Accurate Modeling of Spin-State Energetics in Spin-Crossover Systems with Modern Density Functional Theory

Force-Activated Spin-Crossover in Fe2+ and Co2+ Transition Metal Mechanophores

Transition metal mechanophores exhibiting force-activated spin-crossover are attractive design targets, yet large-scale discovery of them has not been pursued due in large part to the time-consuming nature of trial-and-error experiments. Instead, we leverage density functional theory (DFT) and external force explicitly included (EFEI) modeling to study a set of 395 feasible Fe2+ and Co2+ mechanophore candidates with tridentate ligands that we curate from the Cambridge Structural Database. Among nitrogen-coordinating low-spin complexes, we observe the prevalence of spin crossover at moderate force, and we identify 155 Fe2+ and Co2+ spin-crossover mechanophores and derive their threshold force for low-spin to high-spin transition (FSCO). The calculations reveal strong correlations of FSCO with spin-splitting energies and coordination bond lengths, facilitating rapid prediction of FSCO using force-free DFT calculations. Then, among all Fe2+ and Co2+ spin-crossover mechanophores, we further identity 11 mechanophores that combine labile spin-crossover and good mechanical robustness that are thus predicted to be the most versatile for force-probing applications. We discover two classes of mer-symmetric complexes comprising specific heteroaromatic rings within extended π-conjugation that give rise to Fe2+ mechanophores with these characteristics. We expect the set of spin-crossover mechanophores, the design principles, and the computational approach to be useful in guiding the high-throughput discovery of transition metal mechanophores with diverse functionalities and broad applications, including mechanically activated catalysis.

Clusters of solvated ferrous ion in water-ammonia mixture: Structures and noncovalent interactions

The behavior of metal ions is commonly studied in pure solvent although, in our daily life, these metals are involved in mixtures of solvents. In the present study, we investigated structures, relative stabilities and temperature dependance of solvated ferrous ion in water-ammonia mixture solvent at 0K and at various temperatures ranging from 25K to 400K. All the calculations are performed at the MN15 level of theory associated with the aug-cc-pVDZ basis set. For deep understanding of binding patterns in solvated ferrous ion in water-ammonia mixture solvent, noncovalent interactions are presented based on the QTAIM analysis using AIMAll. Our results prove that the ferrous ion is more stable when it is solvated by ammonia instead of water. In addition, hydrogen bonds are weakened by the presence of ammonia molecules. The temperature dependence of the different obtained geometries indicates that from s=6 (s is the sum of water and ammonia molecules around the ferrous ion), when the number of water molecules is almost equal to that of ammonia, the structures with coordination number 5 are dominant. However, the coordination number is six when there are a maximum water molecules (rich water solution) or maximum ammonia molecules (rich ammonia solution) around the ferrous ion (for s≥6). The QTAIM analysis shows that there are two coordination bondings and four hydrogen bondings. Furthermore, it is found that the Fe2+⋯N coordination bondings are stronger than the Fe2+⋯O confirming that the ferrous ion prefers to be solvated by ammonia instead of water.

Quantum effects in CH activation with [Cu2O2]2+ complexes

We investigate the mechanism of primary alkane CH bond activation with dioxo-dicopper ([Cu2O2]2+) complexes, which serve as model catalysts for enzymes capable of activating CH bonds under mild conditions. As large H/D kinetic isotope effects (KIEs) are observed in enzymes and their synthetic mimics, we employ density functional theory along with variational transition-state theory with multidimensional tunneling to estimate reaction rate coefficients. By systematically varying ligand electrophilicity and substrate chain length, we examine trends in rate coefficients and kinetic isotope effects for the two proposed CH activation pathways - one-step oxo-insertion and two-step radical recombination. Although larger tunneling transmission coefficients are obtained for the radical pathway, the oxo-insertion mechanism yields higher rate coefficients on account of lower activation barriers. The question of the preferred CH activation mechanism, however, remains open: excellent agreement is observed between the predicted and known experimental KIE results for the radical pathway, while calculated Hammett slopes for the oxo-insertion pathway closely mirror experiments.

Stereoelectronic Tuning of Bioinspired Nonheme Iron(IV)-Oxo Species by Amide Groups in Primary and Secondary Coordination Spheres for Selective Oxygenation Reactions

Two mononuclear iron(II) complexes, [(6-amide2-BPMEN)FeII](OTf)2 (1) and [(6-amide-Me-BPMEN)FeII(OTf)](OTf) (2), supported by two BPMEN-derived (BPMEN = N1,N2-dimethyl-N1,N2-bis(pyridine-2-yl-methyl)ethane-1,2-diamine) ligands bearing one or two amide functionalities have been isolated to study their reactivity in the oxygenation of C-H and C═C bonds using isopropyl 2-iodoxybenzoate (iPr-IBX ester) as the oxidant. Both 1 and 2 contain six-coordinate high-spin iron(II) centers in the solid state and in solution. The 6-amide2-BPMEN ligand stabilizes an S = 1 iron(IV)-oxo intermediate, [(6-amide2-BPMEN)FeIV(O)]2+ (1A). The oxidant (1A) oxygenates the C-H and C═C bonds with a high selectivity. Oxidant 1A, upon treatment with 2,6-lutidine, is transformed into another oxidant [{(6-amide2-BPMEN)-(H)}FeIV(O)]+ (1B) through deprotonation of an amide group, resulting in a stronger equatorial ligand field and subsequent stabilization of the triplet ground state. In contrast, no iron-oxo species could be observed from complex 2 and [(6-Me2-BPMEN)FeII(OTf)2] (3) under similar experimental conditions. The iron(IV)-oxo oxidant 1A shows the highest A/K selectivity in cyclohexane oxidation and 3°/2° selectivity in adamantane oxidation reported for any synthetic nonheme iron(IV)-oxo complexes. Theoretical investigation reveals that the hydrogen bonding interaction between the -NH group of the noncoordinating amide group and Fe═O core smears out the equatorial charge density, reducing the triplet-quintet splitting, and thus helping complex 1A to achieve better reactivity.

Improving the Accuracy in the Prediction of Transition-Metal Spin-State Energetics Using a Robust Variation-Based Approach: Density Functional Theory, CASPT2 and MC-PDFT Applied to the Case Study of Tris-Diimine Fe(II) Complexes

