chemistry and compositions.

Machine Learning Models Predict Calculation Outcomes with the Transferability Necessary for Computational Catalysis

Virtual high-throughput screening (VHTS) and machine learning (ML) have greatly accelerated the design of single-site transition-metal catalysts. VHTS of catalysts, however, is often accompanied with a high calculation failure rate and wasted computational resources due to the difficulty of simultaneously converging all mechanistically relevant reactive intermediates to expected geometries and electronic states. We demonstrate a dynamic classifier approach, i.e., a convolutional neural network that monitors geometry optimizations on the fly, and exploit its good performance and transferability in identifying geometry optimization failures for catalyst design. We show that the dynamic classifier performs well on all reactive intermediates in the representative catalytic cycle of the radical rebound mechanism for the conversion of methane to methanol despite being trained on only one reactive intermediate. The dynamic classifier also generalizes to chemically distinct intermediates and metal centers absent from the training data without loss of accuracy or model confidence. We rationalize this superior model transferability as arising from the use of electronic structure and geometric information generated on-the-fly from density functional theory calculations and the convolutional layer in the dynamic classifier. When used in combination with uncertainty quantification, the dynamic classifier saves more than half of the computational resources that would have been wasted on unsuccessful calculations for all reactive intermediates being considered.

Efficient Adversarial Generation of Thermally Activated Delayed Fluorescence Molecules

Adversarial generative models are becoming an essential tool in molecular design and discovery due to their efficiency in exploring the desired chemical space with the assistance of deep learning. In this article, we introduce an integrated framework by combining the modules of algorithmic synthesis, deep prediction, adversarial generation, and fine screening for the purpose of effective design of the thermally activated delayed fluorescence (TADF) molecules that can be used in the organic light-emitting diode devices. The retrosynthetic rules are employed to algorithmically synthesize the D-A complex based on the empirically defined donor and acceptor moieties, which is followed by the high-throughput labeling and prediction with the deep neural network. The new D-A molecules are subsequently generated via the adversarial autoencoder, with the excited-state property distributions perfectly matching those of the original samples. Fine screening of the generated molecules, including the spin-orbital coupling calculation and the excited-state optimization, is eventually implemented to select the qualified TADF candidates within the novel chemical space. Further investigation shows that the created structures fully mimic the original D-A samples by maintaining a significant charge transfer characteristic, a minimal adiabatic singlet-triplet gap, and a moderate spin-orbital coupling that are desirable for the delayed fluorescence.

Organic materials repurposing, a data set for theoretical predictions of new applications for existing compounds

We present a data set of 48182 organic semiconductors, constituted of molecules that were prepared with a documented synthetic pathway and are stable in solid state. We based our search on the Cambridge Structural Database, from which we selected semiconductors with a computational funnel procedure. For each entry we provide a set of electronic properties relevant for organic materials research, and the electronic wavefunction for further calculations and/or analyses. This data set has low bias because it was not built from a set of materials designed for organic electronics, and thus it provides an excellent starting point in the search of new applications for known materials, with a great potential for novel physical insight. The data set contains molecules used as benchmarks in many fields of organic materials research, allowing to test the reliability of computational screenings for the desired application, “rediscovering” well-known molecules. This is demonstrated by a series of different applications in the field of organic materials, confirming the potential for the repurposing of known organic molecules.

Measurement(s)	excited state energy
Technology Type(s)	quantum chemistry computational method

Machine-accessible metadata file describing the reported data: 10.6084/m9.figshare.17076254

Detection of multi-reference character imbalances enables a transfer learning approach for virtual high throughput screening with coupled cluster accuracy at DFT cost

Appropriately identifying and treating molecules and materials with significant multi-reference (MR) character is crucial for achieving high data fidelity in virtual high-throughput screening (VHTS). Despite development of numerous MR diagnostics, the extent to which a single value of such a diagnostic indicates the MR effect on a chemical property prediction is not well established. We evaluate MR diagnostics for over 10 000 transition-metal complexes (TMCs) and compare to those for organic molecules. We observe that only some MR diagnostics are transferable from one chemical space to another. By studying the influence of MR character on chemical properties (i.e., MR effect) that involve multiple potential energy surfaces (i.e., adiabatic spin splitting, ΔE_H–L, and ionization potential, IP), we show that differences in MR character are more important than the cumulative degree of MR character in predicting the magnitude of an MR effect. Motivated by this observation, we build transfer learning models to predict CCSD(T)-level adiabatic ΔE_H–L and IP from lower levels of theory. By combining these models with uncertainty quantification and multi-level modeling, we introduce a multi-pronged strategy that accelerates data acquisition by at least a factor of three while achieving coupled cluster accuracy (i.e., to within 1 kcal mol⁻¹ MAE) for robust VHTS.

