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At least 1,189 records · Page 66

Quantifying Actinide–Carbon Bond Covalency in a Uranyl–Aryl Complex Utilizing Solution 13 C NMR Spectroscopy

Reaction of [UO 2 Cl 2 (THF) 2 ] 2 with in situ generated LiFmes (FmesH = 1,3,5-(CF 3 ) 3 C 6 H 3 ) in Et 2 O resulted in the formation of the uranyl aryl complexes [Li(THF) 3 ][UO 2 (Fmes) 3 ] ([Li(THF) 3 ][1]) and [Li(Et 2 O) 3 (THF)][UO 2 (Fmes) 3 ] ([Li(Et 2 O) 3 (THF)][1]) in good to moderate yields after crystallization from hexanes and Et 2 O, respectively. Both complexes were characterized by X-ray crystallography and NMR spectroscopy. DFT calculations reveal that the C ispo resonance in [1] – exhibits a deshielding of 51 ppm from spin–orbit coupling effects originating at uranium, which indicates an appreciable covalency in the U–C bonding interaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Reining in Radium for Nuclear Medicine: Extra-Large Chelator Development for an Extra-Large Ion

Targeted α therapy (TAT) of soft-tissue cancers using the α particle-emitting radionuclide 223 Ra holds great potential because of its favorable nuclear properties, adequate availability, and established clinical use for treating metastatic prostate cancer of the bone. Despite these advantages, the use of 223 Ra has been largely overshadowed by other α emitters due to its challenging chelation chemistry. A key criterion that needs to be met for a radionuclide to be used in TAT is its stable attachment to a targeting vector via a bifunctional chelator. The low charge density of Ra 2+ arising from its large ionic radius weakens its electrostatic binding interactions with chelators, leading to insufficient complex stability in vivo. In this study, we synthesized and evaluated macropa-XL as a novel chelator for 223 Ra. It bears a large 21-crown-7 macrocyclic core and two picolinate pendent groups, which we hypothesized would effectively saturate the large coordination sphere of the Ra 2+ ion. The structural chemistry of macropa-XL was first established with the nonradioactive Ba 2+ ion using X-ray diffraction and X-ray absorption spectroscopy, which revealed the formation of an 11-coordinate complex in a rare anti pendent-arm configuration. Subsequently, the stability constant of the [Ra(macropa-XL)] complex was determined via competitive cation exchange with 223 Ra and 224 Ra radiotracers and compared with that of macropa, the current state-of-the-art chelator for Ra 2+ . A moderate log K ML value of 8.12 was measured for [Ra(macropa-XL)], which is approximately 1.5 log K units lower than the stability constant of [Ra(macropa)]. This relative decrease in Ra 2+ complex stability for macropa-XL versus macropa was further probed using density functional theory calculations. Additionally, macropa-XL was radiolabeled with 223 Ra, and the kinetic stability of the resulting complex was evaluated in human serum. Furthermore, although macropa-XL could effectively bind 223 Ra under mild conditions, the complex appeared to be unstable to transchelation. Collectively, this study sheds additional light on the chelation chemistry of the exotic Ra 2+ ion and contributes to the small, but growing, number of chelator development efforts for 223 Ra-based TAT.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Rhenium-Sulfido and -Dithiolato Corroles: Reflections on Chalcophilicity

The high-temperature (~180 °C) reaction between free-base meso-triarylcorroles and Re 2 (CO) 10 , followed by exposure to PCl 3 and thiols (or elemental sulfur), affords rhenium-sulfido (ReS) corroles in 67-76% yields. The use of shorter reaction times, lower temperatures (~130 °C), and a dithiol (e.g., ethane-1,2-dithiol) also allows the isolation of rhenium-dithiolato corroles, presumptive intermediates on the path to ReS corroles. The ReS corroles exhibit high thermal stability and two reversible oxidations and reductions in their cyclic voltammograms, with redox potentials nearly identical to those observed for analogous ReO corroles. The electrochemical HOMO-LUMO gaps of the complexes, at 2.2 eV, are consistent with ligand-centered oxidation and reduction. The UV-vis spectra of ReS corroles, on the other hand, differ significantly from those of their ReO counterparts. Scalar-relativistic DFT calculations suggest that this difference reflects low-energy LUMO+2 and LUMO+3 levels, consisting of Re-S π-antibonding interactions; the ReO corroles, in contrast, exhibit a larger LUMO+1/LUMO+2 gap, as expected for a relatively classical Gouterman-type metalloporphyrin analogue. The high stability of ReS corroles is consistent with geochemists' view of rhenium as a moderately chalcophilic element (i.e., one that partitions into sulfide melts) as well as with a recent quantitative analysis of thiophilicity, which indicates that rhenium's oxophilicity and thiophilicity are essentially evenly balanced.