Designing ligands for transition metal complexes with a specified low-spin, high-spin or spin-crossover behavior is challenging. A major advance was recently made by Phan et al. [J. Am. Chem. Soc. 2017, 139, 6437-6447] who showed that the spin state of a homoleptic tris-diimine Fe(II) complex can be predicted from the N-N distance in the free diimine. They could thus predict the change in magnetic behavior on passing from the complexes of 2,2'-bipyridine (bpy), 2,2'-biimidazole (bim) and 2,2'-bis-2-imidazoline (bimz) ligands to those obtained with the modified analogs 4,5-diazafluoren-9-one (dafo), 1,1'-(α,α'-o-xylyl)-2,2'-bisimidazole (xbim) and 2,3,5,6,8,9-hexahydrodiimidazo[1,2-a:2', 1'-c]pyrazine (etbimz), respectively. Theoretically, the challenge lies in the accurate determination of the HS-LS zero-point energy difference ΔEHL°. The issue can be circumvented by using a variation-based approach, wherein ΔEHL° is not directly evaluated but obtained from the estimate of its variation Δ(ΔEHL°) in series of related systems, which include one whose ΔEHL° is accurately known [Phys. Chem. Chem. Phys. 2013, 15, 3752-3763; J. Phys. Chem. A 2022, 126, 6221-6235]. In this study, density functional theory (DFT), second-order multireference perturbation theory in its CASPT2 formulation, multiconfigurational pair DFT (MC-PDFT) and its hybrid formulation (HMC-PDFT) have been applied to the determination of Δ(ΔEHL°) in the pairs of complexes ( [ F e ( b p y ) 3 ] 2 + , [ F e ( d a f o ) 3 ] 2 + ) , ( [ F e ( b i m ) 3 ] 2 + , [ F e ( x b i m ) 3 ] 2 + ) and ( [ F e ( b i m z ) 3 ] 2 + , [ F e ( e t b i m z ) 3 ] 2 + ) . In DFT, we used several semilocal functionals and their global hybrids, as well as their D2, D3, D3BJ and D4 dispersion-corrected forms; and in MC-PDFT, different translated and fully translated functionals. The results are consistent with one another and in very good agreement with experiments. They show small to vanishing dependence on key details of the methods used: namely, the exact-exchange contribution to global hybrids; the ionization potential-electron affinity shift and basis sets used in the CASPT2 calculations; and the active spaces employed for the CASSCF wave functions used in the MC-PDFT and HMC-PDFT calculations. Insights into the change in the spin-state energetics accompanying the ligand exchanges were gained through a complexation energy analysis. Using the accurate CCSD(T) estimate of the HS-LS adiabatic energy difference in [ F e ( N C H ) 6 ] 2 + [J. Chem. Theory Comput. 2012, 8, 4216-4231], the Δ(ΔEHL°)-approach has been applied to the determination of ΔEHL° in the diimine complexes. The CASPT2 and DFT-D2 methods only give results in agreement with experiments. This suggests for the other methods a limitation in their treatment of dispersion which prevents them from accurately describing the spin-state energetics change accompanying the passing from [ F e ( N C H ) 6 ] 2 + with the tetragonal arrangement of its nitrile ligands to the tris-diimine complexes with the trigonal packing of their bulkier ligands.

Tuning the spin-crossover properties of [Fe2] metal-organic cages

A computational study on the interplay between ligand functionalization and guest effects on the transition temperature (T1/2) in the [Fe2(L1R)3]@X (L1 = 1,3-bis-(3-(pyridin-2-yl)-1H-pyrazol-5-yl)benzene, X = H-, F-, Cl-, Br-, I- and [BF4]-, R = H, F, or CH3) family of metal-organic cages (MOCs) is presented. Our results indicate that ligand functionalization with electron-donating or electron-withdrawing groups can significantly impact the T1/2 as expected, while the guest effect in lowering the T1/2 has a linear correlation with the increasing guest size. More importantly, small guests can move away from the center of the cavity, thus enhancing the two-step characteristic of the transition. All the data can be understood by analyzing the underlying electronic structure of the studied systems in terms of the relevant d-based molecular orbitals. These results can help in the rational design of new MOCs that can operate as sensors at specific temperatures, thus accelerating the discovery of new SCO devices with tailored properties.

Benchmarking Periodic Density Functional Theory Calculations for Spin-State Energies in Spin-Crossover Systems

Spin energetics is one of the biggest challenges associated with energy calculations for electronic structure methods. The energy differences of the spin states in spin-crossover compounds are very small, making them one of the most difficult systems to calculate. Few methods provide accurate results for calculating these energy differences. In addition, studies have usually focused on calculating energetics of single molecules, while spin-crossover properties are usually experimentally studied in the solid phase. In this paper, we have used periodic boundary conditions employing methods based on density functional theory to calculate the high- and low-spin energy differences for a test case of 20 extended systems. Compounds with different metals and ligands have been selected, and the results indicate that a semiquantitative description of the energy differences can be obtained with the combination of geometry optimization using the PBE functional including many-body dispersion approach and the use of meta-GGA functionals, such as r2SCAN but especially KTBM24, for the energy calculation. Other hybrid functionals, such as TPSSh, give generally good results, but the calculation of the exact exchange with periodic boundary conditions involves a huge increase in computer time and computational resources. It makes the proposed nonhybrid functional approach (KTBM24//PBE+MB) a great advantage for the study of periodic systems.

Accurate state energetics in spin-crossover systems using pure density functional theory

The energy difference between different spin states of systems with transition metals is an outstanding challenge for electronic structure calculation methods. The small energy difference between high- and low-spin states in spin-crossover systems makes most post-Hartree-Fock or density functional theory-based methods provide inaccurate values. A test case of twenty systems showing spin transitions has been used to evaluate the accuracy of a new family of training meta-GGA (Generalized Gradient Approximation) functionals. One of the functionals of this new family provides comparable or even better values than the best functional reported so far for this type of system, the TPSSh hybrid meta-GGA functional, but without having to use the exact exchange term. It also improves the results obtained with the r2SCAN meta-GGA functional, which was the best alternative to the TPSSh hybrid functional. This makes it possible to calculate the spin energetics of any kind of compound, especially large systems or periodic structures where the exact exchange requires large computational resources.

A combined theoretical and experimental approach to determine the right choice of co-ligand to impart spin crossover in Fe(II) complexes based on 1,3,4-oxadiazole ligands

We present the synthesis of two new novel tetradentate ligands based on 1,3,4-oxadiazole, 2-(2-pyridyl)-5-[N,N-bis(2-pyridylmethyl)aminomethyl]-1,3,4-oxadiazole (LTetraPy-ODA) and 2-(2-phenyl)-5-[N,N-bis(2-pyridylmethyl)aminomethyl]-1,3,4-oxadiazole (LTetraPh-ODA). The ligands were used to prepare six mononuclear complexes [FeII(LTetraPy-ODA)(NCE)] (C1-C3) and [FeII(LTetraPh-ODA)(NCE)] (C4-C6) where E = S, Se or BH3. In addition, the ligand LTetraPy-ODA was employed in the synthesis of a new di-nuclear complex [FeII2(LTetraPh)](ClO4)4·1 CH3NO2·1.5 H2O (C7). Characterization of all complexes was carried out using single-crystal X-ray crystallography, elemental analysis, and infrared spectroscopy. Magnetic susceptibility measurements, performed in the temperature range of 2-300 K using a SQUID magnetometer, revealed spin crossover behaviour exclusively in the mononuclear complexes C3 and C6, in which two monodentate NCBH3- co-ligands coordinate. The presence of the lattice solvent was found to be crucial to the spin transition property, with complex C3 exhibiting a switching temperature (T1/2) of approximately 165 K and C6 approximately 194 K. The other four mononuclear complexes C1, C2, C4, C5, as well as the dinuclear complex C7 are locked in the high spin state over the measured temperature range. Density Functional Theory (DFT) calculations were performed on complexes C1-C6 to rationalise the observed magnetic behaviour, demonstrating the significant effect of the NCS-, NCSe- and NCBH3- co-ligands ligands on the spin-crossover behaviour of the [FeII(L)(NCE)] complexes.