We demonstrate that cancellation in multi-reference effect outweighs accumulation in evaluating chemical properties. We combine transfer learning and uncertainty quantification for accelerated data acquisition with chemical accuracy.

Machine Learning-Assisted Development of Organic Solar Cell Materials: Issues, Analyses, and Outlooks

Nonfullerene, a small molecular electron acceptor, has substantially improved the power conversion efficiency of organic photovoltaics (OPVs). However, the large structural freedom of π-conjugated polymers and molecules makes it difficult to explore with limited resources. Machine learning, which is based on rapidly growing artificial intelligence technology, is a high-throughput method to accelerate the speed of material design and process optimization; however, it suffers from limitations in terms of prediction accuracy, interpretability, data collection, and available data (particularly, experimental data). This recognition motivates the present Perspective, which focuses on utilizing the experimental data set for ML to efficiently aid OPV research. This Perspective discusses the trends in ML-OPV publications, the NFA category, and the effects of data size and explanatory variables (fingerprints or Mordred descriptors) on the prediction accuracy and explainability, which broadens the scope of ML and would be useful for the development of next-generation solar cell materials.

Machine learning to tame divergent density functional approximations: a new path to consensus materials design principles

Virtual high-throughput screening (VHTS) with density functional theory (DFT) and machine-learning (ML)-acceleration is essential in rapid materials discovery. By necessity, efficient DFT-based workflows are carried out with a single density functional approximation (DFA). Nevertheless, properties evaluated with different DFAs can be expected to disagree for cases with challenging electronic structure (e.g., open-shell transition-metal complexes, TMCs) for which rapid screening is most needed and accurate benchmarks are often unavailable. To quantify the effect of DFA bias, we introduce an approach to rapidly obtain property predictions from 23 representative DFAs spanning multiple families, “rungs” (e.g., semi-local to double hybrid) and basis sets on over 2000 TMCs. Although computed property values (e.g., spin state splitting and frontier orbital gap) differ by DFA, high linear correlations persist across all DFAs. We train independent ML models for each DFA and observe convergent trends in feature importance, providing DFA-invariant, universal design rules. We devise a strategy to train artificial neural network (ANN) models informed by all 23 DFAs and use them to predict properties (e.g., spin-splitting energy) of over 187k TMCs. By requiring consensus of the ANN-predicted DFA properties, we improve correspondence of computational lead compounds with literature-mined, experimental compounds over the typically employed single-DFA approach.

Machine learning (ML)-based feature analysis reveals universal design rules regardless of density functional choices. Using the consensus among multiple functionals, we identify robust lead complexes in ML-accelerated chemical discovery.

Maximizing TADF via Conformational Optimization

We investigate a new strategy to enhance thermally activated delayed fluorescence (TADF) in organic light-emitting diodes (OLEDs). Given that the TADF rate of a molecule depends on its conformation, we hypothesize that there exists a conformation that maximizes the TADF rate. To test this idea, we use time-dependent density functional theory (TDDFT) to simulate the TADF rates of several TADF emitters while varying their geometries in a select subspace of internal coordinates. We find that geometric changes in this subspace can increase the TADF rate up to 3 orders of magnitude with respect to the minimum energy conformation, and the simulated TADF rate can even be brought into the submicrosecond time scales under the right conditions. Furthermore, the TADF rate enhancement can be maintained with a conformational energy that might be within the reach of modern synthetic chemistry. Analyzing the maximum TADF conformation, we extract a number of structural motifs that might provide a useful handle on the TADF rate of a donor-acceptor (DA) system. The incorporation of conformational engineering into the TADF technology could usher in a new paradigm of OLEDs.