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Insights into the Complexation of Actinides by Diethylenetriaminepentaacetic Acid from Characterization of the Americium(III) Complex

Diethylenetriaminepentaacetic acid (DTPA) is a frequently used chelator in the nuclear and medical industries, especially for the complexation of trivalent actinides. However, structural data on these complexes in the solid-state have long remained elusive. Herein, a detailed structural analysis of the presented crystal structures of [C(NH 2 ) 3 ] 4 [Nd(DTPA)] 2 · n H 2 O and [C(NH 2 ) 3 ] 4 [Am(DTPA)] 2 · n H 2 O, where [C(NH 2 ) 3 ] + is guanidinium, details the subtle differences in the Lewis acidity between a lanthanide/actinide pair of similar ionic sizes. Contractions in nitrogen–metal bond lengths between neodymium(III) and americium(III) were observed, while the metal–oxygen bonds remained relatively consistent, highlighting the marginal favorability for actinide complexation over the lanthanides with moderately soft N-donors. Spectroscopic analysis shows significant splitting of many transitions and relatively strong electronic interactions with traditionally low-intensity transitions in the americium complex, as is demonstrated in the 7 F 0 → 7 F 5 transitions. Pressure-induced spectroscopic analysis showed surprisingly little effect on the americium complex, with 5 f →5 f transitions either not shifting or marginally shifting from 2 to 3 nm at 11.93 ± 0.06 GPa─atypical of a soft, N-donor americium complex under pressure. Finally, large voids occupied by water molecules in between the complexes within the crystal structure may be responsible for the lack of pressure response in the 5 f →5 f transitions.

absorption spectroscopy↗

Oxygen Defect Configurations in Single-Phase UO 2.15

Hyperstoichiometric UO 2.15 was characterized by neutron total scattering at high temperature in the single-phase UO 2+x region of the U/O phase diagram. The diffraction data confirmed a single-phase fluorite structure at high temperature. Analysis of the short-range data showed that the same structural model does not fit the pair distribution functions well. Instead, structural models containing specific configurations of oxygen defect clusters best represent the local atomic arrangement. In conclusion, prevalent defect clusters previously proposed were fit to the experimental data, and moderately distorted oxygen cuboctahedra hypothesized by recent molecular dynamics simulations fit the data most accurately.

neutron pair-distribution function analysis↗

Magnetosynthesis Effect on the Structure and Ground State of Cu 2+ -Based Antiferromagnets

Synthetic variables can have an outsized influence on the crystal structure and magnetic properties of a material, particularly those of quantum materials. In this work, we investigate the impact of synthesis under a magnetic field (magnetosynthesis) on the crystal structure and magnetic properties of several Cu 2+ (S = 1/2)-based materials with antiferromagnetic interactions and varying levels of magnetic frustration, from simple antiferromagnets to a quantum spin liquid. Here, we develop methods to apply small (0.09–0.37 T) magnetic fields during low-temperature hydrothermal, evaporative, and rehydration syntheses of the simple antiferromagnet CuCl 2 ·2H 2 O, the canted antiferromagnet (Cu,Zn) 3 Cl 4 (OH) 2 ·2H 2 O, the frustrated and canted antiferromagnet atacamite Cu 2 (OH) 3 Cl, and the highly frustrated quantum spin liquid herbertsmithite Cu 3 Zn(OH) 6 Cl 2 . We report the first single-crystal X-ray structural determination of the Cu 3 Cl 4 (OH) 2 ·2H 2 O structure type and probe the stability of this phase both experimentally and computationally. Atacamite Cu 2 (OH) 3 Cl synthesized under a 0.19 T field experiences a 0.15 K (∼3%) decrease in its Néel transition temperature. This result suggests that magnetosynthesis with small applied fields may have a very subtle influence upon the magnetic properties of moderately magnetically frustrated 3 d materials.

