Where Does the Density Localize in the Solid State? Divergent Behavior for Hybrids and DFT+U

Approximate density functional theory (DFT) is widely used in chemistry and physics, despite delocalization errors that affect energetic and density properties. DFT+U (i.e., semilocal DFT augmented with a Hubbard U correction) and global hybrid functionals are two commonly employed practical methods to address delocalization error. Recent work demonstrated that in transition-metal complexes both methods localize density away from the metal and onto surrounding ligands, regardless of metal or ligand identity. In this work, we compare density localization trends with DFT+U and global hybrids on a diverse set of 34 transition-metal-containing solids with varying magnetic state, electron configuration and valence shell, and coordinating-atom orbital diffuseness (i.e., O, S, Se). We also study open-framework solids in which the metal is coordinated by molecular ligands, i.e., MCO₃, M­(OH)₂, M­(NCNH)₂, K₃M­(CN)₆ (M = V–Ni). As in transition-metal complexes, incorporation of Hartree–Fock exchange consistently localizes density away from the metal, but DFT+U exhibits diverging behavior, localizing density (i) onto the metal in low-spin and late transition metals and (ii) away from the metal in other cases in agreement with hybrids. To isolate the effect of the crystal environment, we extract molecular analogues from open-framework transition-metal solids and observe consistent localization of the density away from the metal in all cases with both DFT+U and hybrid exchange. These observations highlight the limited applicability of trends established for functional tuning on transition-metal complexes even to equivalent coordination environments in the solid state

Electronic Structure Origins of Surface-Dependent Growth in III-V Quantum Dots

<div><div><div><p>Indium phosphide quantum dots (QDs) have emerged as a primary candidate to replace more toxic II-VI CdSe QDs, but production of high-quality III-V InP QDs with targeted properties requires a better understanding of their growth. We develop a first-principles-derived model that unifies InP QD formation from isolated precursor and early stage cluster reactions to 1.3-nm magic size clusters, and we rationalize experimentally-observed properties of full sized > 3 nm QDs. Our first-principles study on realistic QD models reveals large surface-dependent reactivity for all elementary growth process steps including In-ligand bond cleavage and P precursor addition. These thermodynamic trends correlate well to kinetic properties at all stages of growth, indicating the presence of labile and stable spots on cluster and QD surfaces. Correlation of electronic or geometric properties to energetics identifies surprising sources for these variations: short In...In separation on the surface produces the most reactive sites, at odds with conventional understanding of strain (i.e., separation) in bulk metallic surfaces increasing reactivity and models for ionic II-VI QD growth. These differences are rationalized by the covalent, directional nature of bonding in III-V QDs and explained by bond order metrics derived directly from the In-O bond density. The unique constraints of carboxylate and P precursor bonding to In atoms rationalizes why all sizes of InP clusters and QDs are In-rich but become less so as QDs mature. These observations support the development of alternate growth recipes that take into account strong surface-dependence of kinetics as well as the shapes of both In and P precursors to control both kinetics and surface morphology in III-V QDs.</p></div></div></div

When Is Ligand p<i>K</i>_a a Good Descriptor for Catalyst Energetics? In Search of Optimal CO₂ Hydration Catalysts