Ab initio calculation of magnetic anisotropy and thermal spin transition in the variable temperature crystal conformations of [Co(terpy)2]2

The structure-property correlation of [Co(terpy)2]2+, which shows a spin crossover at 270 K, has been computationally investigated based on its variable temperature crystal structures. Among the employed DFT functionals, only the re-parametrized hybrid B3LYP* functional could describe the correct spin transition temperature. Explicit consideration of metal-ligand sigma bonding with dynamic electron correlation is found to be necessary for an accurate determination of the SCO temperature with multi-reference calculations. The metal-ligand axial bond distances are found to be the most significant internal coordinates in deciding SCO. A small structural change along the axial distance causes a change in the t2g orbital splitting pattern and a reorientation of the magnetization axes at the SCO temperature. The complex shows an unusual triaxial magnetic anisotropy, with an easy axis of magnetization developing at higher temperatures. The strong coupling of low-frequency wagging motion of the two terpyridine ligands with the spin states of the complex provides an effective pathway for the relaxation of magnetization, resulting in a small magnetic anisotropy barrier.

Computational Analysis of Low Overpotential Ammonia Oxidation by Metal-Metal Bonded Ruthenium Catalysts, and Predictions for Related Osmium Catalysts

The catalyzed electrochemical oxidation of ammonia to nitrogen (AOR) is an important fuel-cell half-reaction that underpins a future nitrogen-based energy economy. Our laboratory has reported spontaneous chemical and electrochemical oxidation of ammonia to dinitrogen via reaction of ammonia with the metal-metal bonded diruthenium complex Ru2(chp)4OTf (chp- = 2-chloro-6-hydroxypyridinate, TfO- = trifluoromethanesulfonate). This complex facilitates electrocatalytic ammonia oxidation at mild applied potentials of -255 mV vs ferrocene, which is the [Ru2(chp)4(NH3)]0/+ redox potential. We now report a comprehensive computational investigation of possible mechanisms for this reaction and electronic structure analysis of key intermediates therein. We extend this analysis to proposed second-generation electrocatalysts bearing structurally similar fhp and hmp (2-fluoro-6-hydroxypyridinate and 2-hydroxy-6-methylpyridinate, respectively) equatorial ligands, and we further expand this study from Ru2 to analogous Os2 cores. Predicted M24+/5+ redox potentials, which we expect to correlate with experimental AOR overpotential, depend strongly on the identity of the metal center, and to a lesser degree on the nature of the equatorial supporting ligand. Os2 complexes are easier to oxidize than analogous Ru2 complexes by ∼640 mV, on average. In contrast to mono-Ru catalysts, which oxidize ammonia via a rate-limiting activation of the strong N-H bond, we find lowest-energy reaction pathways for Ru2 and Os2 complexes that involve direct N-N bond formation onto electrophilic intermediates having terminal amido, imido, or nitrido groups. While transition state energies for Os2 complexes are high, those for Ru2 complexes are moderate and notably lower than those for mono-Ru complexes. We attribute these lower barriers to enhanced electrophilicity of the Ru2 intermediates, which is a consequence of their metal-metal bonded structure. Os2 intermediates are found to be, surprisingly, less electrophilic, and we suggest that Os2 complexes may require access to oxidation states higher than Os25+ in order to perform AOR at reasonable reaction rates.

Unravelling the Highest Magnetic Anisotropy Among all the n-Shells in 20 Metallocene

Single-molecule magnets (SMMs) with a large magnetization reversal barrier are predominated by the lanthanide systems due to their strong spin-orbit coupling (SOC). However, the transition metals have also emerged as potential contenders and the largest magnetic anisotropy has been identified for a cobalt system among any d-series-based SMMs (Bunting et al. Science 2018, 362, eaat7319). In this work, we have explored the magnetic anisotropy in highly axial ligand field systems of metallocene, having different d-subshell (3d4, 4d4, and 5d4). The wave function-based multireference methods including static and dynamic electron correlations have been employed to investigate the zero-field splitting (ZFS) parameters. Here, we report exceptionally large magnetic anisotropy for a 5d complex of [WCp2]0 with the highest energy barrier that is nearly twice as high as the previous record value for the Co complex. We have also observed that the axial ZFS parameter (D) is increasing down the group in the order of 3d < 4d < 5d, pertaining to a large SOC.

Theoretical Photoelectron Spectroscopy of Quadruple-Bonded Dimolybdenum(II,II) and Ditungsten(II,II) Paddlewheel Complexes: Performance of Common Density Functional Theory Methods

We have revisited the gas-phase photoelectron spectra of quadruple-bonded dimolybdenum(II,II) and ditungsten(II,II) paddlewheel complexes with modern density functional theory methods and obtained valuable calibration of four well-known exchange-correlation functionals, namely, BP86, OLYP, B3LYP*, and B3LYP. All four functionals were found to perform comparably, with discrepancies between calculated and experimental ionization potentials ranging from <0.1 to ∼0.5 eV, with the lowest errors observed for the classic pure functional BP86. All four functionals were found to reproduce differences in ionization potentials (IPs) between analogous Mo2 and W2 complexes, as well as large, experimentally observed ligand field effects on the IPs, with near-quantitative accuracy. The calculations help us interpret a number of differences between analogous Mo2 and W2 complexes through the lens of relativistic effects. Thus, relativity results in not only significantly lower IPs for the W2 complexes but also smaller HOMO-LUMO gaps and different triplet states relative to their Mo2 counterparts.

Is Mn(I) More Promising Than Fe(II)-A Comparison of Mn vs Fe Complexes for Olefin Metathesis

Olefin metathesis is one of the most significant transformations in organic chemistry and is an excellent example for efficient homogeneous catalysis. Although most currently used catalysts are primarily based on 4d and 5d metals, cycloaddition and cycloreversion reactions can also be attributed to first-row transition metals, such as Fe. Surprisingly, the potential of Mn(I)-based catalysts for olefin metathesis has been unexplored despite their prominence in homogeneous catalysis and their diagonal relationship to Ru(II). In the present study, we have investigated the prospective capabilities of Mn complexes for cycloaddition and reversion reactions using density functional theory. Therefore, we have initially compared the literature known iron model systems and their isoelectronic Mn counterparts regarding their reactivity and electronic structure. Next, we constructed potential Mn complexes derived from synthetically accessible species, including carbonyl ligands and obeying octahedral geometry. Based on thermodynamic parameters and the calculation of electronic descriptors, we were able to validate the isodiagonal relationship. Our study serves as guidance for the experimental chemist.

Solvation energies of the ferrous ion in water and in ammonia at various temperatures

CONTEXT

The solvation of metal ions is crucial to understanding relevant properties in physics, chemistry, or biology. Therefore, we present solvation enthalpies and solvation free energies of the ferrous ion in water and ammonia. Our results agree well with the experimental reports for the hydration free energy and hydration enthalpy. We obtained [Formula: see text] kJ mol[Formula: see text] for the hydration free energy and [Formula: see text] kJ mol[Formula: see text] for the hydration enthalpy of ferrous ion in water at room temperature. At ambient temperature, we obtained [Formula: see text] kJ mol[Formula: see text] as the [Formula: see text] ammoniation free energy and [Formula: see text] kJ mol[Formula: see text] for the ammoniation enthalpy. In addition, the free energy of solvation is deeply affected when the temperature increases. This pattern can be attributed to the rise of entropy when the temperature rises. Besides, the temperature does not affect the ammoniation enthalpies and the hydration enthalpy of the [Formula: see text] ion.

METHOD

All the geometry optimizations are performed at the MP2 methods associated with the 6-31++g(d,p) basis set of Pople. solvated phase structures of [Formula: see text] ion in water or in ammonia are performed using the PCM model. The [Formula: see text] program suite was used to perform all the calculations. The program TEMPO was also used to evaluate the temperature sensitivity of the different obtained geometries.

