Benchmarking Density Functional Methods for Calculation of State Energies of First Row Spin-Crossover Molecules

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.

DFT Struggles to Predict the Energy Landscape for Iron Pyridine Diimine-Catalyzed [2 + 2] Cycloaddition of Alkenes: Insights into the Problem and Alternative Solutions

In recent years, noninnocent pyridine diimine (PDI) complexes featuring first-row transition metals have emerged as prominent catalysts, demonstrating efficacy in a diverse range of vital organometallic transformations. However, the inherent complexity of the fundamental reactivity paradigm in these systems arises from the presence of a noninnocent ligand and the multispin feasibility of 3d metals. While density functional theory (DFT) has been widely used to unravel mechanistic insights, its limitations as a single-reference method can potentially misrepresent spin-state energetics, compromising our understanding of these intricate systems. In this study, we employ extensive high-level ab initio state averaged-complete active space self-consistent field/N-electron valence state perturbation theory (SA-CASSCF/NEVPT2) calculations in combination with DFT to investigate an iron-PDI-catalyzed [2 + 2] cycloaddition reaction of alkenes. The transformation proceeds through two major steps: oxidative cyclization and reductive elimination. Contrary to the predictions of DFT calculations, which suggest two-state reactivity in the reaction and identify reductive elimination as the turnover-limiting step, SA-CASSCF/NEVPT2-corrected results unequivocally establish a single-state reactivity scenario with oxidative cyclization as the turnover-limiting step. SA-CASSCF/NEVPT2-based insights into electronic ground states and electron distribution elucidate the intriguing interactions between the PDI ligand and the iron center, revealing the highly multiconfigurational nature of these species and providing a precise depiction of metal-ligand cooperativity throughout the transformation. A comparative assessment of several widely recognized DFT functionals against SA-CASSCF/NEVPT2-corrected data indicates that single-point energy calculations using the modern density functional MN15 on TPSSh geometries offer the most reliable density functional methodology, in scenarios where SA-CASSCF/NEVPT2 computational cost is a consideration.

Questing for homoleptic mononuclear manganese complexes with monodentate O-donor ligands

Compounds containing Mn-O bonds are of utmost importance in biological systems and catalytic processes. Nevertheless, mononuclear manganese complexes containing all O-donor ligands are still rare. Taking advantage of the low tendency of the pentafluoroorthotellurate ligand (teflate, OTeF5) to bridge metal centers, we have synthesized two homoleptic manganese complexes with monomeric structures and an all O-donor coordination sphere. The tetrahedrally distorted MnII anion, [Mn(OTeF5)4]2-, can be described as a high spin d5 complex (S = 5/2), as found experimentally (magnetic susceptibility measurements and EPR spectroscopy) and using theoretical calculations (DFT and CASSCF/NEVPT2). The high spin d4 electronic configuration (S = 2) of the MnIII anion, [Mn(OTeF5)5]2-, was also determined experimentally and theoretically, and a square pyramidal geometry was found to be the most stable one for this complex. Finally, the bonding situation in both complexes was investigated by means of the Interacting Quantum Atoms (IQA) methodology and compared to that of hypothetical mononuclear fluoromanganates. Within each pair of [MnXn]2- (n = 4, 5) species (X = OTeF5, F), the Mn-X interaction is found to be comparable, therefore proving that the similar electronic properties of the teflate and the fluoride are also responsible for the stabilization of these unique species.

Ligand Field Sensitive Spin Acceleration in the Iron-Catalyzed [2 + 2] Cycloaddition of Unactivated Alkenes and Dienes

Redox-active pyridine(diimine) (PDI) iron catalysts promote the reversible [2 + 2] cycloaddition of alkenes and dienes to cyclobutane derivatives that have applications ranging from fuels to chemically recyclable polymers. Metallacycles were identified as key intermediates, and spin crossover from the singlet to the triplet surface was calculated to facilitate the reductive coupling step responsible for the formation of the four-membered ring. In this work, a series of sterically and electronically differentiated PDI ligands was studied for the [2 + 2] cycloaddition of ethylene and butadiene to vinylcyclobutane. Kinetic studies revealed that the fastest and slowest turnover were observed with equally electron-deficient supporting ligands that either feature phenyl-substituted imine carbon atoms (MeBPDI) or a pyrazine core (MePZDI). While the oxidative cyclization was comparatively slow for both catalysts, the rate of reductive coupling─determined by stoichiometric 13C2H4 labeling studies─correlated with the turnover frequencies. Two-state density functional theory studies and the distinct electronic structures of related (iPrBPDI) and (iPrPZDI) iron methyl complexes revealed significantly different ligand field strengths due to either diminished ligand σ-donation (MeBPDI) or promoted metal π-backbonding (MePZDI). Spin acceleration, leading to fast reductive coupling and catalytic turnover, was promoted in the case of the weaker ligand field and depends on both the nature and position of the electron-withdrawing group. This study provides strong evidence for the role of two-state reactivity in C(sp3)-C(sp3) bond formation and insights on how ligand design either promotes or inhibits spin acceleration in earth-abundant metal catalysis.