Unified Framework for Photophysical Rate Calculations in TADF Molecules

One of the challenges in organic light-emitting diodes research is finding ways to increase device efficiency by making use of the triplet excitons that are inevitably generated in the process of electroluminescence. One way to do so is by thermally activated delayed fluorescence (TADF), a process in which triplet excitons undergo upconversion to singlet states, allowing them to relax radiatively. The discovery of this phenomenon has ensued a quest for new materials that are able to effectively take advantage of this mechanism. From a theoretical standpoint, this requires the capacity to estimate the rates of the various processes involved in the photophysics of candidate molecules, such as intersystem crossing, reverse intersystem crossing, fluorescence, and phosphorescence. Here, we present a method that is able to, within a single framework, compute all of these rates and predict the photophysics of new molecules. We apply the method to two TADF molecules and show that results compare favorably with other theoretical approaches and experimental results. Finally, we use a kinetic model to show how the calculated rates act in concert to produce different photophysical behavior.

A Ranked-Orbital Approach to Select Active Spaces for High-Throughput Multireference Computation

The past decade has seen a great increase in the application of high-throughput computation to a variety of important problems in chemistry. However, one area which has been resistant to the high-throughput approach is multireference wave function methods, in large part due to the technicalities of setting up these calculations and in particular the not always intuitive challenge of active space selection. As we look toward a future of applying high-throughput computation to all areas of chemistry, it is important to prepare these methods for large-scale automation. Here, we propose a ranked-orbital approach to select active spaces with the goal of standardizing multireference methods for high-throughput computation. This method allows for the meaningful comparison of different active space selection schemes and orbital localizations, and we demonstrate the utility of this approach across 1120 multireference calculations for the excitation energies of small molecules. Our results reveal that it is helpful to distinguish the method used to generate orbitals from the method of ranking orbitals in terms of importance for the active space. Additionally, we propose our own orbital ranking scheme that estimates the importance of an orbital for the active space through a pair-interaction framework from orbital energies and features of the Hartree-Fock exchange matrix. We call this new scheme the "approximate pair coefficient" (APC) method and we show that it performs quite well for the test systems presented.

Direct coherent switching with decay of mixing for intersystem crossing dynamics of thioformaldehyde: The effect of decoherence

We evaluate the effect of electronic decoherence on intersystem crossing in the photodynamics of thioformaldehyde. First, we show that the state-averaged complete-active-space self-consistent field electronic structure calculations with a properly chosen active space of 12 active electrons in 10 active orbitals can predict the potential energy surfaces and the singlet-triplet spin-orbit couplings quite well for CH₂S, and we use this method for direct dynamics by coherent switching with decay of mixing (CSDM). We obtain similar dynamical results with CSDM or by adding energy-based decoherence to trajectory surface hopping, with the population of triplet states tending to a small steady-state value over 500 fs. Without decoherence, the state populations calculated by the conventional trajectory surface hopping method or the semiclassical Ehrenfest method gradually increase. This difference shows that decoherence changes the nature of the results not just quantitatively but qualitatively.

Ab-initio search for efficient red thermally activated delayed fluorescence molecules for organic light emitting diodes

In this work, we present a computational study on 105 selected organic molecules in order to find suitable candidates for using as thermally activated delayed fluorescent (TADF) emitters in organic light emitting diodes (OLEDs), in the emission range of red light. Based on time-dependent density functional theory (TD-DFT) computations, three promising candidates were found, predicted to have low singlet-triplet splittings, lower than 0.06 eV, and TADF rates of 0.124, 0.154 and 0.231 1/μs. Then, using an experimental-theory calibration approach, the emission wavelength of the molecules were estimated to be 570, 476, and 623 nm, respectively. For the molecule whose emission wavelength (623 nm) is predicted to be in our desired range, we measured the photoluminescence (PL) spectrum and find out that its emission peak is within the predicted accuracy of the employed method. Moreover, we benchmarked the performance of density functional based tight-binding (DFTB) method for future screening works and find out that, this method is an efficient pre-screening tool, useful in searching for molecules with desired emission wavelengths.