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. 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 (T1/2) 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 T1/2 values. We then compare ML T1/2 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 T1/2 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 T1/2 values are available. Upon excluding outliers from this set, the RF-RFA RF model shows a strong correlation to estimated T1/2 values with a Pearson's r of 0.82. In contrast, DFA-predicted T1/2 values have large errors and show no correlation to estimated T1/2 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.

Electrocatalytic Interconversions of CO2 and Formate on a Versatile Iron-Thiolate Platform

Exploring bidirectional CO2/HCO2- catalysis holds significant potential in constructing integrated (photo)electrochemical formate fuel cells for energy storage and applications. Herein, we report selective CO2/HCO2- electrochemical interconversion by exploiting the flexible coordination modes and rich redox properties of a versatile iron-thiolate platform, Cp*Fe(II)L (L = 1,2-Ph2PC6H4S-). Upon oxidation, this iron complex undergoes formate binding to generate a diferric formate complex, [(L-)2Fe(III)(μ-HCO2)Fe(III)]+, which exhibits remarkable electrocatalytic performance for the HCO2--to-CO2 transformation with a maximum turnover frequency (TOFmax) ∼103 s-1 and a Faraday efficiency (FE) ∼92(±4)%. Conversely, this iron system also allows for reduction at -1.85 V (vs Fc+/0) and exhibits an impressive FE ∼93 (±3)% for the CO2-to-HCO2- conversion. Mechanism studies revealed that the HCO2--to-CO2 electrocatalysis passes through dicationic [(L2)-•Fe(III)(μ-HCO2)Fe(III)]2+ generated by unconventional oxidation of the diferric formate species taking place at ligand L, while the CO2-to-HCO2- reduction involves a critical intermediate of [Fe(II)-H]- that was independently synthesized and structurally characterized.

A closed-shell phenalenyl-based dinuclear iron(III) complex as a robust cathode for a one-compartment H2O2 fuel cell

Closed-shell phenalenyl (PLY) systems are increasingly becoming more attractive as building blocks for developing promising catalysts and electroactive cathode materials, as they have tremendous potential to accept electrons and participate in redox reactions. Herein, we report a PLY-based dinuclear [FeIII2(hmbh-PLY)3] complex, 1, and its utility as a cathode material in a H2O2 fuel cell. Complex 1 was synthesized from a new Schiff base ligand, (E)-9-(2-(2-hydroxy-3-methoxybenzylidene)hydrazineyl)-1H-phenalen-1-one, hmbh-PLYH2, designed using a PLY precursor, Hz-PLY. The newly derived ligand and complex 1 were characterized by various analytical techniques, including single-crystal X-ray diffraction (SCXRD). The cyclic voltammetry (CV) study revealed that complex 1 undergoes five electron reductions under an applied electric potential. When the electroactive complex 1 was employed as a cathode in a membrane-less one-compartment H2O2 fuel cell, with Ni foam as the corresponding anode, the designed fuel cell exhibited an exceptionally high peak power density (PPD) of 2.41 mW cm-2, in comparison with those of all the previously reported Fe-based molecular complexes. DFT studies were performed to gain reasonable insights into the two-electron catalytic reduction (pathway I) of H2O2 by the Fe-center of complex 1 and to explore the geometries, energetics of the electrocatalyst, reactive intermediates and transition states.

Local Oxidation States in {FeNO}6-8 Porphyrins: Insights from DMRG/CASSCF-CASPT2 Calculations

A first DMRG/CASSCF-CASPT2 study of a series of paradigmatic {FeNO}6, {FeNO}7, and {FeNO}8 heme-nitrosyl complexes has led to substantial new insight as well as uncovered key shortcomings of the DFT approach. By virtue of its balanced treatment of static and dynamic correlation, the calculations have provided some of the most authoritative information available to date on the energetics of low- versus high-spin states of different classes of heme-nitrosyl complexes. Thus, the calculations indicate low doublet-quartet gaps of 1-4 kcal/mol for {FeNO}7 complexes and high singlet-triplet gaps of ≳20 kcal/mol for both {FeNO}6 and {FeNO}8 complexes. In contrast, DFT calculations yield widely divergent spin state gaps as a function of the exchange-correlation functional. DMRG-CASSCF calculations also help calibrate DFT spin densities for {FeNO}7 complexes, pointing to those obtained from classic pure functionals as the most accurate. The general picture appears to be that nearly all the spin density of Fe[P](NO) is localized on the Fe, while the axial ligand imidazole (ImH) in Fe[P](NO)(ImH) pushes a part of the spin density onto the NO moiety. An analysis of the DMRG-CASSCF wave function in terms of localized orbitals and of the resulting configuration state functions in terms of resonance forms with varying NO(π*) occupancies has allowed us to address the longstanding question of local oxidation states in heme-nitrosyl complexes. The analysis indicates NO(neutral) resonance forms [i.e., Fe(II)-NO0 and Fe(III)-NO0] as the major contributors to both {FeNO}6 and {FeNO}7 complexes. This finding is at variance with the common formulation of {FeNO}6 hemes as Fe(II)-NO+ species but is consonant with an Fe L-edge XAS analysis by Solomon and co-workers. For the {FeNO}8 complex {Fe[P](NO)}-, our analysis suggests a resonance hybrid description: Fe(I)-NO0 ↔ Fe(II)-NO-, in agreement with earlier DFT studies. Vibrational analyses of the compounds studied indicate an imperfect but fair correlation between the NO stretching frequency and NO(π*) occupancy, highlighting the usefulness of vibrational data as a preliminary indicator of the NO oxidation state.

Benchmarks for transition metal spin-state energetics: why and how to employ experimental reference data?

Accurate prediction of energy differences between alternative spin states of transition metal complexes is essential in computational (bio)inorganic chemistry-for example, in characterization of spin crossover materials and in the theoretical modeling of open-shell reaction mechanisms-but it remains one of the most compelling problems for quantum chemistry methods. A part of this challenge is to obtain reliable reference data for benchmark studies, as even the highest-level applicable methods are known to give divergent results. This Perspective discusses two possible approaches to method benchmarking for spin-state energetics: using either theoretically computed or experiment-derived reference data. With the focus on the latter approach, an extensive general review is provided for the available experimental data of spin-state energetics and their interpretations in the context of benchmark studies, targeting the possibility of back-correcting the vibrational effects and the influence of solvents or crystalline environments. With a growing amount of experience, these effects can be now not only qualitatively understood, but also quantitatively modeled, providing the way to derive nearly chemically accurate estimates of the electronic spin-state gaps to be used as benchmarks and advancing our understanding of the phenomena related to spin states in condensed phases.

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.

Surface-Induced Electronic and Vibrational Level Shifting of [Fe(py)2bpym(NCS)2] on Al(100)

It is essential that one understands how the surface degrees of freedom influence molecular spin switching to successfully integrate spin crossover (SCO) molecules into devices. This study uses density functional theory calculations to investigate how spin state energetics and molecular vibrations change in a Fe(II) SCO compound named [Fe(py)2bpym(NCS)2] when deposited on an Al(100) surface. The calculations consider an environment-dependent U to assess the local Coulomb correlation of 3d electrons. The results show that the adsorption configurations heavily affect the spin state splitting, which increases by 10-40 kJmol-1 on the surface, and this is detrimental to spin conversion. This effect is due to the surface binding energy variation across the spin transition. The preference for the low-spin state originates partly from the strong correlation effect. Furthermore, the surface environment constrains the vibrational entropy difference, which decreases by 8-17 Jmol-1K-1 (at 300 K) and leads to higher critical temperatures. These results suggest that the electronic energy splitting and vibrational level shifting are suitable features for characterizing the spin transition process on surfaces, and they can provide access to high-throughput screening of spin crossover devices.

