A US perspective on closing the carbon cycle to defossilize difficult-to-electrify segments of our economy.

Electrification to reduce or eliminate greenhouse gas emissions is essential to mitigate climate change. However, a substantial portion of our manufacturing and transportation infrastructure will be difficult to electrify and/or will continue to use carbon as a key component, including areas in aviation, heavy-duty and marine transportation, and the chemical industry. In this Roadmap, we explore how multidisciplinary approaches will enable us to close the carbon cycle and create a circular economy by defossilizing these difficult-to-electrify areas and those that will continue to need carbon. We discuss two approaches for this: developing carbon alternatives and improving our ability to reuse carbon, enabled by separations. Furthermore, we posit that co-design and use-driven fundamental science are essential to reach aggressive greenhouse gas reduction targets.

Organic Reactivity Made Easy and Accurate with Automated Multireference Calculations.

In organic reactivity studies, quantum chemical calculations play a pivotal role as the foundation of understanding and machine learning model development. While prevalent black-box methods like density functional theory (DFT) and coupled-cluster theory (e.g., CCSD(T)) have significantly advanced our understanding of chemical reactivity, they frequently fall short in describing multiconfigurational transition states and intermediates. Achieving a more accurate description necessitates the use of multireference methods. However, these methods have not been used at scale due to their often-faulty predictions without expert input. Here, we overcome this deficiency with automated multiconfigurational pair-density functional theory (MC-PDFT) calculations. We apply this method to 908 automatically generated organic reactions. We find 68% of these reactions present significant multiconfigurational character in which the automated multiconfigurational approach often provides a more accurate and/or efficient description than DFT and CCSD(T). This work presents the first high-throughput application of automated multiconfigurational methods to reactivity, enabled by automated active space selection algorithms and the computation of electronic correlation with MC-PDFT on-top functionals. This approach can be used in a black-box fashion, avoiding significant active space inconsistency error in both single- and multireference cases and providing accurate multiconfigurational descriptions when needed.

State Preparation in Quantum Algorithms for Fragment-Based Quantum Chemistry.

State preparation for quantum algorithms is crucial for achieving high accuracy in quantum chemistry and competing with classical algorithms. The localized active space-unitary coupled cluster (LAS-UCC) algorithm iteratively loads a fragment-based multireference wave function onto a quantum computer. In this study, we compare two state preparation methods, quantum phase estimation (QPE) and direct initialization (DI), for each fragment. We test the two state preparation methods on three systems, ranging from a model system, a set of interacting hydrogen molecules, to more realistic chemical problems, like the C-C double bond breaking in transbutadiene and the spin ladder in a bimetallic system. We analyze the impact of QPE parameters, such as the number of ancilla qubits and Trotter steps, on the prepared state. We find a trade-off between the methods, where DI requires fewer resources for smaller fragments, while QPE is more efficient for larger fragments. Our resource estimates highlight the benefits of system fragmentation in state preparation for subsequent quantum chemical calculations. These findings have broad applications for preparing multireference quantum chemical wave functions on quantum circuits that can be used for realistic chemical applications.

Catalytic, Spectroscopic, and Theoretical Studies of Fe4S4-Based Coordination Polymers as Heterogenous Coupled Proton-Electron Transfer Mediators for Electrocatalysis.

Iron-sulfur clusters play essential roles in biological systems, and thus synthetic [Fe4S4] clusters have been an area of active research. Recent studies have demonstrated that soluble [Fe4S4] clusters can serve as net H atom transfer mediators, improving the activity and selectivity of a homogeneous Mn CO2 reduction catalyst. Here, we demonstrate that incorporating these [Fe4S4] clusters into a coordination polymer enables heterogeneous H atom transfer from an electrode surface to a Mn complex dissolved in solution. A previously reported solution-processable Fe4S4-based coordination polymer was successfully deposited on the surfaces of different electrodes. The coated electrodes serve as H atom transfer mediators to a soluble Mn CO2 reduction catalyst displaying good product selectivity for formic acid. Furthermore, these electrodes are recyclable with a minimal decrease in activity after multiple catalytic cycles. The heterogenization of the mediator also enables the characterization of solution-phase and electrode surface species separately. Surface enhanced infrared absorption spectroscopy (SEIRAS) reveals spectroscopic signatures for an in situ generated active Mn-H species, providing a more complete mechanistic picture for this system. The active species, reaction mechanism, and the protonation sites on the [Fe4S4] clusters were further confirmed by density functional theory calculations. The observed H atom transfer reactivity of these coordination polymer-coated electrodes motivates additional applications of this composite material in reductive H atom transfer electrocatalysis.