36 MATERIALS SCIENCE↗

Generalizing Reversible Triplet–Triplet Energy Transfer as a Strategy to Increase Excited-State Lifetime in Copper(I) Charge-Transfer Chromophores

In this work, we generalize reversible triplet–triplet energy transfer (TTET) as a strategy to achieve long (μs range) excited-state lifetimes in copper(I) photosensitizers of the general formula Cu(RNacNac)(CN-Ar) (RNacNac is a substituted β-diketiminate and CN-Ar is an aryl isocyanide). Six new complexes are presented where the isocyanide is substituted with a triplet–acceptor moiety─anthracene, naphthalene, or phenanthrene. In-depth photophysical analysis reveals that energetic matching of the charge-transfer ( 3 CT) and acceptor-localized 3 (π→π*) states is key to achieving long triplet excited-state lifetimes via reversible TTET. With 2-isocyanoanthracene as the acceptor ligand, 3 CT and 3(π→π*) are not energetically proximate, and irreversible quenching of 3 CT occurs. With a small 0.1–0.2 eV gap between the two triplet states, luminescence originates from the 3 CT state with a moderate excited-state lifetime of 250 or 283 ns observed. As key to the success of this approach, we demonstrate that altering the N-substituent on the RNacNac ligand modulates the energy of the 3 CT state, giving three complexes where the 3 CT and 3 (π→π*) energies are perfectly matched and the excited-state lifetimes are much longer, spanning 1.9–2.7 μs. As such, the key lesson of this work is that long triplet-state lifetimes in these compounds can be achieved by proper “mixing and matching” of the RNacNac ligand, which influences the 3 CT energy, and the triplet acceptor group which dictates the energy of the 3 (π→π*) state.

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Molecular Simulations Probing the Adsorption and Diffusion of Ammonia, Nitrogen, Hydrogen, and Their Mixtures in Bulk MFI Zeolite and MFI Nanosheets at High Temperature and Pressure

Recent advances in the synthesis of MFI zeolite nanosheets have led to highly selective membranes that are promising candidates for small-scale ammonia separation from ammonia/nitrogen/hydrogen mixtures in distributed green ammonia production plants. Using force-field-based molecular simulations, we evaluate the performance of bulk all-silica MFI zeolite and a 3 nm thick all-silica MFI nanosheet for ammonia/nitrogen/hydrogen separations at moderate temperature and pressure conditions (T = 373 K, p = 5 bar) as well as conditions relevant for a membrane-based reactor–separator process (T = 523 or 623 K, p = 80 bar). Isobaric–isothermal Gibbs ensemble Monte Carlo (GEMC) simulations were carried out to understand the selective adsorption behavior for these mixtures. Molecular dynamics simulations in the canonical ensemble were performed to examine the transport behavior of ammonia in a mixture with nitrogen or hydrogen at loadings obtained from the GEMC simulations. Our results show that both bulk MFI and the nanosheet with explicit surface silanols are highly selective toward ammonia adsorption, but the adsorption selectivity decreases by factors of 4 and 10 for ammonia/nitrogen and ammonia/hydrogen mixtures as the temperature is increased from 373 to 623 K. Conversely, the diffusion selectivities toward ammonia are more favorable at process-relevant temperatures and for the MFI nanosheet. Here, at T = 523 K and p = 80 bar, our simulations predict overall separation factors of 3.8 ± 0.2 and 4.5 ± 0.3 for ammonia/nitrogen and ammonia/hydrogen mixtures, respectively, in the bulk MFI zeolite, and separation factors of 8.6 ± 0.4 and 12.5 ± 0.8, respectively, for the MFI nanosheet.

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How Accurate Are Approximate Density Functionals for Noncovalent Interaction of Very Large Molecular Systems?