Dynamic effects on ligand field from rapid hydride motion in an iron(ii) dimer with an S = 3 ground state

Hydride complexes are important in catalysis and in iron-sulfur enzymes like nitrogenase, but the impact of hydride mobility on local iron spin states has been underexplored. We describe studies of a dimeric diiron(ii) hydride complex using X-ray and neutron crystallography, Mössbauer spectroscopy, magnetism, DFT, and ab initio calculations, which give insight into the dynamics and the electronic structure brought about by the hydrides. The two iron sites in the dimer have differing square-planar (intermediate-spin) and tetrahedral (high-spin) iron geometries, which are distinguished only by the hydride positions. These are strongly coupled to give an S total = 3 ground state with substantial magnetic anisotropy, and the merits of both localized and delocalized spin models are discussed. The dynamic nature of the sites is dependent on crystal packing, as shown by changes during a phase transformation that occurs near 160 K. The change in dynamics of the hydride motion leads to insight into its influence on the electronic structure. The accumulated data indicate that the two sites can trade geometries by rotating the hydrides, at a rate that is rapid above the phase transition temperature but slow below it. This small movement of the hydrides causes large changes in the ligand field because they are strong-field ligands. This suggests that hydrides could be useful in catalysis not only due to their reactivity, but also due to their ability to rapidly modulate the local electronic structure and spin states at metal sites.

Spin-crossover complexes: Self-interaction correction vs density correction

Complexes containing a transition metal atom with a 3d⁴-3d⁷ electron configuration typically have two low-lying, high-spin (HS) and low-spin (LS) states. The adiabatic energy difference between these states, known as the spin-crossover energy, is small enough to pose a challenge even for electronic structure methods that are well known for their accuracy and reliability. In this work, we analyze the quality of electronic structure approximations for spin-crossover energies of iron complexes with four different ligands by comparing energies from self-consistent and post-self-consistent calculations for methods based on the random phase approximation and the Fermi-Löwdin self-interaction correction. Considering that Hartree-Fock densities were found by Song et al., J. Chem. Theory Comput. 14, 2304 (2018), to eliminate the density error to a large extent, and that the Hartree-Fock method and the Perdew-Zunger-type self-interaction correction share some physics, we compare the densities obtained with these methods to learn their resemblance. We find that evaluating non-empirical exchange-correlation energy functionals on the corresponding self-interaction-corrected densities can mitigate the strong density errors and improves the accuracy of the adiabatic energy differences between HS and LS states.

Spin-state gaps and self-interaction-corrected density functional approximations: Octahedral Fe(II) complexes as case study

Accurate prediction of a spin-state energy difference is crucial for understanding the spin crossover phenomena and is very challenging for density functional approximations, especially for local and semi-local approximations due to delocalization errors. Here, we investigate the effect of the self-interaction error removal from the local spin density approximation (LSDA) and Perdew-Burke-Ernzerhof generalized gradient approximation on the spin-state gaps of Fe(II) complexes with various ligands using recently developed locally scaled self-interaction correction (LSIC) by Zope et al. [J. Chem. Phys. 151, 214108 (2019)]. The LSIC method is exact for one-electron density, recovers the uniform electron gas limit of the underlying functional, and approaches the well-known Perdew-Zunger self-interaction correction (PZSIC) as a particular case when the scaling factor is set to unity. Our results, when compared with reference diffusion Monte Carlo results, show that the PZSIC method significantly overestimates spin-state gaps favoring low spin states for all ligands and does not improve upon density functional approximations. The perturbative LSIC-LSDA using PZSIC densities significantly improves the gaps with a mean absolute error of 0.51 eV but slightly overcorrects for the stronger CO ligands. The quasi-self-consistent LSIC-LSDA, such as coupled-cluster single double and perturbative triple [CCSD(T)], gives a correct sign of spin-state gaps for all ligands with a mean absolute error of 0.56 eV, comparable to that of CCSD(T) (0.49 eV).

Spin-State Splittings in 3d Transition-Metal Complexes Revisited: Benchmarking Approximate Methods for Adiabatic Spin-State Energy Differences in Fe(II) Complexes

The CASPT2+δMRCI composite approach reported in a companion paper has been extended and used to provide high-quality reference data for a series of adiabatic spin gaps (defined as ΔE = E_quintet - E_singlet) of [Fe^IIL₆]²⁺ complexes (L = CNH, CO, NCH, NH₃, H₂O), either at nonrelativistic level or including scalar relativistic effects. These highly accurate data have been used to evaluate the performance of various more approximate methods. Coupled-cluster theory with singles, doubles, and perturbative triples, CCSD(T), is found to agree well with the new reference data for Werner-type complexes but exhibits larger underestimates by up to 70 kJ/mol for the π-acceptor ligands, due to appreciable static correlation in the low-spin states of these systems. Widely used domain-based local CCSD(T) calculations, DLPNO-CCSD(T), are shown to depend very sensitively on the cutoff values used to construct the localized domains, and standard values are not sufficient. A large number of density functional approximations have been evaluated against the new reference data. The B2PLYP double hybrid gives the smallest deviations, but several functionals from different rungs of the usual ladder hierarchy give mean absolute deviations below 20 kJ/mol. This includes the B97-D semilocal functional, the PBE0* global hybrid with 15% exact-exchange admixture, as well as the local hybrids LH07s-SVWN and LH07t-SVWN. Several further functionals achieve mean absolute errors below 30 kJ/mol (M06L-D4, SSB-D, B97-1-D4, LC-ωPBE-D4, LH12ct-SsirPW92-D4, LH12ct-SsifPW92-D4, LH14t-calPBE-D4, LHJ-HFcal-D4, and several further double hybrids) and thereby also still overall outperform CCSD(T) or uncorrected CASPT2. While exact-exchange admixture is a crucial factor in favoring high-spin states, the present evaluations confirm that other aspects can be important as well. A number of the better-performing functionals underestimate the spin gaps for the π-acceptor ligands but overestimate them for L = NH₃, H₂O. In contrast to a previous suggestion, non-self-consistent density functional theory (DFT) computations on top of Hartree-Fock orbitals are not a promising path to produce accurate spin gaps in such complexes.

CH4 activation by PtX+ (X = F, Cl, Br, I)

Reactions of PtX⁺ (X = F, Cl, Br, I) with methane have been investigated at the density functional theory (DFT) level. These reactions take place more easily along the low-spin potential energy surface. For HX (X = F, Cl, Br, I) elimination, the formal oxidation state of the metal ion appears to be conserved, and the importance of this reaction channel decreases in going as the sequence: X = F, Cl, Br, I. A reversed trend is observed in the loss of H₂ for X = F, Cl, Br, while it is not favorable for PtI⁺ in the loss of either HI or H₂. For HX eliminations, the transfer form of H is from proton to atom, last to hydride, and the mechanisms are from PCET to HAT, last to HT for the sequence of X = F, Cl, Br, I. One reason is mainly due to the electronegativity of halogens. Otherwise, the mechanisms of HX eliminations also can be explained by the analysis of Frontier Molecular Orbitals. While for the loss of H₂, the transfer of H is in the form of hydride for all the X ligands. Noncovalent interactions analysis also can be explained the reaction mechanisms.

