Inferring the Energetics of CO2-Aniline Adduct Formation from Vibrational Spectroscopy.

Control of atmospheric CO2 is an important contemporary scientific and engineering challenge. Toward this goal, the reaction of CO2 with amines to form carbamate bonds is an established method for CO2 capture. However, controllable reversal of this reaction remains difficult and requires tuning the energetics of the carbamate bond. Through IR spectroscopy, we show that a characteristic frequency observed upon carbamate formation varies as a function of the substituent's Hammett parameter for a family of para-substituted anilines. We present computational evidence that the vibrational frequency of the adducted CO2 serves as a predictor of the energy of formation of the carbamate. Electron donating groups typically enhance the driving force of carbamate formation by transferring more charge to the adducted CO2 and thus increasing the occupancy of the antibonding orbital in the carbon-oxygen bonds. Increased occupancy of the antibonding orbital within adducted CO2 indicates a weaker bond, leading to a red-shift in the characteristic carbamate frequency. Our work serves the large field of CO2 capture research where spectroscopic observables, such as IR frequencies, are more easily obtainable and can stand in as a descriptor of driving forces.

Recent Advances toward Efficient Calculation of Higher Nuclear Derivatives in Quantum Chemistry.

In this paper, we provide an overview of state-of-the-art techniques that are being developed for efficient calculation of second and higher nuclear derivatives of quantum mechanical (QM) energy. Calculations of nuclear Hessians and anharmonic terms incur high costs and memory and scale poorly with system size. Three emerging classes of methods─machine learning (ML), automatic differentiation (AD), and matrix completion (MC)─have demonstrated promise in overcoming these challenges. We illustrate studies that employ unsupervised ML methods to reduce the need for multiple Hessian calculations in dynamics simulations and those that utilize supervised ML to construct approximate potential energy surfaces and estimate Hessians and anharmonic terms at reduced cost. By extension, if electronic structure operations could be written in a manner similar to functions underlying ML methods, rapid differentiation or AD routines can be employed to inexpensively calculate higher arbitrary-order derivatives. While ML approaches are typically black-box, we describe methods such as compressed sensing (CS) and MC, which explicitly leverage problem-specific mathematical properties of higher derivatives such as sparsity and low-rank, to complete higher derivative information using only a small, incomplete sample. The three classes of methods facilitate reliable predictions of observables ranging from infrared spectra to thermal conductivity and constitute a promising way forward in accurately capturing otherwise intractable higher-order responses of QM energy to nuclear perturbations.

Organic photoredox catalysts for CO2 reduction: Driving discovery with genetic algorithms.

This work implements a genetic algorithm (GA) to discover organic catalysts for photoredox CO2 reduction that are both highly active and resistant to degradation. The lowest unoccupied molecular orbital energy of the ground state catalyst is chosen as the activity descriptor and the average Mulliken charge on all ring carbons is chosen as the descriptor for resistance to degradation via carboxylation (both obtained using density functional theory) to construct the fitness function of the GA. We combine the results of multiple GA runs, each based on different relative weighting of the two descriptors, and rigorously assess GA performance by calculating electron transfer barriers to CO2 reduction. A large majority of GA predictions exhibit improved performance relative to experimentally studied o-, m-, and p-terphenyl catalysts. Based on stringent cutoffs imposed on the average charge, barrier to electron transfer to CO2, and excitation energy, we recommend 25 catalysts for further experimental investigation of viability toward photoredox CO2 reduction.

A matrix completion algorithm for efficient calculation of quantum and variational effects in chemical reactions.