Noncovalent intermolecular interactions are very important in many research areas. Therefore, it is vital to understand the extent to which approximate density functionals give a proper description of noncovalent interactions. Previous research has demonstrated that some approximate density functionals can predict usefully accurate interaction energies for many noncovalent systems; however, most of that work is limited to small and moderate-sized molecules. Very recently though, accurate benchmarks have become available for some very large molecules. Here, the present work applies 21 approximate density functionals to compute the binding energies of seven large molecular systems that have a number of atoms ranging from 200 to 910. The results are judged by comparison to the recently published CIM-DLPNO-CCSD(T) results, which are assumed to provide a reliable benchmark. The five most accurate methods among those tested are found to be PW6B95-D4, PW6B95-D3(BJ), revM11, M06-L, and MN15.

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Dipole Moment Calculations Using Multiconfiguration Pair-Density Functional Theory and Hybrid Multiconfiguration Pair-Density Functional Theory

The dipole moment is the molecular property that most directly indicates molecular polarity. The accuracy of computed dipole moments depends strongly on the quality of the calculated electron density, and the breakdown of single-reference methods for strongly correlated systems can lead to poor predictions of the dipole moments in those cases. Here, we derive the analytical expression for obtaining the electric dipole moment by multiconfiguration pair density functional theory (MCPDFT), and we assess the accuracy of MC-PDFT for predicting dipole moments at equilibrium and nonequilibrium geometries. We show that MC-PDFT dipole moment curves have reasonable behavior even for stretched geometries, and they significantly improve upon the CASSCF results by capturing more electron correlation. Herein, the analysis of a dataset consisting of 18 first-row transition metal diatomics and 6 main-group polyatomic molecules with multireference character suggests that MC-PDFT and its hybrid extension (HMC-PDFT) perform comparably to CASPT2 and MRCISD+Q methods and have a mean unsigned deviation of 0.2–0.3 D with respect to the best available dipole moment reference values. We explored the dependence of the predicted dipole moments upon the choice of the on-top density functional and active space, and we recommend the tPBE and hybrid tPBE0 on-top choices for the functionals combined with the moderate correlated participating orbital scheme for selecting the active space. With these choices, the mean unsigned deviations (in debyes) of the calculated equilibrium dipole moments from the best estimates are 0.77 for CASSCF, 0.29 for MC-PDFT, 0.24 for HMCPDFT, 0.28 for CASPT2, and 0.25 for MRCISD+Q. These results are encouraging because the computational cost of MC-PDFT or HMC-PDFT is largely reduced compared to the CASPT2 and MRCISD+Q methods.

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Optimized Quantum Phase Estimation for Simulating Electronic States in Various Energy Regimes

While quantum algorithms for simulation exhibit better asymptotic scaling than their classical counterparts, they currently cannot be implemented on real-world devices. Instead, chemists and computer scientists rely on costly classical simulations of these quantum algorithms. In particular, the quantum phase estimation (QPE) algorithm is among several approaches that have attracted much attention in recent years for its genuine quantum character. However, it is memory-intensive to simulate and intractable for moderate system sizes. Herein, this paper discusses the performance and applicability of QPESIM, a new simulation of the QPE algorithm designed to take advantage of modest computational resources. In particular, we demonstrate the versatility of QPESIM in simulating various electronic states by examining the ground and core-level states of H 2 O. For these states, we also discuss the effect of the active-space size on the quality of the calculated energies. For the high-energy core-level states, we demonstrate that new QPE simulations for active spaces defined by 15 active orbitals significantly reduce the errors in core-level excitation energies compared to earlier QPE simulations using smaller active spaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Open-Shell Tensor Hypercontraction

The extension of least-squares tensor hypercontracted second- and third-order Møller–Plesset perturbation theory (LS-THC-MP2 and LS-THC-MP3) to open-shell systems is an important development due to the scaling reduction afforded by THC and the ubiquity of molecular ions, radicals, and other open-shell reactive species. The complexity of wavefunction-based quantum-chemical methods such as Møller–Plesset and coupled cluster theory is reflected in the steep scaling of the computational costs with the molecular size. The least-squares tensor hypercontraction (LS-THC) method is an efficient, single-step factorization for the two-electron integral tensor but can also be used to factorize the double excitation amplitudes, leading to significant scaling reduction. Herein we extend this promising method to open-shell variants of LS-THC-MP2 and -MP3 by using diagrammatic techniques and explicit spin summation. The accuracy of the resulting methods for open-shell species is benchmarked on standard test systems such as regular alkanes as well as realistic systems involving bond breaking, radical stabilization, and other effects. We find that open-shell LS-THC-MPn methods exhibit errors highly comparable to those produced by closed-shell LS-THC-MPn and are highly insensitive to particular chemical interactions, geometries, or even moderate spin contamination.