We present a detailed study of nearly 70 Zn molecular catalysts for CO₂ hydration from four diverse ligand classes ranging from well-studied carbonic anhydrase mimics (e.g., cyclen) to new structures we obtain by leveraging diverse hits from large organic libraries. Using microkinetic analysis and establishing linear free energy relationships, we confirm that turnover is sensitive to the relative thermodynamic stability of reactive hydroxyl and bound bicarbonate moieties. We observe a wide range of thermodynamic stabilities for these intermediates, showing up to 6 kcal/mol improvement over well-studied cyclen catalysts. We observe a good correlation between the p<i>K</i>_a of the Zn–OH₂ moiety and the resulting relative stability of hydroxyl moieties over bicarbonate, which may be rationalized by the dominant effect of the difference in higher Zn−OH bond order in comparison to weaker bonding in bicarbonate and water. A direct relationship is identified between isolated organic ligand p<i>K</i>_a and the p<i>K</i>_a of a bound water molecule on the catalyst. Thus, organic ligand p<i>K</i>_a, which is intuitive, easy to compute or tabulate, and much less sensitive to electronic structure method choice than whole-catalyst properties, is a good quantitative descriptor for predicting the effect of through-bond electronic effects on relative CO₂ hydration energetics. We expect this to be applicable to other reactions where is it essential to stabilize turnover-determining hydroxyl species with respect to more weakly bound moieties. Finally, we note exceptions for rigid ligands (e.g., porphyrins) that are observed to preferentially stabilize hydroxyl over bicarbonate without reducing p<i>K</i>_a values as substantially. We expect the strategy outlined here, to (i) curate diverse ligands from large organic libraries and (ii) identify when ligand-only properties can determine catalyst energetics, to be broadly useful for both experimental and computational catalyst design

When Is Ligand p<i>K</i>_a a Good Descriptor for Catalyst Energetics? In Search of Optimal CO₂ Hydration Catalysts

We present a detailed study of nearly 70 Zn molecular catalysts for CO₂ hydration from four diverse ligand classes ranging from well-studied carbonic anhydrase mimics (e.g., cyclen) to new structures we obtain by leveraging diverse hits from large organic libraries. Using microkinetic analysis and establishing linear free energy relationships, we confirm that turnover is sensitive to the relative thermodynamic stability of reactive hydroxyl and bound bicarbonate moieties. We observe a wide range of thermodynamic stabilities for these intermediates, showing up to 6 kcal/mol improvement over well-studied cyclen catalysts. We observe a good correlation between the p<i>K</i>_a of the Zn–OH₂ moiety and the resulting relative stability of hydroxyl moieties over bicarbonate, which may be rationalized by the dominant effect of the difference in higher Zn−OH bond order in comparison to weaker bonding in bicarbonate and water. A direct relationship is identified between isolated organic ligand p<i>K</i>_a and the p<i>K</i>_a of a bound water molecule on the catalyst. Thus, organic ligand p<i>K</i>_a, which is intuitive, easy to compute or tabulate, and much less sensitive to electronic structure method choice than whole-catalyst properties, is a good quantitative descriptor for predicting the effect of through-bond electronic effects on relative CO₂ hydration energetics. We expect this to be applicable to other reactions where is it essential to stabilize turnover-determining hydroxyl species with respect to more weakly bound moieties. Finally, we note exceptions for rigid ligands (e.g., porphyrins) that are observed to preferentially stabilize hydroxyl over bicarbonate without reducing p<i>K</i>_a values as substantially. We expect the strategy outlined here, to (i) curate diverse ligands from large organic libraries and (ii) identify when ligand-only properties can determine catalyst energetics, to be broadly useful for both experimental and computational catalyst design

Depolymerization Pathways for Branching Lignin Spirodienone Units Revealed with <i>ab Initio</i> Steered Molecular Dynamics

Lignocellulosic biomass is an abundant, rich source of aromatic compounds, but direct utilization of raw lignin has been hampered by both the high heterogeneity and variability of linking bonds in this biopolymer. <i>Ab initio</i> steered molecular dynamics (AISMD) has emerged both as a fruitful direct computational screening approach to identify products that occur through mechanical depolymerization (i.e., in sonication or ball-milling) and as a sampling approach. By varying the direction of force and sampling over 750 AISMD trajectories, we identify numerous possible pathways through which lignin depolymerization may occur in pyrolysis or through catalytic depolymerization as well. Here, we present eight unique major depolymerization pathways discovered via AISMD for the recently characterized spirodienone lignin branching linkage that may comprise around 10% weight of all lignin in some softwoods. We extract representative trajectories from AISMD and carry out reaction pathway analysis to identify energetically favorable pathways for lignin depolymerization. Importantly, we identify dynamical effects that could not be observed through more traditional calculations of bond dissociation energies. Such effects include thermodynamically favorable recovery of aromaticity in the dienone ring that leads to near-barrierless subsequent ether cleavage and hydrogen-bonding effects that stabilize newly formed radicals. Some of the most stable spirodienone fragments that reside at most 1 eV above the reactant structure are formed with only 2 eV barriers for C–C bond cleavage, suggesting key targets for catalyst design to drive targeted depolymerization of lignin