Aliovalent Substitution Tunes Physical Properties in a Conductive Bis(dithiolene) Two-Dimensional Metal-Organic Framework.

Two-dimensional conductive metal-organic frameworks have emerged as promising electronic materials for applications in (opto)electronic, thermoelectric, magnetic, electrocatalytic, and energy storage devices. Many bottom-up or postsynthetic protocols have been developed to isolate these materials or further modulate their electronic properties. However, some methodologies commonly used in classic semiconductors, notably, aliovalent substitution, are conspicuously absent. Here, we demonstrate how aliovalent Fe(III) to Ni(II) substitution enables the isolation of a Ni bis(dithiolene) material from a previously reported Fe analogue. Detailed characterization supports the idea that aliovalent substitution of Fe(III) to Ni(II) results in an in situ oxidation of the organic dithiolene linker. This substitution-induced redox tuning modulates the electronic properties in the system, leading to higher electrical conductivity and Hall mobility but slightly lower carrier densities and weaker antiferromagnetic interactions. Moreover, this aliovalent substitution improves the material's electrochemical stability and thus enables pseudocapacitive behavior in the Ni material. These results demonstrate how classic aliovalent substitution strategies in semiconductors can also be leveraged in conductive MOFs and add further support to this class of compounds as emerging electronic materials.

Analytic Nuclear Gradients for Complete Active Space Linearized Pair-Density Functional Theory.

Accurately modeling photochemical reactions is difficult due to the presence of conical intersections and locally avoided crossings, as well as the inherently multiconfigurational character of excited states. As such, one needs a multistate method that incorporates state interaction in order to accurately model the potential energy surface at all nuclear coordinates. The recently developed linearized pair-density functional theory (L-PDFT) is a multistate extension of multiconfiguration PDFT, and it has been shown to be a cost-effective post-MCSCF method (as compared to more traditional and expensive multireference many-body perturbation methods or multireference configuration interaction methods) that can accurately model potential energy surfaces in regions of strong nuclear-electronic coupling in addition to accurately predicting Franck-Condon vertical excitations. In this paper, we report the derivation of analytic gradients for L-PDFT and their implementation in the PySCF-forge software, and we illustrate the utility of these gradients for predicting ground- and excited-state equilibrium geometries and adiabatic excitation energies for formaldehyde, s-trans-butadiene, phenol, and cytosine.

Minimum-Energy Conical Intersections by Compressed Multistate Pair-Density Functional Theory.

Compressed multistate pair-density functional theory (CMS-PDFT) is a multistate version of multiconfiguration pair-density functional theory that can capture the correct topology of coupled potential energy surfaces (PESs) around conical intersections. In this work, we develop interstate coupling vectors (ISCs) for CMS-PDFT in the OpenMolcas and PySCF/mrh electronic structure packages. Yet, the main focus of this work is using ISCs to calculate minimum-energy conical intersections (MECIs) by CMS-PDFT. This is performed using the projected constrained optimization method in OpenMolcas, which uses ISCs to restrain the iterations to the conical intersection seam. We optimize the S1/S0 MECIs for ethylene, butadiene, and benzene and show that CMS-PDFT gives smooth PESs in the vicinities of the MECIs. Furthermore, the CMS-PDFT MECIs are in good agreement with the MECI calculated by the more expensive XMS-CASPT2 method.

Harvesting Water from Air with High-Capacity, Stable Furan-Based Metal-Organic Frameworks.