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Even Faster Exact Exchange for Solids via Tensor Hypercontraction

Hybrid density functional theory (DFT) remains intractable for large periodic systems due to the demanding computational cost of exact exchange. We apply the tensor hypercontraction (THC) (or interpolative separable density fitting) approximation to periodic hybrid DFT calculations with Gaussian-type orbitals using the Gaussian plane wave approach. This is done to lower the computational scaling with respect to the number of basis functions (N) and k-points (N k ) at a fixed system size. Additionally, we propose an algorithm to fit only occupied orbital products via THC (i.e., a set of points, N ISDF ) to further reduce computation time and memory usage. This algorithm has linear scaling cost with k-points, no explicit dependence of N ISDF on basis set size, and overall cubic scaling with unit cell size. Significant speedups and reduced memory usage may be obtained for moderately sized k-point meshes, with additional gains for large k-point meshes. Adequate accuracy can be obtained using THC-oo-K for self-consistent calculations. In conclusion, we perform illustrative hybrid density function theory calculations on the benzene crystal in the basis set and thermodynamic limits to highlight the utility of this algorithm.

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Static Subspace Approximation for Random Phase Approximation Correlation Energies: Applications to Materials for Catalysis and Electrochemistry

Modeling complex materials using high-fidelity, ab initio methods at low cost is a fundamental goal for quantum chemical software packages. The GW approximation and random phase approximation (RPA) provide a unified description of both electronic structure and total energies using the same physics in a many-body perturbative approach that can be more accurate than generalized-gradient density functional theory (DFT) methods. However, GW/RPA implementations have historically been limited to either specific materials classes or application toward small chemical systems. Here, the static subspace approximation allows for reduced cost full-frequency GW/RPA calculations and has previously been benchmarked thoroughly for GW calculations. Here, we describe our approach to including partial occupations of electronic orbitals in full-frequency GW and RPA calculations for the study of electrocatalysts. We benchmarked RPA total energy calculations using the subspace approximation across a diverse test suite of materials for a variety of computational parameters. The benchmarking quantifies the impact of different extrapolation procedures for representing the static polarizability at infinite screened cutoff, and shows that using screened cutoffs above 20-25 Ryd result in diminishing accuracy returns for predicting RPA total energies. Additionally, for moderately sized electrocatalytic models, 2-3 times fewer computational resources are used to compute RPA total energies by representing the static polarizability with 20-30% of the static subspace basis, with an error of approximately 0.01 eV or better in RPA adsorption energy calculations. Finally, we show that for these electrochemical models RPA can shift DFT adsorption energy shifts by up to 0.5 eV and that GW can frequently shift DFT eigenvalues of surface and adsorbate states by approximately 0.5-1 eV.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

CASSCF with Extremely Large Active Spaces Using the Adaptive Sampling Configuration Interaction Method

The complete active space self-consistent field (CASSCF) method is the principal approach employed for studying strongly correlated systems. However, exact CASSCF can only be performed on small active spaces of ~20 electrons in ~20 orbitals due to exponential growth in the computational cost. Here, we show that employing the Adaptive Sampling Configuration Interaction (ASCI) method as an approximate Full CI solver in the active space allows CASSCF-like calculations within chemical accuracy (<1 kcal/mol for relative energies) in active spaces with more than ~50 active electrons in ~50 active orbitals, significantly increasing the sizes of systems amenable to accurate multiconfigurational treatment. The main challenge with using any selected CI-based approximate CASSCF is the orbital optimization problem; they tend to exhibit large numbers of local minima in orbital space due to their lack of invariance to active–active rotations (in addition to the local minima that exist in exact CASSCF). We highlight methods that can avoid spurious local extrema as a practical solution to the orbital optimization problem. We employ ASCI-SCF to demonstrate a lack of polyradical character in moderately sized periacenes with up to 52 correlated electrons and compare against heat-bath CI on an iron porphyrin system with more than 40 correlated electrons.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Polarized, V-Shaped, and Conjoined Biscoumarins: From Lack of Dipole Moment Alignment to High Brightness