Transfer learning with graph neural networks for optoelectronic properties of conjugated oligomers

Despite the remarkable progress of machine learning (ML) techniques in chemistry, modeling the optoelectronic properties of long conjugated oligomers and polymers with ML remains challenging due to the difficulty in obtaining sufficient training data. Here, we use transfer learning to address the data scarcity issue by pre-training graph neural networks using data from short oligomers. With only a few hundred training data, we are able to achieve an average error of about 0.1 eV for the excited-state energy of oligothiophenes against time-dependent density functional theory (TDDFT) calculations. We show that the success of our transfer learning approach relies on the relative locality of low-lying electronic excitations in long conjugated oligomers. Finally, we demonstrate the transferability of our approach by modeling the lowest-lying excited-state energies of poly(3-hexylthiophene) in its single-crystal and solution phases using the transfer learning models trained with the data of gas-phase oligothiophenes. The transfer learning predicted excited-state energy distributions agree quantitatively with TDDFT calculations and capture some important qualitative features observed in experimental absorption spectra.

Rapid Detection of Strong Correlation with Machine Learning for Transition-Metal Complex High-Throughput Screening

Despite its widespread use in chemical discovery, approximate density functional theory (DFT) is poorly suited to many targets, such as those containing open-shell, 3d transition metals that can be expected to have strong multireference (MR) character. For discovery workflows to be predictive, we need automated, low-cost methods that can distinguish the regions of chemical space where DFT should be applied from those where it should not. We curate more than 4800 open-shell transition-metal complexes up to hundreds of atoms in size from prior high-throughput DFT studies and evaluate affordable, finite-temperature DFT fractional occupation number (FON)-based MR diagnostics. We show that intuitive measures of strong correlation (i.e., the HOMO-LUMO gap) are not predictive of MR character as judged by FON-based diagnostics. Analysis of independently trained machine learning (ML) models to predict HOMO-LUMO gaps and FON-based diagnostics reveals differences in the metal and ligand sensitivity of the two quantities. We use our trained ML models to rapidly evaluate MR character over a space of ∼187000 theoretical complexes, identifying large-scale trends in spin-state-dependent MR character and finding small HOMO-LUMO gap complexes while ensuring low MR character.

Evaluation-oriented exploration of photo energy conversion systems: from fundamental optoelectronics and material screening to the combination with data science

Light is a form of energy that can be converted to electric and chemical energies. Thus, organic photovoltaics (OPVs), perovskite solar cells (PSCs), photocatalysts, and photodetectors have evolved as scientific and commercial enterprises. However, the complex photochemical reactions and multicomponent materials involved in these systems have hampered rapid progress in their fundamental understanding and material design. This review showcases the evaluation-oriented exploration of photo energy conversion materials by using electrodeless time-resolved microwave conductivity (TRMC) and materials informatics (MI). TRMC with its unique options (excitation sources, environmental control, frequency modulation, etc.) provides not only accelerated experimental screening of OPV and PSC materials but also a versatile route toward shedding light on their charge carrier dynamics. Furthermore, MI powered by machine learning is shown to allow extremely high-throughput exploration in the large molecular space, which is compatible with experimental screening and combinatorial synthesis.

Semi-supervised Machine Learning Enables the Robust Detection of Multireference Character at Low Cost

Multireference (MR) diagnostics are common tools for identifying strongly correlated electronic structure that makes single-reference (SR) methods (e.g., density functional theory or DFT) insufficient for accurate property prediction. However, MR diagnostics typically require computationally demanding correlated wave function theory (WFT) calculations, and diagnostics often disagree or fail to predict MR effects on properties. To overcome these challenges, we introduce a semi-supervised machine learning (ML) approach with virtual adversarial training (VAT) of an MR classifier using 15 WFT and DFT MR diagnostics as inputs. In semi-supervised learning, only the most extreme SR or MR points are labeled, and the remaining point labels are learned. The resulting VAT model outperforms the alternatives, as quantified by the distinct property distributions of SR- and MR-classified molecules. To reduce the cost of generating inputs to the VAT model, we leverage the VAT model's robustness to noisy inputs by replacing WFT MR diagnostics with regression predictions in an MR decision engine workflow that preserves excellent performance. We demonstrate the transferability of our approach to larger molecules and those with distinct chemical composition from the training set. This MR decision engine demonstrates promise as a low-cost, high-accuracy approach to the automatic detection of strong correlation for predictive high-throughput screening.