Reconciling Local Coupled Cluster with Multireference Approaches for Transition Metal Spin-State Energetics

Spin-state energetics of transition metal complexes remain one of the most challenging targets for electronic structure methods. Among single-reference wave function approaches, local correlation approximations to coupled cluster theory, most notably the domain-based local pair natural orbital (DLPNO) approach, hold the promise of bringing the accuracy of coupled cluster theory with single, double, and perturbative triple excitations, CCSD(T), to molecular systems of realistic size with acceptable computational cost. However, recent studies on spin-state energetics of iron-containing systems raised doubts about the ability of the DLPNO approach to adequately and systematically approximate energetics obtained by the reference-quality complete active space second-order perturbation theory with coupled-cluster semicore correlation, CASPT2/CC. Here, we revisit this problem using a diverse set of iron complexes and examine several aspects of the application of the DLPNO approach. We show that DLPNO-CCSD(T) can accurately reproduce both CASPT2/CC and canonical CCSD(T) results if two basic principles are followed. These include the consistent use of the improved iterative (T₁) versus the semicanonical perturbative triple corrections and, most importantly, a simple two-point extrapolation to the PNO space limit. The latter practically eliminates errors arising from the default truncation of electron-pair correlation spaces and should be viewed as standard practice in applications of the method to transition metal spin-state energetics. Our results show that reference-quality results can be readily achieved with DLPNO-CCSD(T) if these principles are followed. This is important also in view of the applicability of the method to larger single-reference systems and multinuclear clusters, whose treatment of dynamic correlation would be challenging for multireference-based approaches.

Improving Results by Improving Densities: Density-Corrected Density Functional Theory

Density functional theory (DFT) calculations have become widespread in both chemistry and materials, because they usually provide useful accuracy at much lower computational cost than wavefunction-based methods. All practical DFT calculations require an approximation to the unknown exchange-correlation energy, which is then used self-consistently in the Kohn-Sham scheme to produce an approximate energy from an approximate density. Density-corrected DFT is simply the study of the relative contributions to the total energy error. In the vast majority of DFT calculations, the error due to the approximate density is negligible. But with certain classes of functionals applied to certain classes of problems, the density error is sufficiently large as to contribute to the energy noticeably, and its removal leads to much better results. These problems include reaction barriers, torsional barriers involving π-conjugation, halogen bonds, radicals and anions, most stretched bonds, etc. In all such cases, use of a more accurate density significantly improves performance, and often the simple expedient of using the Hartree-Fock density is enough. This Perspective explains what DC-DFT is, where it is likely to improve results, and how DC-DFT can produce more accurate functionals. We also outline challenges and prospects for the field.

A Parent Iron Amido Complex in Catalysis of Ammonia Oxidation

Parent amido complexes are crucial intermediates in ammonia-based transformations. We report a well-defined ferric ammine system [Cp*Fe(1,2-Ph₂PC₆H₄NH)(NH₃)]⁺ ([1-NH₃]⁺), which processes electrocatalytic ammonia oxidation to N₂ and H₂ at a mild potential. Through establishing elementary e^-/H⁺ conversions with the ferric ammine, a formal Fe(IV)-amido species, [1-NH₂]⁺, together with its conjugated Lewis acid, [1-NH₃]²⁺, was isolated and structurally characterized for the first time. Mechanism studies indicated that further oxidation of [1-NH₂]⁺ induces the reaction of the parent amido unit with NH₃. The formation of hydrazine is realized by the non-innocent nature of the phenylamido ligand that facilitates the concerted transfer of one proton and two electrons.

A radical mechanism for C–H bond cross-coupling and N2 activation catalysed by β-diketiminate iron complexes

Density functional theory calculations and electronic structure analyses reveal a radical mechanism with spin-crossovers for C–H bond cross-coupling and N2 activation catalysed by β-diketiminate iron complexes.

A DMRG/CASPT2 Investigation of Metallocorroles: Quantifying Ligand Noninnocence in Archetypal 3d and 4d Element Derivatives

Hybrid density functional theory (B3LYP) and density matrix renormalization group (DMRG) theory have been used to quantitatively compare the degree of ligand noninnocence (corrole radical character) in seven archetypal metallocorroles. The seven complexes, in decreasing order of corrole noninnocent character, are Mn[Cor]Cl > Fe[Cor]Cl > Fe[Cor](NO) > Mo[Cor]Cl2 > Ru[Cor](NO) ≈ Mn[Cor]Ph ≈ Fe[Cor]Ph ≈ 0, where [Cor] refers to the unsubstituted corrolato ligand. DMRG-based second-order perturbation theory calculations have also yielded detailed excited-state energetics data on the compounds, shedding light on periodic trends involving middle transition elements. Thus, whereas the ground state of Fe[Cor](NO) (S = 0) is best described as a locally S = 1/2 {FeNO}7 unit antiferromagnetically coupled to a corrole A' radical, the calculations confirm that Ru[Cor](NO) may be described as simply {RuNO}6-Cor3-, that is, having an innocent corrole macrocycle. Furthermore, whereas the ferromagnetically coupled S = 1{FeNO}7-Cor•2- state of Fe[Cor](NO) is only ∼17.5 kcal/mol higher than the S = 0 ground state, the analogous triplet state of Ru[Cor](NO) is higher by a far larger margin (37.4 kcal/mol) relative to the ground state. In the same vein, Mo[Cor]Cl2 exhibits an adiabatic doublet-quartet gap of 36.1 kcal/mol. The large energy gaps associated with metal-ligand spin coupling in Ru[Cor](NO) and Mo[Cor]Cl2 reflect the much greater covalent character of 4d-π interactions relative to analogous interactions involving 3d orbitals. As far as excited-state energetics is concerned, DMRG-CASPT2 calculations provide moderate validation for hybrid density functional theory (B3LYP) for qualitative purposes, but underscore the possibility of large errors (>10 kcal/mol) in interstate energy differences.

Spin-crossover complexes in nanoscale devices: main ingredients of the molecule-substrate interactions

Spin-crossover complexes embedded in nanodevices experience effects that are absent in the bulk that can modulate, quench and even suppress the spin-transition. In this work we explore, by means of state-of-the-art quantum chemistry calculations, different aspects of the integration of SCO molecules on active nanodevices, such as the geometry and energetics of the interaction with the substrate, extension of the charge transfer between the substrate and SCO molecule, impact of the applied external electric field on the spin-transition, and sensitivity of the transport properties on the local conditions of the substrate. We focus on the recently reported encapsulation of Fe(II) spin-crossover complexes in single-walled carbon nanotubes, with new measurements that support the theoretical findings. Even so our results could be useful to many other systems where SCO phenomena take place at the nanoscale, the spin-state switching is probed by an external electric field or current, or the substrate is responsible for the quenching of the SCO mechanism.

