Ultrafast Computational Screening of Molecules with Inverted Singlet-Triplet Energy Gaps Using the Pariser-Parr-Pople Semiempirical Quantum Chemistry Method.

Molecules with an inverted energy gap between their first singlet and triplet excited states have promising applications in the next generation of organic light-emitting diode (OLED) materials. Unfortunately, such molecules are rare, and only a handful of examples are currently known. High-throughput virtual screening could assist in finding novel classes of these molecules, but current efforts are hampered by the high computational cost of the required quantum chemical methods. We present a method based on the semiempirical Pariser-Parr-Pople theory augmented by perturbation theory and show that it reproduces inverted gaps at a fraction of the cost of currently employed excited-state calculations. Our study paves the way for ultrahigh-throughput virtual screening and inverse design to accelerate the discovery and development of this new generation of OLED materials.

Inverse molecular design and parameter optimization with Hückel theory using automatic differentiation.

Semiempirical quantum chemistry has recently seen a renaissance with applications in high-throughput virtual screening and machine learning. The simplest semiempirical model still in widespread use in chemistry is Hückel's π-electron molecular orbital theory. In this work, we implemented a Hückel program using differentiable programming with the JAX framework based on limited modifications of a pre-existing NumPy version. The auto-differentiable Hückel code enabled efficient gradient-based optimization of model parameters tuned for excitation energies and molecular polarizabilities, respectively, based on as few as 100 data points from density functional theory simulations. In particular, the facile computation of the polarizability, a second-order derivative, via auto-differentiation shows the potential of differentiable programming to bypass the need for numeric differentiation or derivation of analytical expressions. Finally, we employ gradient-based optimization of atom identity for inverse design of organic electronic materials with targeted orbital energy gaps and polarizabilities. Optimized structures are obtained after as little as 15 iterations using standard gradient-based optimization algorithms.

Putting Chemical Knowledge to Work in Machine Learning for Reactivity.

Machine learning has been used to study chemical reactivity for a long time in fields such as physical organic chemistry, chemometrics and cheminformatics. Recent advances in computer science have resulted in deep neural networks that can learn directly from the molecular structure. Neural networks are a good choice when large amounts of data are available. However, many datasets in chemistry are small, and models utilizing chemical knowledge are required for good performance. Adding chemical knowledge can be achieved either by adding more information about the molecules or by adjusting the model architecture itself. The current method of choice for adding more information is descriptors based on computed quantum-chemical properties. Exciting new research directions show that it is possible to augment deep learning with such descriptors for better performance in the low-data regime. To modify the models, differentiable programming enables seamless merging of neural networks with mathematical models from chemistry and physics. The resulting methods are also more data-efficient and make better predictions for molecules that are different from the initial dataset on which they were trained. Application of these chemistry-informed machine learning methods promise to accelerate research in fields such as drug design, materials design, catalysis and reactivity.

Three-Dimensional Fully π-Conjugated Macrocycles: When 3D-Aromatic and When 2D-Aromatic-in-3D?

Several fully π-conjugated macrocycles with puckered or cage-type structures were recently found to exhibit aromatic character according to both experiments and computations. We examine their electronic structures and put them in relation to 3D-aromatic molecules (e.g., closo-boranes) and to 2D-aromatic polycyclic aromatic hydrocarbons. Using qualitative theory combined with quantum chemical calculations, we find that the macrocycles explored hitherto should be described as 2D-aromatic with three-dimensional molecular structures (abbr. 2D-aromatic-in-3D) and not as truly 3D-aromatic. 3D-aromatic molecules have highly symmetric structures (or nearly so), leading to (at least) triply degenerate molecular orbitals, and for tetrahedral or octahedral molecules, an aromatic closed-shell electronic structure with 6n + 2 electrons. Conversely, 2D-aromatic-in-3D structures exhibit aromaticity that results from the fulfillment of Hückel's 4n + 2 rule for each macrocyclic path, yet their π-electron counts are coincidentally 6n + 2 numbers for macrocycles with three tethers of equal lengths. It is notable that 2D-aromatic-in-3D macrocyclic cages can be aromatic with tethers of different lengths, i.e., with π-electron counts different from 6n + 2, and they are related to naphthalene. Finally, we identify tetrahedral and cubic π-conjugated molecules that fulfill the 6n + 2 rule and exhibit significant electron delocalization. Yet, their properties resemble those of analogous compounds with electron counts that differ from 6n + 2. Thus, despite the fact that these molecules show substantial π-electron delocalization, they cannot be classified as true 3D-aromatics.