Data-Driven Approaches Can Overcome the Cost-Accuracy Trade-Off in Multireference Diagnostics

High-throughput computational screening typically employs methods (i.e., density functional theory or DFT) that can fail to describe challenging molecules, such as those with strongly correlated electronic structure. In such cases, multireference (MR) correlated wavefunction theory (WFT) would be the appropriate choice but remains more challenging to carry out and automate than single-reference (SR) WFT or DFT. Numerous diagnostics have been proposed for identifying when MR character is likely to have an effect on the predictive power of SR calculations, but conflicting conclusions about diagnostic performance have been reached on small data sets. We compute 15 MR diagnostics, ranging from affordable DFT-based to more costly MR-WFT-based diagnostics, on a set of 3165 equilibrium and distorted small organic molecules containing up to six heavy atoms. Conflicting MR character assignments and low pairwise linear correlations among diagnostics are also observed over this set. We evaluate the ability of existing diagnostics to predict the percent recovery of the correlation energy, %E_corr. None of the DFT-based diagnostics are nearly as predictive of %E_corr as the best WFT-based diagnostics. To overcome the limitation of this cost-accuracy trade-off, we develop machine learning (ML, i.e., kernel ridge regression) models to predict WFT-based diagnostics from a combination of DFT-based diagnostics and a new, size-independent 3D geometric representation. The ML-predicted diagnostics correlate as well with MR effects as their computed (i.e., with WFT) values, significantly improving over the DFT-based diagnostics on which the models were trained. These ML models thus provide a promising approach to improve upon DFT-based diagnostic accuracy while remaining suitably low cost for high-throughput screening.

Understanding and Designing Thermally Activated Delayed Fluorescence Emitters: Beyond the Energy Gap Approximation

In this article recent progress in the development of molecules exhibiting Thermally Activated Delayed Fluorescence (TADF) is discussed with a particular focus upon their application as emitters in highly efficient organic light emitting diodes (OLEDs). The key aspects controlling the desirable functional properties, e. g. fast intersystem crossing, high radiative rate and unity quantum yield, are introduced with a particular focus upon the competition between the key requirements needed to achieve high performance OLEDs. The design rules required for organic and metal organic materials are discussed, and the correlation between them outlined. Recent progress towards understanding the influence of the interaction between a molecule and its environment are explained as is the role of the mechanism for excited state formation in OLEDs. Finally, all of these aspects are combined to discuss the ability to implement high level design rules for achieving higher quality materials for commercial applications. This article highlights the significant progress that has been made in recent years, but also outlines the significant challenges which persist to achieve a full understanding of the TADF mechanism and improve the stability and performance of these materials.

Investigation of Thermally Activated Delayed Fluorescence from a Donor-Acceptor Compound with Time-Resolved Fluorescence and Density Functional Theory Applying an Optimally Tuned Range-Separated Hybrid Functional

Emitters showing thermally activated delayed fluorescence (TADF) in electroluminescent devices rely on efficient reverse intersystem crossing (rISC) arising from small thermal activation barriers between the lowest excited triplet and singlet manifolds. A small donor-acceptor compound consisting of a demethylacridine donor and a methylbenzoate acceptor group is used as a model TADF emitter. The spectroscopic signatures of this system are characterized using a combination of photoluminescence and photoluminescence excitation, and the photoluminescence decay dynamics are recorded between delays of 2 ns and 20 ms. Above T = 200 K, our data provide convincing evidence for TADF at intermediate delays in the microsecond range, whereas triplet-triplet annihilation and slow triplet decay at later times can be observed over the entire temperature range from T = 80 K to room temperature. Moreover, close to room temperature, we find a second and faster up-conversion mechanism, tentatively assigned to reverse internal conversion between different triplet configurations. An interpretation of these experimental findings requires a calculation of the deformation patterns and potential minima of several electronic configurations. This task is performed with a range-separated hybrid functional, outperforming standard density functionals or global hybrids. In particular, the systematic underestimation of the energy of charge transfer (CT) states with respect to local excitations within the constituting chromophores is replaced by more reliable transition energies for both kinds of excitations. Hence, several absorption and emission features can be assigned unambiguously, and the observed activation barriers for rISC and reverse internal conversion correspond to calculated energy differences between the potential surfaces in different electronic configurations.