Peculiar Spin-Crossover Behavior in the 2D Polymer K[FeIII(5Cl-thsa)2]

A potassium salt of the N₂S₂O₂-coordination Fe(III) anion K[Fe(5Cl-thsa)₂] (1) (5Cl-thsa - 5-chlorosalicylaldehyde thiosemicarbazone) is synthesized and characterized structurally and magnetically over a wide temperature range. Two polymorphs of salt 1 characterized by the common 2D polymer nature and assigned to the same orthorhombic Pbcn space group have been identified. The molecular structure of the minor polymorph of 1 was solved and refined at 100, 250, and 300 K is shown to correspond to the LS configuration. The dominant polymorph of 1 features K⁺ cations disordered over a few crystallographic sites, while the minor polymorph includes fully ordered K⁺ cations. The major polymorph exhibits a complete three-step cooperative spin-crossover transition both in the heating and cooling modes: The first step occurs in a temperature range from 2 to 50 K; the second abrupt hysteretic step occurs from 200 to 250 K with T_1/2 = 230 K and a 6 K hysteresis loop. The third gradual step occurs from 250 to 440 K. According to ⁵⁷Fe Mössbauer, XRPD, and EXAFS data, the spin-crossover transition for the dominant polymorph is quite peculiar. Indeed, the increase in the HS concentration by 57% at the second step does not result in the expected significant increase in the iron(III)-ligand bond lengths. In addition, the final step of the spin conversion (Δγ_HS = 26%) is associated with a structural phase transition with a symmetry lowering from the orthorhombic (Pbcn) to the monoclinic (P2₁/n) space group. This nontrivial phenomenon was investigated in detail by applying magnetization measurements, electron spin resonance, ⁵⁷Fe Mössbauer spectroscopy, and DFT calculations. These results provide a new platform for understanding the multistep spin-crossover character in the Fe(III) thsa-complexes and related compounds.

Asymmetric Design of Spin-Crossover Complexes to Increase the Volatility for Surface Deposition

A mononuclear complex [Fe(tBu₂qsal)₂] has been obtained by a reaction between an Fe(II) precursor salt and a tridentate ligand 2,4-di(tert-butyl)-6-((quinoline-8-ylimino)methyl)phenol (tBu₂qsalH) in the presence of triethylamine. The complex exhibits a hysteretic spin transition at 117 K upon cooling and 129 K upon warming, as well as light-induced excited spin-state trapping at lower temperatures. Although the strongly cooperative spin transition suggests substantial intermolecular interactions, the complex is readily sublimable, as evidenced by the growth of its single crystals by sublimation at 573 → 373 K and ∼10^-3 mbar. This seemingly antagonistic behavior is explained by the asymmetric coordination environment, in which the tBu substituents and quinoline moieties appear on opposite sides of the complex. As a result, the structure is partitioned in well-defined layers separated by van der Waals interactions between the tBu groups, while the efficient cooperative interactions within the layer are provided by the quinoline-based moieties. The abrupt spin transition is preserved in a 20 nm thin film prepared by sublimation, as evidenced by abrupt and hysteretic changes in the dielectric properties in the temperature range comparable to the one around which the spin transition is observed for the bulk material. The changes in the dielectric response are in excellent agreement with differences in the dielectric tensor of the low-spin and high-spin crystal structures evaluated by density functional theory calculations. The substantially higher volatility of [Fe(tBu₂qsal)₂], as compared to a similar complex without tBu substituents, suggests that asymmetric molecular shapes offer an efficient design strategy to achieve sublimable complexes with strongly cooperative spin transitions.

Redox Isomerism in the S3 State of the Oxygen-Evolving Complex Resolved by Coupled Cluster Theory

The electronic and geometric structures of the water-oxidizing complex of photosystem II in the steps of the catalytic cycle that precede dioxygen evolution remain hotly debated. Recent structural and spectroscopic investigations support contradictory redox formulations for the active-site Mn4 CaOx cofactor in the final metastable S3 state. These range from the widely accepted MnIV 4 oxo-hydroxo model, which presumes that O-O bond formation occurs in the ultimate transient intermediate (S4 ) of the catalytic cycle, to a MnIII 2 MnIV 2 peroxo model representative of the contrasting "early-onset" O-O bond formation hypothesis. Density functional theory energetics of suggested S3 redox isomers are inconclusive because of extreme functional dependence. Here, we use the power of the domain-based local pair natural orbital approach to coupled cluster theory, DLPNO-CCSD(T), to present the first correlated wave function theory calculations of relative stabilities for distinct redox-isomeric forms of the S3 state. Our results enabled us to evaluate conflicting models for the S3 state of the oxygen-evolving complex (OEC) and to quantify the accuracy of lower-level theoretical approaches. Our assessment of the relevance of distinct redox-isomeric forms for the mechanism of biological water oxidation strongly disfavors the scenario of early-onset O-O formation advanced by literal interpretations of certain crystallographic models. This work serves as a case study in the application of modern coupled cluster implementations to redox isomerism problems in oligonuclear transition metal systems.

First-Principles Investigations of Magnetic Anisotropy and Spin-Crossover Behavior of Fe(III)-TBP Complexes

With the ongoing effort to obtain mononuclear 3d-transition-metal complexes that manifest slow relaxation of magnetization and, hence, can behave as single-molecule magnets (SMMs), we have modeled 14 Fe(III) complexes based on an experimentally synthesized (PMe₃)₂FeCl₃ complex [J. Am. Chem. Soc. 2017, 139 (46), 16474-16477], by varying the axial ligands with group XV elements (N, P, and As) and equatorial halide ligands from F, Cl, Br, and I. Out of these, nine complexes possess large zero field splitting (ZFS) parameter D in the range of -40 to -60 cm^-1. The first-principles investigation of the ground-spin state applying density functional theory (DFT) and wave function-based multiconfigurations methods, e.g., SA-CASSCF/NEVPT2, are found to be quite consistent except for few delicate cases with near-degenerate spin states. In such cases, the hybrid B3LYP functional is found to be biased toward high-spin (HS) state. Altering the percentage of exact exchange admixed in the B3LYP functional leads to intermediate-spin (IS) ground state consistent with the multireference calculations. The origin of large zero field splitting (ZFS) in the Fe(III)-based trigonal bipyramidal (TBP) complexes is investigated. Furthermore, a number of complexes are identified with very small ΔG_HS-IS^adia. values indicating the possible spin-crossover phenomenon between the bistable spin states.

Ligand symmetry significantly affects spin crossover behaviour in isomeric [Fe(pybox)2]2+ complexes

The understanding of the correlation between the spin-state behaviour and the structural features in transition-metal complexes is of pronounced importance to the design of spin crossover compounds with high performance. However, the study of the influence of ligand symmetry on the spin crossover properties is still limited due to the shortage of suitable structural systems. Herein we report the magneto-structural correlations of three mononuclear Fe(ii) isomers with respect to their ligand symmetry. In this work, two phenyl-substituted meso and optically pure pybox ligands were employed to construct meso (1), optically pure (2), and racemic (3) ligand types of [Fe(pybox)₂]²⁺ complexes. Their magnetic susceptibilities were measured via temperature-dependent paramagnetic ¹H NMR spectroscopy. We fitted the midpoint temperatures of the transition (T_1/2) of 260 K for 1(ClO₄), 247 K for 2(ClO₄), and 281 K for 3(ClO₄). The influence of structural symmetry on spin crossover was rationalized through density functional theory calculations. The optimized structures of [Fe(pybox)₂]²⁺ complex cations show that the geometric distortion of the central FeN₆ coordination sphere is mainly caused by the steric congestions between adjacent phenyl substituents. In these compounds, there is a distinct correlation that more steric congestions produce larger coordination distortion and favor the electron configuration in the high-spin state, which reflects in the increase of T_1/2. Additionally, the influence of the counter anion and lattice solvent on the meso series compounds was inspected. It is revealed that multiple factors dominate the spin-state behaviour in the solid state. This work provides deep insight into the effect of ligand symmetry on the spin transition behaviour in spin crossover compounds. It demonstrates that molecular symmetry should be considered in the design of spin crossover compounds.