This work examines the viability of matrix completion methods as cost-effective alternatives to full nuclear Hessians for calculating quantum and variational effects in chemical reactions. The harmonic variety-based matrix completion (HVMC) algorithm, developed in a previous study [S. J. Quiton et al., J. Chem. Phys. 153, 054122 (2020)], exploits the low-rank character of the polynomial expansion of potential energy to recover vibrational frequencies (square roots of eigenvalues of nuclear Hessians) constituting the reaction path using a small sample of its entities. These frequencies are essential for calculating rate coefficients using variational transition state theory with multidimensional tunneling (VTST-MT). HVMC performance is examined for four SN2 reactions and five hydrogen transfer reactions, with each H-transfer reaction consisting of at least one vibrational mode strongly coupled to the reaction coordinate. HVMC is robust and captures zero-point energies, vibrational free energies, zero-curvature tunneling, and adiabatic ground state and free energy barriers as well as their positions on the reaction coordinate. For medium to large reactions involving H-transfer, with the sole exception of the most complex Ir catalysis system, less than 35% of total eigenvalue information is necessary for accurate recovery of key VTST-MT observables.

Modeling and Characterization of Exciplexes in Photoredox CO2 Reduction: Insights from Quantum Chemistry and Fluorescence Spectroscopy.

Interactions between excited-state arenes and amines can lead to the formation of structures with a distinct emission behavior. These excited-state complexes or exciplexes can reduce the ability of the arene to participate in other reactions, such as CO2 reduction, or increase the likelihood of degradation via Birch reduction. Exciplex geometries are necessary to understand photophysical behavior and probe degradation pathways but are challenging to calculate. We establish a detailed computational protocol for calculation, verification, and characterization of exciplexes. Using fluorescence spectroscopy, we first demonstrate the formation of exciplexes between excited-state oligo-(p-phenylene) (OPP), shown to successfully carry out CO2 reduction, and triethylamine. Time-dependent density functional theory is employed to optimize the geometries of these exciplexes, which are validated by comparing both emission energies and their solvatochromism with the experiment. Excited-state energy decomposition analysis confirms the predominant role played by charge transfer interactions in the red shift of emissions relative to the isolated excited-state OPP*. We find that although the exciplex emission frequency depends strongly on solvent dielectric, the extent of charge separation in an exciplex does not. Our results also suggest that the formation of solvent-separated ionic radical states upon complete electron transfer competes with exciplex formation in higher-dielectric solvents, thereby leading to reduced exciplex emission intensities in fluorescence experiments.

Photoredox Chemistry with Organic Catalysts: Role of Computational Methods.

Organic catalysts have the potential to carry out a wide range of otherwise thermally inaccessible reactions via photoredox routes. Early demonstrated successes of organic photoredox catalysts include one-electron CO2 reduction and H2 generation via water splitting. Photoredox systems are challenging to study and design owing to the sheer number and diversity of phenomena involved, including light absorption, emission, intersystem crossing, partial or complete charge transfer, and bond breaking or formation. Designing a viable photoredox route therefore requires consideration of a host of factors such as absorption wavelength, solvent, choice of electron donor or acceptor, and so on. Quantum chemistry methods can play a critical role in demystifying photoredox phenomena. Using one-electron CO2 reduction with phenylene-based chromophores as an illustrative example, this perspective highlights recent developments in quantum chemistry that can advance our understanding of photoredox processes and proposes a way forward for driving the design and discovery of organic catalysts.

Perspective and challenges in electrochemical approaches for reactive CO2 separations.

The desire toward decarbonization and renewable energy has sparked research interests in reactive CO2 separations, such as direct air capture that utilize electricity as opposed to conventional thermal and pressure swing processes, which are energy-intensive, cost-prohibitive, and fossil-fuel dependent. Although the electrochemical approaches in CO2 capture that support negative emissions technologies are promising in terms of modularity, smaller footprint, mild reaction conditions, and possibility to integrate into conversion processes, their practice depends on the wider availability of renewable electricity. This perspective discusses key advances made in electrolytes and electrodes with redox-active moieties that reversibly capture CO2 or facilitate its transport from a CO2-rich side to a CO2-lean side within the last decade. In support of the discovery of new heterogeneous electrode materials and electrolytes with redox carriers, the role of computational chemistry is also discussed.

Computational Analysis of Electron Transfer Kinetics for CO2 Reduction with Organic Photoredox Catalysts.