Search for Catalysts by Inverse Design: Artificial Intelligence, Mountain Climbers, and Alchemists

In silico catalyst design is a grand challenge of chemistry. Traditional computational approaches have been limited by the need to compute properties for an intractably large number of possible catalysts. Recently, inverse design methods have emerged, starting from a desired property and optimizing a corresponding chemical structure. Techniques used for exploring chemical space include gradient-based optimization, alchemical transformations, and machine learning. Though the application of these methods to catalysis is in its early stages, further development will allow for robust computational catalyst design. This review provides an overview of the evolution of inverse design approaches and their relevance to catalysis. The strengths and limitations of existing techniques are highlighted, and suggestions for future research are provided.

Designing in the Face of Uncertainty: Exploiting Electronic Structure and Machine Learning Models for Discovery in Inorganic Chemistry

Recent transformative advances in computing power and algorithms have made computational chemistry central to the discovery and design of new molecules and materials. First-principles simulations are increasingly accurate and applicable to large systems with the speed needed for high-throughput computational screening. Despite these strides, the combinatorial challenges associated with the vastness of chemical space mean that more than just fast and accurate computational tools are needed for accelerated chemical discovery. In transition-metal chemistry and catalysis, unique challenges arise. The variable spin, oxidation state, and coordination environments favored by elements with well-localized d or f electrons provide great opportunity for tailoring properties in catalytic or functional (e.g., magnetic) materials but also add layers of uncertainty to any design strategy. We outline five key mandates for realizing computationally driven accelerated discovery in inorganic chemistry: (i) fully automated simulation of new compounds, (ii) knowledge of prediction sensitivity or accuracy, (iii) faster-than-fast property prediction methods, (iv) maps for rapid chemical space traversal, and (v) a means to reveal design rules on the kilocompound scale. Through case studies in open-shell transition-metal chemistry, we describe how advances in methodology and software in each of these areas bring about new chemical insights. We conclude with our outlook on the next steps in this process toward realizing fully autonomous discovery in inorganic chemistry using computational chemistry.

An evolutionary algorithm for the discovery of porous organic cages

The chemical and structural space of possible molecular materials is enormous, as they can, in principle, be built from any combination of organic building blocks. Here we have developed an evolutionary algorithm (EA) that can assist in the efficient exploration of chemical space for molecular materials, helping to guide synthesis to materials with promising applications. We demonstrate the utility of our EA to porous organic cages, predicting both promising targets and identifying the chemical features that emerge as important for a cage to be shape persistent or to adopt a particular cavity size. We identify that shape persistent cages require a low percentage of rotatable bonds in their precursors (<20%) and that the higher topicity building block in particular should use double bonds for rigidity. We can use the EA to explore what size ranges for precursors are required for achieving a given pore size in a cage and show that 16 Å pores, which are absent in the literature, should be synthetically achievable. Our EA implementation is adaptable and easily extendable, not only to target specific properties of porous organic cages, such as optimal encapsulants or molecular separation materials, but also to any easily calculable property of other molecular materials.

Accurate Treatment of Charge-Transfer Excitations and Thermally Activated Delayed Fluorescence Using the Particle-Particle Random Phase Approximation

Thermally activated delayed florescence (TADF) is a mechanism that increases the electroluminescence efficiency in organic light-emitting diodes by harnessing both singlet and triplet excitons. TADF is facilitated by a small energy difference between the first singlet (S1) and triplet (T1) excited states (Δ E(ST)), which is minimized by spatial separation of the donor and acceptor moieties. The resultant charge-transfer (CT) excited states are difficult to model using time-dependent density functional theory (TDDFT) because of the delocalization error present in standard density functional approximations to the exchange-correlation energy. In this work we explore the application of the particle-particle random phase approximation (pp-RPA) for the determination of both S1 and T1 excitation energies. We demonstrate that the accuracy of the pp-RPA is functional dependent and that, when combined with the hybrid functional B3LYP, the pp-RPA computed Δ E(ST) have a mean absolute deviation (MAD) of 0.12 eV for the set of examined molecules. A key advantage of the pp-RPA approach is that the S1 and T1 states are characterized as CT states for all of experimentally reported TADF molecules examined here, which allows for an estimate of the singlet-triplet CT excited state energy gap (Δ E(ST) = 1CT - 3CT). For experimentally known TADF molecules with a small (<0.2 eV) Δ E(ST) in this data set, a high accuracy is demonstrated for the prediction of both the S1 (MAD = 0.18 eV) and T1 (MAD = 0.20 eV) excitation energies as well as Δ E(ST) (MAD = 0.05 eV). This result is attributed to the consideration of correct antisymmetry in the particle-particle interaction leading to the use of full exchange kernel in addition to the Coulomb contribution, as well as a consistent treatment of both singlet and triplet excited states. The computational efficiency of this approach is similar to that of TDDFT, and the cost can be reduced significantly by using the active-space approach.