A Comprehensive Discovery Platform for Organophosphorus Ligands for Catalysis.

The design of molecular catalysts typically involves reconciling multiple conflicting property requirements, largely relying on human intuition and local structural searches. However, the vast number of potential catalysts requires pruning of the candidate space by efficient property prediction with quantitative structure-property relationships. Data-driven workflows embedded in a library of potential catalysts can be used to build predictive models for catalyst performance and serve as a blueprint for novel catalyst designs. Herein we introduce kraken, a discovery platform covering monodentate organophosphorus(III) ligands providing comprehensive physicochemical descriptors based on representative conformer ensembles. Using quantum-mechanical methods, we calculated descriptors for 1558 ligands, including commercially available examples, and trained machine learning models to predict properties of over 300000 new ligands. We demonstrate the application of kraken to systematically explore the property space of organophosphorus ligands and how existing data sets in catalysis can be used to accelerate ligand selection during reaction optimization.

Triplet State Baird Aromaticity in Macrocycles: Scope, Limitations, and Complications.

The aromaticity of cyclic 4nπ-electron molecules in their first ππ* triplet state (T1), labeled Baird aromaticity, has gained growing attention in the past decade. Here we explore computationally the limitations of T1 state Baird aromaticity in macrocyclic compounds, [n]CM's, which are cyclic oligomers of four different monocycles (M = p-phenylene (PP), 2,5-linked furan (FU), 1,4-linked cyclohexa-1,3-diene (CHD), and 1,4-linked cyclopentadiene (CPD)). We strive for conclusions that are general for various DFT functionals, although for macrocycles with up to 20 π-electrons in their main conjugation paths we find that for their T1 states single-point energies at both canonical UCCSD(T) and approximative DLPNO-UCCSD(T) levels are lowest when based on UB3LYP over UM06-2X and UCAM-B3LYP geometries. This finding is in contrast to what has earlier been observed for the electronic ground state of expanded porphyrins. Yet, irrespective of functional, macrocycles with 2,5-linked furans ([n]CFU's) retain Baird aromaticity until larger n than those composed of the other three monocycles. Also, when based on geometric, electronic and energetic aspects of aromaticity, a 3[n]CFU with a specific n is more strongly Baird-aromatic than the analogous 3[n]CPP while the magnetic indices tell the opposite. To construct large T1 state Baird-aromatic [n]CM's, the design should be such that the T1 state Baird aromaticity of the macrocyclic perimeter dominates over a situation with local closed-shell Hückel aromaticity of one or a few monocycles and semilocalized triplet diradical character. Monomers with lower Hückel aromaticity in S0 than benzene (e.g., furan) that do not impose steric congestion are preferred. Structural confinement imposed by, e.g., methylene bridges is also an approach to larger Baird-aromatic macrocycles. Finally, by using the Zilberg-Haas description of T1 state aromaticity, we reveal the analogy to the Hückel aromaticity of the corresponding closed-shell dications yet observe stronger Hückel aromaticity in the macrocyclic dications than Baird aromaticity in the T1 states of the neutral macrocycles.

Substituent Effects in Chain-Breaking Aryltellurophenol Antioxidants.

2-Aryltellurophenols substituted in the aryltelluro or phenolic parts of the molecule were prepared by lithiation of the corresponding tetrahydropyran-protected 2-bromophenol, followed by reaction with a suitable diaryl ditelluride then deprotection. In a two-phase system containing N-acetylcysteine as a co-antioxidant in the aqueous phase, all of the compounds quenched lipid peroxyl radicals more efficiently than α-tocopherol, with three to five-fold longer inhibition times. Thus, these compounds offer better and longer-lasting antioxidant protection than recently prepared alkyltellurophenols. Compounds with electron-donating para substituents in the aryltelluro or phenolic part of the molecule showed the best results. The mechanism for quenching peroxyl radicals was considered and discussed with respect to the calculated O-H bond-dissociation energies, deuterium-labelling experiments and studies of thiol consumption in the aqueous phase.