We synthesized two isoreticular furan-based metal-organic frameworks (MOFs), MOF-LA2-1(furan) and MOF-LA2-2(furan) with rod-like secondary building units (SBUs) featuring 1D channels, as sorbents for atmospheric water harvesting (LA = long arm). These aluminum-based MOFs demonstrated a combination of high water uptake and stability, exhibiting working capacities of 0.41 and 0.48 gwater/gMOF (under isobaric conditions of 1.70 kPa), respectively. Remarkably, both MOFs showed a negligible loss in water uptake after 165 adsorption-desorption cycles. These working capacities rival that of MOF-LA2-1(pyrazole), which has a working capacity of 0.55 gwater/gMOF. The current MOFs stand out for their high water stability, as evidenced by 165 cycles of water uptake and release. MOF-LA2-2(furan) is the first aluminum MOF to employ a double 'long arm' extension strategy, which is confirmed through single-crystal X-ray diffraction (SCXRD). The MOFs were synthesized by using a straightforward synthesis route. This study offers valuable insights into the design of durable, water-stable MOFs and underscores their potential for efficient water harvesting.

Divergent Bimetallic Mechanisms in Copper(II)-Mediated C-C, N-N, and O-O Oxidative Coupling Reactions.

Copper-catalyzed aerobic oxidative coupling of diaryl imines provides a route for conversion of ammonia to hydrazine. The present study uses experimental and density functional theory computational methods to investigate the mechanism of N-N bond formation, and the data support a mechanism involving bimolecular coupling of Cu-coordinated iminyl radicals. Computational analysis is extended to CuII-mediated C-C, N-N, and O-O coupling reactions involved in the formation of cyanogen (NC-CN) from HCN, 1,3-butadiyne from ethyne (i.e., Glaser coupling), hydrazine from ammonia, and hydrogen peroxide from water. The results reveal two different mechanistic pathways. Heteroatom ligands with an uncoordinated lone pair (iminyl, NH2, OH) undergo charge transfer to CuII, generating ligand-centered radicals that undergo facile bimolecular radical-radical coupling. Ligands lacking a lone pair (CN and CCH) form bridged binuclear diamond-core structures that undergo C-C coupling. This mechanistic bifurcation is rationalized by analysis of spin densities in key intermediates and transition states, as well as multiconfigurational calculations. Radical-radical coupling is especially favorable for N-N coupling owing to energetically favorable charge transfer in the intermediate and thermodynamically favorable product formation.

Mechanism of Benzene Hydroxylation on Tri-Iron Oxo-Centered Cluster-Based Metal-Organic Frameworks.

High-valent Fe(IV)-oxo species derived upon reactions of N2O with Fe(II) centers-embedded in the framework of tri-iron oxo-centered-based metal-organic frameworks (MOFs)- selectively affect the conversion of benzene-to-phenol via electrophilic addition to arene C-H bonds akin to oxygen transfer mechanisms in the P450 enzyme. The Fe(II) species identified by Mössbauer spectroscopy can be titrated in situ by the addition of NO to completely suppress benzene oxidation, verifying the relevance of Fe(II) centers. Observed inverse kinetic isotope effects in benzene hydroxylation preclude the involvement of H atom transfer steps from benzene to the Fe(IV)-oxo species and instead suggest that the electrophilic iron-oxo group adds to an sp2 carbon of benzene, resulting in a change in the hybridization from sp2-to-sp3. These mechanistic postulates are affirmed in Kohn-Sham density functional calculations, which predict lower barriers for additive mechanisms for arene oxidation than H atom abstraction steps. The calculations show that the reaction proceeds on the pentadectet spin surface and that a non-innocent ligand participates in the transfer of the H atom. Following precedent literature which demonstrates that these Fe(IV)-oxo species react with C-H bonds in alkanes via hydrogen atom abstraction to form alcohols, it appears that iron(IV)-oxo species in MOFs exhibit duality in their reactions with inert hydrocarbon substrates akin to enzymes-if the C-H bonds are in saturated aliphatic hydrocarbons, then activation occurs via hydrogen abstraction, while if the C-H bonds are aromatic, then activation occurs by addition rearrangement.

Shaping the Water-Harvesting Behavior of Metal-Organic Frameworks Aided by Fine-Tuned GPT Models.