Theoretical modeling of the singlet-triplet spin transition in different Ni(II)-diketo-pyrphyrin-based metal-ligand octahedral complexes

The structural stability, charge transfer effects and strength of the spin-orbit couplings in different Ni(ii)-ligand complexes have been studied at the DFT (B3LYP and CAM-B3LYP) and coupled cluster (DLPNO-CCSD(T)) levels of theory. Accordingly, two different, porphyrin- and diketo-pyrphyrin-based four-coordination macrocycles as planar ligands as well as pyridine (or pyrrole) and mesylate anion molecular groups as vertical ligands were considered in order to build metal-organic complexes with octahedral coordination configurations. For each molecular system, the identification of equilibrium geometries and the intersystem crossing (the minimum energy crossing) points between the potential energy surfaces of the singlet and triplet spin states is followed by computing the spin-orbit couplings between the two spin states. Structures, based on the diketo-pyrphyrin macrocycle as the planar ligand, show stronger six-coordination metal-organic complexes due to the extra electrostatic interaction between the positively charged central metal cation and the negatively charged vertical ligands. The results also show that the magnitude of the spin-orbit coupling is influenced by the atomic positions of deprotonations of the ligands, and implicitly the direction of the charge transfer between the ligand and the central metal ion.

Theoretical inspection of the spin-crossover [Fe(tzpy)2(NCS)2] complex on Au(100) surface

We explore the deposition of the spin-crossover [Fe(tzpy)₂(NCS)₂] complex on the Au(100) surface by means of density functional theory (DFT) based calculations. Two different routes have been employed: low-cost finite cluster-based calculations, where both the Fe complex and the surface are maintained fixed while the molecule approaches the surface; and periodic DFT plane-wave calculations, where the surface is represented by a four-layer slab and both the molecule and surface are relaxed. Our results show that the bridge adsorption site is preferred over the on-top and fourfold hollow ones for both spin states, although they are energetically close. The LS molecule is stabilized by the surface, and the HS-LS energy difference is enhanced by about 15%-25% once deposited. The different Fe ligand field for LS and HS molecules manifests on the composition and energy of the low-lying bands. Our simulated STM images indicate that it is possible to distinguish the spin state of the deposited molecules by tuning the bias voltage of the STM tip. Finally, it should be noted that the use of a reduced size cluster to simulate the Au(100) surface proves to be a low-cost and reliable strategy, providing results in good agreement with those resulting from state-of-the-art periodic calculations for this system.

Spin-state dependence of exchange-correlation holes

Applications of density-functional theory (DFT) in computational chemistry rely on an approximate exchange-correlation (xc) functional. However, existing approximations can fail dramatically for open-shell molecules, in particular for transition-metal complexes or radicals. Most importantly, predicting energy differences between different spin-states with approximate exchange-correlation functionals remains extremely challenging. Formally, it is known that the exact xc functional should be spin-state dependent, but none of the available approximations feature such an explicit spin-state dependence [C. R. Jacob and M. Reiher, Int. J. Quantum Chem., 2012, 112, 3661-3684]. Thus, to find novel approximations for the xc functional for open-shell systems, the development of spin-state dependent xc functionals appears to be a promising avenue. Here, we set out to shed light on the spin-state dependence of the xc functional by investigating the underlying xc holes, which we extract from configuration interaction calculations for model systems. We analyze the similarities and differences between the xc holes of the lowest-energy singlet and triplet states of the dihydrogen molecule, the helium atom, and the lithium dimer. To shed further light on the spin-state dependence of these xc holes we also discuss exact conditions that can be derived from the spin structure of the reduced two-electron density matrix. Altogether, our results suggest several possible routes towards the construction of explicitly spin-state dependent approximations for the xc functional.

Quantitative and Chemically Intuitive Evaluation of the Nature of M-L Bonds in Paramagnetic Compounds: Application of EDA-NOCV Theory to Spin Crossover Complexes

To improve understanding of M-L bonds in 3d transition metal complexes, analysis by energy decomposition analysis and natural orbital for chemical valence model (EDA-NOCV) is desirable as it provides a full, quantitative and chemically intuitive ab initio description of the M-L interactions. In this study, a generally applicable fragmentation and computational protocol was established and validated by using octahedral spin crossover (SCO) complexes, as the transition temperature (T1/2 ) is sensitive to subtle changes in M-L bonding. Specifically, EDA-NOCV analysis of Fe-N bonds in five [FeII (Lazine )2 (NCBH3 )2 ], in both low-spin (LS) and paramagnetic high-spin (HS) states led to: 1) development of a general, widely applicable, corrected M+L6 fragmentation, tested against a family of five LS [FeII (Lazine )3 ](BF4 )2 complexes; this confirmed that three Lazine are stronger ligands (ΔEorb,σ+π =-370 kcal mol-1 ) than 2 Lazine +2 NCBH3 (=-335 kcal mol-1 ), as observed. 2) Analysis of Fe-L bonding on LS→HS, reveals more ionic (ΔEelstat ) and less covalent (ΔEorb ) character (ΔEelstat :ΔEorb 55:45 LS→64:36 HS), mostly due to a big drop in σ (ΔEorb,σ ↓50 %; -310→-145 kcal mol-1 ), and a drop in π contributions (ΔEorb,π ↓90 %; -30→-3 kcal mol-1 ). 3) Strong correlation of observed T1/2 and ΔEorb,σ+π , for both LS and HS families (R2 =0.99 LS, R2 =0.95 HS), but no correlation of T1/2 and ΔΔEorb,σ+π (LS-HS) (R2 =0.11). Overall, this study has established and validated an EDA-NOCV protocol for M-L bonding analysis of any diamagnetic or paramagnetic, homoleptic or heteroleptic, octahedral transition metal complex. This new and widely applicable EDA-NOCV protocol holds great promise as a predictive tool.

Influence of Varying Functionalization on the Peroxidase Activity of Nickel(II)–Pyridine Macrocycle Catalysts: Mechanistic Insights from Density Functional Theory

Nickel(II) complexes of mono-functionalized pyridine-tetraazamacrocycles (PyMACs) are a new class of catalysts that possess promising activity similar to biological peroxidases. Experimental studies with ABTS (2,2′-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid), substrate) and H2O2 (oxidant) proposed that hydrogen-bonding and proton-transfer reactions facilitated by their pendant arm were responsible for their catalytic activity. In this work, density functional theory calculations were performed to unravel the influence of pendant arm functionalization on the catalytic performance of Ni(II)–PyMACs. Generated frontier orbitals suggested that Ni(II)–PyMACs activate H2O2 by satisfying two requirements: (1) the deprotonation of H2O2 to form the highly nucleophilic HOO−, and (2) the generation of low-spin, singlet state Ni(II)–PyMACs to allow the binding of HOO−. COSMO solvation-based energies revealed that the O–O Ni(II)–hydroperoxo bond, regardless of pendant arm type, ruptures favorably via heterolysis to produce high-spin (S = 1) [(L)Ni3+–O·]2+ and HO−. Aqueous solvation was found crucial in the stabilization of charged species, thereby favoring the heterolytic process over homolytic. The redox reaction of [(L)Ni3+–O·]2+ with ABTS obeyed a 1:2 stoichiometric ratio, followed by proton transfer to produce the final intermediate. The regeneration of Ni(II)–PyMACs at the final step involved the liberation of HO−, which was highly favorable when protons were readily available or when the pKa of the pendant arm was low.