Cyclopropyl Group: An Excited-State Aromaticity Indicator?

The cyclopropyl (cPr) group, which is a well-known probe for detecting radical character at atoms to which it is connected, is tested as an indicator for aromaticity in the first ππ* triplet and singlet excited states (T1 and S1 ). Baird's rule says that the π-electron counts for aromaticity and antiaromaticity in the T1 and S1 states are opposite to Hückel's rule in the ground state (S0 ). Our hypothesis is that the cPr group, as a result of Baird's rule, will remain closed when attached to an excited-state aromatic ring, enabling it to be used as an indicator to distinguish excited-state aromatic rings from excited-state antiaromatic and nonaromatic rings. Quantum chemical calculations and photoreactivity experiments support our hypothesis; calculated aromaticity indices reveal that openings of cPr substituents on [4n]annulenes ruin the excited-state aromaticity in energetically unfavorable processes. Yet, polycyclic compounds influenced by excited-state aromaticity (e.g., biphenylene), as well as 4nπ-electron heterocycles with two or more heteroatoms represent limitations.

Can Baird's and Clar's Rules Combined Explain Triplet State Energies of Polycyclic Conjugated Hydrocarbons with Fused 4nπ- and (4n + 2)π-Rings?

Compounds that can be labeled as "aromatic chameleons" are π-conjugated compounds that are able to adjust their π-electron distributions so as to comply with the different rules of aromaticity in different electronic states. We used quantum chemical calculations to explore how the fusion of benzene rings onto aromatic chameleonic units represented by biphenylene, dibenzocyclooctatetraene, and dibenzo[a,e]pentalene modifies the first triplet excited states (T1) of the compounds. Decreases in T1 energies are observed when going from isomers with linear connectivity of the fused benzene rings to those with cis- or trans-bent connectivities. The T1 energies decreased down to those of the parent (isolated) 4nπ-electron units. Simultaneously, we observe an increased influence of triplet state aromaticity of the central 4n ring as given by Baird's rule and evidenced by geometric, magnetic, and electron density based aromaticity indices (HOMA, NICS-XY, ACID, and FLU). Because of an influence of triplet state aromaticity in the central 4nπ-electron units, the most stabilized compounds retain the triplet excitation in Baird π-quartets or octets, enabling the outer benzene rings to adapt closed-shell singlet Clar π-sextet character. Interestingly, the T1 energies go down as the total number of aromatic cycles within a molecule in the T1 state increases.

Analysis of a Compound Class with Triplet States Stabilized by Potentially Baird Aromatic [10]Annulenyl Dicationic Rings.

The low-lying triplet state of a recently published compound (TMTQ) was analyzed quantum chemically in light of suggestions that it is influenced by Baird aromaticity. Two mesomeric structures describe this state: 1) a zwitterionic Baird aromatic structure with a triplet diradical 8π-electron methano[10]annulene (M10A) dicationic ring and 2) a Hückel aromatic with a neutral closed-shell 10π-electron ring. According to charge and spin density distributions, the Hückel aromatic structure dominates the triplet state (the Baird aromatic contributes at most 12 %), and separation of the aromatic fluctuation index (FLU) into α and ß electron contributions emphasizes this finding. The small singlet-triplet energy gap is due to Hückel aromaticity of the M10A ring, clarified by comparison to the smaller analogues of TMTQ. Yet, TMTQ and its analogues are Hückel-Baird hybrids allowing for tuning between closed-shell 4n+2 Hückel aromaticity and open-shell 4n Baird aromaticity.

The Missing C1-C5 Cycloaromatization Reaction: Triplet State Antiaromaticity Relief and Self-Terminating Photorelease of Formaldehyde for Synthesis of Fulvenes from Enynes.