Understanding and Breaking Scaling Relations in Single-Site Catalysis: Methane to Methanol Conversion by Fe^IVO

Computational high-throughput screening is an essential tool for catalyst design, limited primarily by the efficiency with which accurate predictions can be made. In bulk heterogeneous catalysis, linear free energy relationships (LFERs) have been extensively developed to relate elementary step activation energies, and thus overall catalytic activity, back to the adsorption energies of key intermediates, dramatically reducing the computational cost of screening. The applicability of these LFERs to single-site catalysts remains unclear, owing to the directional, covalent metal–ligand bonds and the broader chemical space of accessible ligand scaffolds. Through a computational screen of nearly 500 model Fe­(II) complexes for CH₄ hydroxylation, we observe that (1) tuning ligand field strength yields LFERs by comparably shifting energetics of the metal 3d levels that govern the stability of different intermediates and (2) distortion of the metal coordination geometry breaks these LFERs by increasing the splitting between the d_<i>xz</i>/d_<i>yz</i> and d_<i>z</i>² metal states that govern reactivity. Thus, in single-site catalysts, low Brønsted–Evans–Polanyi slopes for oxo formation, which would limit peak turnover frequency achievable through ligand field tuning alone, can be overcome through structural distortions achievable in experimentally characterized compounds. Observations from this screen also motivate the placement of strong HB donors in targeted positions as a scaffold-agnostic strategy for further activity improvement. More generally, our findings motivate broader variation of coordination geometries in reactivity studies with single-site catalysts

Understanding and Breaking Scaling Relations in Single-Site Catalysis: Methane to Methanol Conversion by Fe^IVO

Computational high-throughput screening is an essential tool for catalyst design, limited primarily by the efficiency with which accurate predictions can be made. In bulk heterogeneous catalysis, linear free energy relationships (LFERs) have been extensively developed to relate elementary step activation energies, and thus overall catalytic activity, back to the adsorption energies of key intermediates, dramatically reducing the computational cost of screening. The applicability of these LFERs to single-site catalysts remains unclear, owing to the directional, covalent metal–ligand bonds and the broader chemical space of accessible ligand scaffolds. Through a computational screen of nearly 500 model Fe­(II) complexes for CH₄ hydroxylation, we observe that (1) tuning ligand field strength yields LFERs by comparably shifting energetics of the metal 3d levels that govern the stability of different intermediates and (2) distortion of the metal coordination geometry breaks these LFERs by increasing the splitting between the d_<i>xz</i>/d_<i>yz</i> and d_<i>z</i>² metal states that govern reactivity. Thus, in single-site catalysts, low Brønsted–Evans–Polanyi slopes for oxo formation, which would limit peak turnover frequency achievable through ligand field tuning alone, can be overcome through structural distortions achievable in experimentally characterized compounds. Observations from this screen also motivate the placement of strong HB donors in targeted positions as a scaffold-agnostic strategy for further activity improvement. More generally, our findings motivate broader variation of coordination geometries in reactivity studies with single-site catalysts

Unifying Exchange Sensitivity in Transition-Metal Spin-State Ordering and Catalysis through Bond Valence Metrics