Eleven conjoined coumarins possessing a chromeno[3,4-c]chromene-6,7-dione skeleton have been synthesized via the reaction of electron-rich phenols with esters of coumarin-3-carboxylic acids, catalyzed by either Lewis acids or 4-dimethylaminopyridine. Furthermore, Michael-type addition to angular benzo[f]coumarins is possible, leading to conjugated helical systems. Arrangement of the electron-donating amino groups at diverse positions on this heterocyclic skeleton makes it possible to obtain π-expanded coumarins with emission either sensitive to, or entirely independent of, solvent polarity with large Stokes shifts. Computational studies have provided a rationale for moderate solvatochromic effects unveiling the lack of collinearity of the dipole moments in the ground and excited states. Depending on the functional groups present, the obtained dyes are highly polarized with dipole moments of ~14 D in the ground state and ~20–25 D in the excited state. Strong emission in nonpolar solvents, in spite of the inclusion of a NO 2 group, is rationalized by the fact that the intramolecular charge transfer introduced into these molecules is strong enough to suppress intersystem crossing yet weak enough to prevent the formation of dark twisted intramolecular charge transfer states. Photochemical transformation of the dye possessing a chromeno[3,4-c]pyridine-4,5-dione scaffold led to the formation of a spirocyclic benzo[g]coumarin.

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Machine Learning Prediction of the Experimental Transition Temperature of Fe(II) Spin-Crossover Complexes

Spin-crossover (SCO) complexes are materials that exhibit changes in the spin state in response to external stimuli, with potential applications in molecular electronics. It is challenging to know a priori how to design ligands to achieve the delicate balance of entropic and enthalpic contributions needed to tailor a transition temperature close to room temperature. Here, we leverage the SCO complexes from the previously curated SCO-95 data set [Vennelakanti et al. J. Chem. Phys. 159, 024120 (2023)] to train three machine learning (ML) models for transition temperature (T 1/2 ) prediction using graph-based revised autocorrelations as features. We perform feature selection using random forest-ranked recursive feature addition (RF-RFA) to identify the features essential to model transferability. Of the ML models considered, the full feature set RF and recursive feature addition RF models perform best, achieving moderate correlation to experimental T 1/2 values. We then compare ML T 1/2 predictions to those from three previously identified best-performing density functional approximations (DFAs) which accurately predict SCO behavior across SCO-95, finding that the ML models predict T 1/2 more accurately than the best-performing DFAs. In addition, we study ML model predictions for a set of 18 SCO complexes for which only estimated T 1/2 values are available. Upon excluding outliers from this set, the RF-RFA RF model shows a strong correlation to estimated T 1/2 values with a Pearson’s r of 0.82. In contrast, DFA-predicted T 1/2 values have large errors and show no correlation to estimated T 1/2 values over the same set of complexes. Overall, our study demonstrates slightly superior performance of ML models in comparison with some of the best-performing DFAs, and we expect ML models to improve further as larger data sets of SCO complexes are curated and become available for model training.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Improving Predictions of Spin-Crossover Complex Properties through DFT Calculations with a Local Hybrid Functional

We conducted a study on the performance of the local hybrid exchange-correlation functional PBE0r for a set of 95 experimentally-characterized iron spin crossover (SCO) complexes. The PBE0r functional is a variant of PBE0 where the exchange correction is restricted to on-site terms formulated within the basis of local orbitals. We determine the free parameters of the PBE0r functional against experimental data and other hybrid functionals. With a Hartree-Fock (HF) exchange factor of 4%, the PBE0r functional accurately reproduces the electronic and free energy trends predicted in prior DFT studies for these 95 complexes using the B3LYP functional. Larger values of HF exchange stabilize high-spin states. The PBE0r-predicted bond lengths tend to exceed the experimental bond lengths, and bond lengths are less sensitive to HF exchange. The predicted SCO transition temperatures T 1/2 from PBE0r correlate moderately with the experimental transition temperatures, showing a slight improvement compared to the previous modB3LYP-predicted T 1/2 . Furthermore, this study suggests the PBE0r functional as computationally cost-effective and offers the possibility of simulating larger complexes with accuracy comparable to other global hybrid functionals, provided the HF exchange parameter is carefully optimized.

25 ENERGY STORAGE↗