The last missing example of the four archetypical cycloaromatizations of enediynes and enynes was discovered by combining a twisted alkene excited state with a new self-terminating path for intramolecular conversion of diradicals into closed-shell products. Photoexcitation of aromatic enynes to a twisted alkene triplet state creates a unique stereoelectronic situation, which is facilitated by the relief of excited state antiaromaticity of the benzene ring. This enables the usually unfavorable 5-endo-trig cyclization and merges it with 5-exo-dig closure. The 1,4-diradical product of the C1-C5 cyclization undergoes internal H atom transfer that is coupled with the fragmentation of an exocyclic C-C bond. This sequence provides efficient access to benzofulvenes from enynes and expands the utility of self-terminating aromatizing enyne cascades to photochemical reactions. The key feature of this self-terminating reaction is that, despite the involvement of radical species in the key cyclization step, no external radical sources or quenchers are needed to provide the products. In these cascades, both radical centers are formed transiently and converted to the closed-shell products via intramolecular H-transfer and C-C bond fragmentation. Furthermore, incorporating C-C bond cleavage into the photochemical self-terminating cyclizations of enynes opens a new way for the use of alkenes as alkyne equivalents in organic synthesis.

Impact of ground- and excited-state aromaticity on cyclopentadiene and silole excitation energies and excited-state polarities.

A new qualitative model for estimating the properties of substituted cyclopentadienes and siloles in their lowest ππ* excited states is introduced and confirmed through quantum chemical calculations, and then applied to explain earlier reported experimental excitation energies. According to our model, which is based on excited-state aromaticity and antiaromaticity, siloles and cyclopentadienes are cross-hyperconjugated "aromatic chameleons" that adapt their electronic structures to conform to the various aromaticity rules in different electronic states (Hückel's rule in the π(2) electronic ground state (S0) and Baird's rule in the lowest ππ* excited singlet and triplet states (S1 and T1)). By using pen-and-paper arguments, one can explain polarity changes upon excitation of substituted cyclopentadienes and siloles, and one can tune their lowest excitation energies by combined considerations of ground- and excited-state aromaticity/antiaromaticity effects. Finally, the "aromatic chameleon" model can be extended to other monocyclic compound classes of potential use in organic electronics, thereby providing a unified view of the S0, T1, and S1 states of a range of different cyclic cross-π-conjugated and cross-hyperconjugated compound classes.

Computational Investigations of the Detailed Mechanism of Reverse Intersystem Crossing in Inverted Singlet-Triplet Gap Molecules.

Inverted singlet-triplet gap (INVEST) materials have promising photophysical properties for optoelectronic applications due to an inversion of their lowest singlet (S1) and triplet (T1) excited states. This results in an exothermic reverse intersystem crossing (rISC) process that potentially enhances triplet harvesting, compared to thermally activated delayed fluorescence (TADF) emitters with endothermic rISCs. However, the processes and phenomena that facilitate conversion between excited states for INVEST materials are underexplored. We investigate the complex potential energy surfaces (PESs) of the excited states of three heavily studied azaphenalene INVEST compounds, namely, cyclazine, pentazine, and heptazine using two state-of-the-art computational methodologies, namely, RMS-CASPT2 and SCS-ADC(2) methods. Our findings suggest that ISC and rISC processes take place directly between the S1 and T1 electronic states in all three compounds through a minimum-energy crossing point (MECP) with an activation energy barrier between 0.11 to 0.58 eV above the S1 state for ISC and between 0.06 and 0.36 eV above the T1 state for rISC. We predict that higher-lying triplet states are not populated, since the crossing point structures to these states are not energetically accessible. Furthermore, the conical intersection (CI) between the ground and S1 states is high in energy for all compounds (between 0.4 to 2.0 eV) which makes nonradiative decay back to the ground state a relatively slow process. We demonstrate that the spin-orbit coupling (SOC) driving the S1-T1 conversion is enhanced by vibronic coupling with higher-lying singlet and triplet states possessing vibrational modes of proper symmetry. We also rationalize that the experimentally observed anti-Kasha emission of cyclazine is due to the energetically inaccessible CI between the bright S2 and the dark S1 states, hindering internal conversion. Finally, we show that SCS-ADC(2) is able to qualitatively reproduce excited state features, but consistently overpredict relative energies of excited state structural minima compared to RMS-CASPT2. The identification of these excited state features elaborates design rules for new INVEST emitters with improved emission quantum yields.