Accelerating Chemical Discovery with Machine Learning: Simulated Evolution of Spin Crossover Complexes with an Artificial Neural Network

Machine learning (ML) has emerged as a powerful complement to simulation for materials discovery by reducing time for evaluation of energies and properties at accuracy competitive with first-principles methods. We use genetic algorithm (GA) optimization to discover unconventional spin-crossover complexes in combination with efficient scoring from an artificial neural network (ANN) that predicts spin-state splitting of inorganic complexes. We explore a compound space of over 5600 candidate materials derived from eight metal/oxidation state combinations and a 32-ligand pool. We introduce a strategy for error-aware ML-driven discovery by limiting how far the GA travels away from the nearest ANN training points while maximizing property (i.e., spin-splitting) fitness, leading to discovery of 80% of the leads from full chemical space enumeration. Over a 51-complex subset, average unsigned errors (4.5 kcal/mol) are close to the ANN's baseline 3 kcal/mol error. By obtaining leads from the trained ANN within seconds rather than days from a DFT-driven GA, this strategy demonstrates the power of ML for accelerating inorganic material discovery.

Resolving Transition Metal Chemical Space: Feature Selection for Machine Learning and Structure-Property Relationships

Machine learning (ML) of quantum mechanical properties shows promise for accelerating chemical discovery. For transition metal chemistry where accurate calculations are computationally costly and available training data sets are small, the molecular representation becomes a critical ingredient in ML model predictive accuracy. We introduce a series of revised autocorrelation functions (RACs) that encode relationships of the heuristic atomic properties (e.g., size, connectivity, and electronegativity) on a molecular graph. We alter the starting point, scope, and nature of the quantities evaluated in standard ACs to make these RACs amenable to inorganic chemistry. On an organic molecule set, we first demonstrate superior standard AC performance to other presently available topological descriptors for ML model training, with mean unsigned errors (MUEs) for atomization energies on set-aside test molecules as low as 6 kcal/mol. For inorganic chemistry, our RACs yield 1 kcal/mol ML MUEs on set-aside test molecules in spin-state splitting in comparison to 15-20× higher errors for feature sets that encode whole-molecule structural information. Systematic feature selection methods including univariate filtering, recursive feature elimination, and direct optimization (e.g., random forest and LASSO) are compared. Random-forest- or LASSO-selected subsets 4-5× smaller than the full RAC set produce sub- to 1 kcal/mol spin-splitting MUEs, with good transferability to metal-ligand bond length prediction (0.004-5 Å MUE) and redox potential on a smaller data set (0.2-0.3 eV MUE). Evaluation of feature selection results across property sets reveals the relative importance of local, electronic descriptors (e.g., electronegativity, atomic number) in spin-splitting and distal, steric effects in redox potential and bond lengths.

Design of efficient molecular organic light-emitting diodes by a high-throughput virtual screening and experimental approach

Virtual screening is becoming a ground-breaking tool for molecular discovery due to the exponential growth of available computer time and constant improvement of simulation and machine learning techniques. We report an integrated organic functional material design process that incorporates theoretical insight, quantum chemistry, cheminformatics, machine learning, industrial expertise, organic synthesis, molecular characterization, device fabrication and optoelectronic testing. After exploring a search space of 1.6 million molecules and screening over 400,000 of them using time-dependent density functional theory, we identified thousands of promising novel organic light-emitting diode molecules across the visible spectrum. Our team collaboratively selected the best candidates from this set. The experimentally determined external quantum efficiencies for these synthesized candidates were as large as 22%.

The Harvard organic photovoltaic dataset

The Harvard Organic Photovoltaic Dataset (HOPV15) presented in this work is a collation of experimental photovoltaic data from the literature, and corresponding quantum-chemical calculations performed over a range of conformers, each with quantum chemical results using a variety of density functionals and basis sets. It is anticipated that this dataset will be of use in both relating electronic structure calculations to experimental observations through the generation of calibration schemes, as well as for the creation of new semi-empirical methods and the benchmarking of current and future model chemistries for organic electronic applications.