Accurate predictions of spin-state ordering, reaction energetics, and barrier heights are critical for the computational discovery of open-shell transition-metal (TM) catalysts. Semilocal approximations in density functional theory, such as the generalized gradient approximation (GGA), suffer from delocalization error that causes them to overstabilize strongly bonded states. Descriptions of energetics and bonding are often improved by introducing a fraction of exact exchange (e.g., erroneous low-spin GGA ground states are instead correctly predicted as high-spin with a hybrid functional). The degree of spin-splitting sensitivity to exchange can be understood based on the chemical composition of the complex, but the effect of exchange on reaction energetics within a single spin state is less well-established. Across a number of model iron complexes, we observe strong exchange sensitivities of reaction barriers and energies that are of the same magnitude as those for spin splitting energies. We rationalize trends in both reaction and spin energetics by introducing a measure of delocalization, the bond valence of the metal–ligand bonds in each complex. The bond valence thus represents a simple-to-compute property that unifies understanding of exchange sensitivity for catalytic properties and spin-state ordering in TM complexes. Close agreement of the resulting per-metal–organic-bond sensitivity estimates, together with failure of alternative descriptors demonstrates the utility of the bond valence as a robust descriptor of how differences in metal–ligand delocalization produce differing relative energetics with exchange tuning. Our unified description explains the overall effect of exact exchange tuning on the paradigmatic two-state FeO⁺/CH₄ reaction that combines challenges of spin-state and reactivity predictions. This new descriptor-sensitivity relationship provides a path to quantifying how predictions in transition-metal complex screening are sensitive to the method used

Ligand-Field-Dependent Behavior of Meta-GGA Exchange in Transition-Metal Complex Spin-State Ordering

Prediction of spin-state ordering in transition metal complexes is essential for understanding catalytic activity and designing functional materials. Semilocal approximations in density functional theory, such as the generalized-gradient approximation (GGA), suffer from several errors including delocalization error that give rise to systematic bias for more covalently bound low-spin electronic states. Incorporation of exact exchange is known to counteract this bias, instead favoring high-spin states, in a manner that has recently been identified to be strongly ligand-field dependent. In this work, we introduce a tuning strategy to identify the effect of incorporating the Laplacian of the density (i.e., a meta-GGA) in exchange on spin-state ordering. We employ a diverse test set of M­(II) and M­(III) first-row transition metal ions from Ti to Cu as well as octahedral complexes of these ions with ligands of increasing field strength (i.e., H₂O, NH₃, and CO). We show that the sensitivity of spin-state ordering to meta-GGA exchange is highly ligand-field dependent, stabilizing high-spin states in strong-field (i.e., CO) cases and stabilizing low-spin states in weak-field (i.e., H₂O, NH₃, and isolated ions) cases. This diverging behavior leads to generally improved treatment of isolated ions and strong field complexes over a standard GGA but worsened treatment for the hexa-aqua or hexa-ammine complexes. These observations highlight the sensitivity of functional performance to subtle changes in chemical bonding

How Do Differences in Electronic Structure Affect the Use of Vanadium Intermediates as Mimics in Nonheme Iron Hydroxylases?

We study active-site models of nonheme iron hydroxylases and their vanadium-based mimics using density functional theory to determine if vanadyl is a faithful structural mimic. We identify crucial structural and energetic differences between ferryl and vanadyl isomers owing to the differences in their ground electronic states, i.e., high spin (HS) for Fe and low spin (LS) for V. For the succinate cofactor bound to the ferryl intermediate, we predict facile interconversion between monodentate and bidentate coordination isomers for ferryl species but difficult rearrangement for vanadyl mimics. We study isomerization of the oxo intermediate between axial and equatorial positions and find the ferryl potential energy surface to be characterized by a large barrier of ca. 10 kcal/mol that is completely absent for the vanadyl mimic. This analysis reveals even starker contrasts between Fe and V in hydroxylases than those observed for this metal substitution in nonheme halogenases. Analysis of the relative bond strengths of coordinating carboxylate ligands for Fe and V reveals that all of the ligands show stronger binding to V than Fe owing to the LS ground state of V in contrast to the HS ground state of Fe, highlighting the limitations of vanadyl mimics of native nonheme iron hydroxylases