We construct a data set of metal-organic framework (MOF) linkers and employ a fine-tuned GPT assistant to propose MOF linker designs by mutating and modifying the existing linker structures. This strategy allows the GPT model to learn the intricate language of chemistry in molecular representations, thereby achieving an enhanced accuracy in generating linker structures compared with its base models. Aiming to highlight the significance of linker design strategies in advancing the discovery of water-harvesting MOFs, we conducted a systematic MOF variant expansion upon state-of-the-art MOF-303 utilizing a multidimensional approach that integrates linker extension with multivariate tuning strategies. We synthesized a series of isoreticular aluminum MOFs, termed Long-Arm MOFs (LAMOF-1 to LAMOF-10), featuring linkers that bear various combinations of heteroatoms in their five-membered ring moiety, replacing pyrazole with either thiophene, furan, or thiazole rings or a combination of two. Beyond their consistent and robust architecture, as demonstrated by permanent porosity and thermal stability, the LAMOF series offers a generalizable synthesis strategy. Importantly, these 10 LAMOFs establish new benchmarks for water uptake (up to 0.64 g g-1) and operational humidity ranges (between 13 and 53%), thereby expanding the diversity of water-harvesting MOFs.

Understanding Antiferromagnetic and Ligand Field Effects on Spin Crossover in a Triple-Decker Dimeric Cr(II) Complex.

Two possible explanations for the temperature dependence of spin-crossover (SCO) behavior in the dimeric triple-decker Cr(II) complex ([(η5-C5Me5)Cr(µ2:η5-P5)Cr(η5-C5Me5)]+) have been offered. One invokes variations in antiferromagnetic interactions between the two Cr(II) ions, whereas the other posits the development of a strong ligand-field effect favoring the low-spin ground state. We perform multireference electronic structure calculations based on the multiconfiguration pair-density functional theory to resolve these effects. We find quintet, triplet, and singlet electronic ground states, respectively, for the experimental geometries at high, intermediate, and low temperatures. The ground-state transition from quintet to triplet at an intermediate temperature derives from increased antiferromagnetic interactions between the two Cr(II) ions. By contrast, the ground-state transition from triplet to singlet at low temperature can be attributed to increased ligand-field effects, which dominate with continued variations in antiferromagnetic coupling. This study provides quantitative detail for the degree to which these two effects can act in concert for the observed SCO behavior in this complex and others subject to temperature-dependent variations in geometry.

Multiconfiguration Pair-Density Functional Theory for Vertical Excitation Energies in Actinide Molecules.

Modeling actinides with electronic structure theories is challenging because these systems present a strong ligand field and metal-ligand covalency. We systematically investigate the effectiveness of pair-density functional theory (PDFT) for the calculation of vertical excitation energies in An(III), [AnIIICl6]3-, and [AnVIO2]2+ (An = U, Np, Pu, and Am). We compare the performance of PDFT, hybrid PDFT, and multistate PDFT with traditional active-space methods followed by perturbation theory, like multistate CASPT2, and with experimental data. Overall, multistate PDFT gives quantitative agreement with multistate CASPT2 at a significantly reduced computational cost.

Variational Active Space Selection with Multiconfiguration Pair-Density Functional Theory.

The selection of an adequate set of active orbitals for modeling strongly correlated electronic states is difficult to automate because it is highly dependent on the states and molecule of interest. Although many approaches have shown some success, no single approach has worked well in all cases. In light of this, we present the "discrete variational selection" (DVS) approach to active space selection, in which one generates multiple trial wave functions from a diverse set of systematically constructed active spaces and then selects between these wave functions variationally. We apply this DVS approach to 207 vertical excitations of small-to-medium-sized organic and inorganic molecules (with 3 to 18 atoms) in the QUESTDB database by (i) constructing various sets of active space orbitals through diagonalization of parametrized operators and (ii) choosing the result with the lowest average energy among the states of interest. This approach proves ineffective when variationally selecting between wave functions using the density matrix renormalization group (DMRG) or complete active space self-consistent field (CASSCF) energy but is able to provide good results when variationally selecting between wave functions using the energy of the translated PBE (tPBE) functional from multiconfiguration pair-density functional theory (MC-PDFT). Applying this DVS-tPBE approach to selection among state-averaged DMRG wave functions, we obtain a mean unsigned error of only 0.17 eV using hybrid MC-PDFT. This result matches that of our previous benchmark without the need to filter out poor active spaces and with no further orbital optimization following active space selection of the SA-DMRG wave functions. Furthermore, we find that DVS-tPBE is able to robustly and effectively select between the new SA-DMRG wave functions and our previous SA-CASSCF results.