Reaction profiles for quantum chemistry-computed [3 + 2] cycloaddition reactions.

Bio-orthogonal click chemistry based on [3 + 2] dipolar cycloadditions has had a profound impact on the field of biochemistry and significant effort has been devoted to identify promising new candidate reactions for this purpose. To gauge whether a prospective reaction could be a suitable bio-orthogonal click reaction, information about both on- and off-target activation and reaction energies is highly valuable. Here, we use an automated workflow, based on the autodE program, to compute over 5000 reaction profiles for [3 + 2] cycloadditions involving both synthetic dipolarophiles and a set of biologically-inspired structural motifs. Based on a succinct benchmarking study, the B3LYP-D3(BJ)/def2-TZVP//B3LYP-D3(BJ)/def2-SVP level of theory was selected for the DFT calculations, and standard conditions and an (aqueous) SMD model were imposed to mimic physiological conditions. We believe that this data, as well as the presented workflow for high-throughput reaction profile computation, will be useful to screen for new bio-orthogonal reactions, as well as for the development of novel machine learning models for the prediction of chemical reactivity more broadly.

Fast evaluation of the adsorption energy of organic molecules on metals via graph neural networks.

Modeling in heterogeneous catalysis requires the extensive evaluation of the energy of molecules adsorbed on surfaces. This is done via density functional theory but for large organic molecules it requires enormous computational time, compromising the viability of the approach. Here we present GAME-Net, a graph neural network to quickly evaluate the adsorption energy. GAME-Net is trained on a well-balanced chemically diverse dataset with C1-4 molecules with functional groups including N, O, S and C6-10 aromatic rings. The model yields a mean absolute error of 0.18 eV on the test set and is 6 orders of magnitude faster than density functional theory. Applied to biomass and plastics (up to 30 heteroatoms), adsorption energies are predicted with a mean absolute error of 0.016 eV per atom. The framework represents a tool for the fast screening of catalytic materials, particularly for systems that cannot be simulated by traditional methods.

Machine learning meets mechanistic modelling for accurate prediction of experimental activation energies.

Accurate prediction of chemical reactions in solution is challenging for current state-of-the-art approaches based on transition state modelling with density functional theory. Models based on machine learning have emerged as a promising alternative to address these problems, but these models currently lack the precision to give crucial information on the magnitude of barrier heights, influence of solvents and catalysts and extent of regio- and chemoselectivity. Here, we construct hybrid models which combine the traditional transition state modelling and machine learning to accurately predict reaction barriers. We train a Gaussian Process Regression model to reproduce high-quality experimental kinetic data for the nucleophilic aromatic substitution reaction and use it to predict barriers with a mean absolute error of 0.77 kcal mol-1 for an external test set. The model was further validated on regio- and chemoselectivity prediction on patent reaction data and achieved a competitive top-1 accuracy of 86%, despite not being trained explicitly for this task. Importantly, the model gives error bars for its predictions that can be used for risk assessment by the end user. Hybrid models emerge as the preferred alternative for accurate reaction prediction in the very common low-data situation where only 100-150 rate constants are available for a reaction class. With recent advances in deep learning for quickly predicting barriers and transition state geometries from density functional theory, we envision that hybrid models will soon become a standard alternative to complement current machine learning approaches based on ground-state physical organic descriptors or structural information such as molecular graphs or fingerprints.

Organic reactivity from mechanism to machine learning.