We present a fundamental description of the electron transfer (ET) step from substituted oligo(p-phenylene) (OPP) radical anions to CO2, with the larger goal of assessing the viability of underexplored, organic photoredox routes for utilization of anthropogenic CO2. This work varies the electrophilicity of para-substituents to OPP and probes the dependence of rate coefficients and interfragment interactions on the substituent Hammett parameter, σp, using constrained density functional theory (CDFT) and energy decomposition analysis (EDA). Large electronic couplings across substituents indicates an adiabatic electron transfer process for reactants at contact. As one might intuitively expect, free energy changes dominate trends in ET rate coefficients in most cases, and rates increase with substituent electron-donating ability. However, we observe an unexpected dip in rate coefficients for the most electron-donating groups, due to the combined impact of flattening free energies and a steep increase in reorganization energies. Our analysis shows that, with decreasing σp, flattening OPP LUMO levels lower the marginal increase in free energy. EDA reveals trends in electrostatics and charge transfer interactions between the catalyst and substrate fragments that influence free energy changes across substituents. Reorganization energies do not exhibit a direct dependence on σp and are largely similar across systems, with the exception of substituents containing lone pairs of electrons that exhibit significant deformation upon electron transfer. Our study therefore suggests that while a wide range of ET rates are observed, there is an upper limit to rate enhancements achievable by only tuning the substituent electrophilicity.

Consistent inclusion of continuum solvation in energy decomposition analysis: theory and application to molecular CO2 reduction catalysts.

To facilitate computational investigation of intermolecular interactions in the solution phase, we report the development of ALMO-EDA(solv), a scheme that allows the application of continuum solvent models within the framework of energy decomposition analysis (EDA) based on absolutely localized molecular orbitals (ALMOs). In this scheme, all the quantum mechanical states involved in the variational EDA procedure are computed with the presence of solvent environment so that solvation effects are incorporated in the evaluation of all its energy components. After validation on several model complexes, we employ ALMO-EDA(solv) to investigate substituent effects on two classes of complexes that are related to molecular CO2 reduction catalysis. For [FeTPP(CO2-κC)]2- (TPP = tetraphenylporphyrin), we reveal that two ortho substituents which yield most favorable CO2 binding, -N(CH3)3 + (TMA) and -OH, stabilize the complex via through-structure and through-space mechanisms, respectively. The coulombic interaction between the positively charged TMA group and activated CO2 is found to be largely attenuated by the polar solvent. Furthermore, we also provide computational support for the design strategy of utilizing bulky, flexible ligands to stabilize activated CO2 via long-range Coulomb interactions, which creates biomimetic solvent-inaccessible "pockets" in that electrostatics is unscreened. For the reactant and product complexes associated with the electron transfer from the p-terphenyl radical anion to CO2, we demonstrate that the double terminal substitution of p-terphenyl by electron-withdrawing groups considerably strengthens the binding in the product state while moderately weakens that in the reactant state, which are both dominated by the substituent tuning of the electrostatics component. These applications illustrate that this new extension of ALMO-EDA provides a valuable means to unravel the nature of intermolecular interactions and quantify their impacts on chemical reactivity in solution.

Divergent Diels-Alder Reactions in the Biosynthesis and Synthesis of Endiandric-Type Tetracycles: A Computational Study.

Endiandric acids and related polyketide natural products arise from polyene precursors and occur naturally as fused and bridged tetracycles. In some cases, the intramolecular Diels-Alder reactions that produce fused and bridged tetracycles result from a diene tether that may act as either a 4π or 2π component in the cycloaddition. To examine the preference for fused or bridged products, we applied density functional theory (using the M06-2X and B3LYP functionals) to reactants with various substituents for both fused and bridged transition states. Fused products were generally preferred except when disfavored by extreme steric hindrance (e.g., a tert-butyl group). These computational results are consistent with experimental data and suggest the existence of as-yet undiscovered natural products.