Linearized Pair-Density Functional Theory for Vertical Excitation Energies.

Multiconfiguration pair-density functional theory (MC-PDFT) is a computationally efficient method that computes the energies of electronic states in a state specific or state average framework via an on-top functional. However, MC-PDFT does not include state interaction among these states since the final energies do not come from the diagonalization of an effective model-space Hamiltonian. Recently, multistate extensions such as linearized PDFT (L-PDFT) have been developed to accurately model the potentials near conical intersections and avoided crossings. However, there has not been any systematic study evaluating their performance for predicting vertical excitations at the equilibrium geometry of a molecule, when the excited states are generally well separated. In this paper, we report the performance of L-PDFT on the extensive QUESTDB data set of vertical excitations using a database of automatically selected active spaces. We show that L-PDFT performs well on all these excitations and successfully reproduces the performance of MC-PDFT. These results further demonstrate the potential of L-PDFT, as its scaling is constant with the number of states included in the state-average manifold, whereas MC-PDFT scales linearly in this regard.

Optical Properties of Neutral F Centers in Bulk MgO with Density Matrix Embedding.

The optical spectra of neutral oxygen vacancies (F0 centers) in the bulk MgO lattice are investigated using density matrix embedding theory. The impurity Hamiltonian is solved with the complete active space self-consistent field and second-order n-electron valence state perturbation theory (NEVPT2-DMET) multireference methods. To estimate defect-localized vertical excitation energies at the nonembedding and thermodynamic limits, a double extrapolation scheme is employed. The extrapolated NEVPT2-DMET vertical excitation energy value of 5.24 eV agrees well with the experimental absorption maxima at 5.03 eV, whereas the excitation energy value of 2.89 eV at the relaxed triplet defect-localized state geometry overestimates the experimental emission at 2.4 eV by only nearly 0.5 eV, indicating the involvement of the triplet-singlet decay pathway.

A Porous Crystalline Nitrone-Linked Covalent Organic Framework.

Herein, we report the synthesis of a nitrone-linked covalent organic framework, COF-115, by combining N, N', N', N'''-(ethene-1, 1, 2, 2-tetrayltetrakis(benzene-4, 1-diyl))tetrakis(hydroxylamine) and terephthaladehyde via a polycondensation reaction. The formation of the nitrone functionality was confirmed by solid-state 13 C multi cross-polarization magic angle spinning NMR spectroscopy of the 13 C-isotope-labeled COF-115 and Fourier-transform infrared spectroscopy. The permanent porosity of COF-115 was evaluated through low-pressure N2 , CO2 , and H2 sorption experiments. Water vapor and carbon dioxide sorption analysis of COF-115 and the isoreticular imine-linked COF indicated a superior potential of N-oxide-based porous materials for atmospheric water harvesting and CO2 capture applications. Density functional theory calculations provided valuable insights into the difference between the adsorption properties of these COFs. Lastly, photoinduced rearrangement of COF-115 to the associated amide-linked material was successfully demonstrated.

Density Matrix Embedding Using Multiconfiguration Pair-Density Functional Theory.

We present a quantum embedding method for ground and excited states of extended systems that uses multiconfiguration pair-density functional theory (MC-PDFT) with densities provided by periodic density matrix embedding theory (pDMET). We compute local excitations in oxygen mono- and divacancies on a magnesium oxide (100) surface and find absolute deviations within 0.05 eV between pDMET using the MC-PDFT, denoted as pDME-PDFT, and the more expensive, nonembedded MC-PDFT approach. We further use pDME-PDFT to calculate local excitations in larger supercells for the monovacancy defect, for which the use of nonembedded MC-PDFT is prohibitively costly.