As more data are introduced in the building of models of chemical reactivity, the mechanistic component can be reduced until 'big data' applications are reached. These methods no longer depend on underlying mechanistic hypotheses, potentially learning them implicitly through extensive data training. Reactivity models often focus on reaction barriers, but can also be trained to directly predict lab-relevant properties, such as yields or conditions. Calculations with a quantum-mechanical component are still preferred for quantitative predictions of reactivity. Although big data applications tend to be more qualitative, they have the advantage to be broadly applied to different kinds of reactions. There is a continuum of methods in between these extremes, such as methods that use quantum-derived data or descriptors in machine learning models. Here, we present an overview of the recent machine learning applications in the field of chemical reactivity from a mechanistic perspective. Starting with a summary of how reactivity questions are addressed by quantum-mechanical methods, we discuss methods that augment or replace quantum-based modelling with faster alternatives relying on machine learning.

Exploiting the Aromatic Chameleon Character of Fulvenes for Computational Design of Baird-Aromatic Triplet Ground State Compounds.

Due to the reversal in electron counts for aromaticity and antiaromaticity in the closed-shell singlet state (normally ground state, S0 ) and lowest ππ* triplet state (T1 or T0 ), as given by Hückel's and Baird's rules, respectively, fulvenes are influenced by their substituents in the opposite manner in the T1 and S0 states. This effect is caused by a reversal in the dipole moment when going from S0 to T1 as fulvenes adapt to the difference in electron counts for aromaticity in various states; they are aromatic chameleons. Thus, a substituent pattern that enhances (reduces) fulvene aromaticity in S0 reduces (enhances) aromaticity in T1 , allowing for rationalizations of the triplet state energies (ET ) of substituted fulvenes. Through quantum chemical calculations, we now assess which substituents and which positions on the pentafulvene core are the most powerful for designing compounds with low or inverted ET . As a means to increase the π-electron withdrawing capacity of cyano groups, we found that protonation at the cyano N atoms of 6,6-dicyanopentafulvenes can be a route to on-demand formation of a fulvenium dication with a triplet ground state (T0 ). The five-membered ring of this species is markedly Baird-aromatic, although less than the cyclopentadienyl cation known to have a Baird-aromatic T0 state.

Triplet state homoaromaticity: concept, computational validation and experimental relevance.

Cyclic conjugation that occurs through-space and leads to aromatic properties is called homoaromaticity. Here we formulate the homoaromaticity concept for the triplet excited state (T1) based on Baird's 4n rule and validate it through extensive quantum-chemical calculations on a range of different species (neutral, cationic and anionic). By comparison to well-known ground state homoaromatic molecules we reveal that five of the investigated compounds show strong T1 homoaromaticity, four show weak homoaromaticity and two are non-aromatic. Two of the compounds have previously been identified as excited state intermediates in photochemical reactions and our calculations indicate that they are also homoaromatic in the first singlet excited state. Homoaromaticity should therefore have broad implications in photochemistry. We further demonstrate this by computational design of a photomechanical "lever" that is powered by relief of homoantiaromatic destabilization in the first singlet excited state.

Energetics of Baird aromaticity supported by inversion of photoexcited chiral [4n]annulene derivatives.

For the concept of aromaticity, energetic quantification is crucial. However, this has been elusive for excited-state (Baird) aromaticity. Here we report our serendipitous discovery of two nonplanar thiophene-fused chiral [4n]annulenes Th4 COT Saddle and Th6 CDH Screw , which by computational analysis turned out to be a pair of molecules suitable for energetic quantification of Baird aromaticity. Their enantiomers were separable chromatographically but racemized thermally, enabling investigation of the ring inversion kinetics. In contrast to Th6 CDH Screw , which inverts through a nonplanar transition state, the inversion of Th4 COT Saddle , progressing through a planar transition state, was remarkably accelerated upon photoexcitation. As predicted by Baird's theory, the planar conformation of Th4 COT Saddle is stabilized in the photoexcited state, thereby enabling lower activation enthalpy than that in the ground state. The lowering of the activation enthalpy, i.e., the energetic impact of excited-state aromaticity, was quantified experimentally to be as high as 21-22 kcal mol-1.Baird's rule applies to cyclic π-conjugated molecules in their excited state, yet a quantification of the involved energetics is elusive. Here, the authors show the ring inversion kinetics of two nonplanar and chiral [4n]annulenes to support Baird's rule from an energetic point of view.