Modeling Fe(II) Complexes Using Neural Networks

We report a Fe(II) data set of more than 23000 conformers in both low-spin (LS) and high-spin (HS) states. This data set was generated to develop a neural network model that is capable of predicting the energy and the energy splitting as a function of the conformation of a Fe(II) organometallic complex. In order to achieve this, we propose a type of scaled electronic embedding to cover the long-range interactions implicitly in our neural network describing the Fe(II) organometallic complexes. For the total energy prediction, the lowest MAE is 0.037 eV, while the lowest MAE of the splitting energy is 0.030 eV. Compared to baseline models, which only incorporate short-range interactions, our scaled electronic embeddings improve the accuracy by over 70% for the prediction of the total energy and the splitting energy. With regard to semiempirical methods, our proposed models reduce the MAE, with respect to these methods, by 2 orders of magnitude.

A Survey of the Angular Distortion Landscape in the Coordination Geometries of High-Spin Iron(II) 2,6-Bis(pyrazolyl)pyridine Complexes

Reaction of 2,4,6-trifluoropyridine with sodium 3,4-dimethoxybenzenethiolate and 2 equiv of sodium pyrazolate in tetrahydrofuran at room temperature affords 4-(3,4-dimethoxyphenylsulfanyl)-2,6-di(pyrazol-1-yl)pyridine (L), in 30% yield. The iron(II) complexes [FeL2][BF4]2 (1a) and [FeL2][ClO4]2 (1b) are high-spin with a highly distorted six-coordinate geometry. This structural deviation from ideal D2d symmetry is common in high-spin [Fe(bpp)2]2+ (bpp = di{pyrazol-1-yl}pyridine) derivatives, which are important in spin-crossover materials research. The magnitude of the distortion in 1a and 1b is the largest yet discovered for a mononuclear complex. Gas-phase DFT calculations at the ω-B97X-D/6-311G** level of theory identified four minimum or local minimum structural pathways across the distortion landscape, all of which are observed experimentally in different complexes. Small distortions from D2d symmetry are energetically favorable in complexes with electron-donating ligand substituents, including sulfanyl groups, which also have smaller energy penalties associated with the lowest energy distortion pathway. Natural population analysis showed that these differences reflect greater changes to the Fe-N{pyridyl} σ-bonding as the distortion proceeds, in the presence of more electron-rich pyridyl donors. The results imply that [Fe(bpp)2]2+ derivatives with electron-donating pyridyl substituents are more likely to undergo cooperative spin transitions in the solid state. The high-spin salt [Fe(bpp)2][CF3SO3]2, which also has a strong angular distortion, is also briefly described and included in the analysis.

Tuning valence tautomerism in a family of dinuclear cobalt complexes incorporating a conjugated bridging bis(dioxolene) ligand with weak communication

Valence tautomerism (VT) involves the stimulated reversible intramolecular electron transfer between a redox-active metal and ligand. Dinuclear cobalt complexes bridged by bis(dioxolene) ligands can undergo thermally-induced VT with access to {CoIII-cat-cat-CoIII}, {CoIII-cat-SQ-CoII} and {CoII-SQ-SQ-CoII} states (cat2- = catecholate, SQ˙- = semiquinonate, CoIII refers to low spin CoIII, CoII refers to high spin CoII). The resulting potential for two-step VT interconversions offers increased functionality over mononuclear examples. In this study, the bis(dioxolene) ligand 3,3',4,4'-tetrahydroxy-5,5'-dimethoxy-benzaldazine (thMH4) was paired with Mentpa (tpa = tris(2-pyridylmethyl)amine, n = 0-3 corresponds to methylation at 6-position of the pyridine rings) to afford [{Co(Mentpa)}2(thM)](PF6)2 (1a, n = 0; 2a, n = 2; 3a, n = 3). Structural, magnetic susceptibility and spectroscopic data show that 1a and 3a remain in the temperature invariant {CoIII-cat-cat-CoIII} and {CoII-SQ-SQ-CoII} forms in the solid state, respectively. In contrast, 2a exhibits incomplete thermally-induced VT between these two tautomeric forms via the mixed {CoIII-cat-SQ-CoII} tautomer. In solution, room temperature electronic absorption spectra are consistent with the assignments from the solid-state, with VT observed only for 2a. From electrochemistry, the proximity of the two 1e--processes for the thMn- ligand indicates weak electronic communication between the two dioxolene units, supporting the potential for a two-step VT interconversion in thMn- containing complexes. Comparison of the redox potentials of the Co and thMn- processes suggests that only 2a has these processes in sufficient proximity to afford the thermally-induced VT observed experimentally. Density functional theory calculations are consistent with the prerequisite energy ordering for a two-step transition for 2a, and temperature invariant {CoIII-cat-cat-CoIII} and {CoII-SQ-SQ-CoII} states for 1a and 3a, respectively. This work presents the third example, and the first formally conjugated example, of a bridging bis(dioxolene) ligand that can afford two-step VT in a Co complex, suggesting new possibilities towards applications based on multistep switching.

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.

Theoretical and DFT Study of Atypical Pentanuclear [(iPr3P)Ni]5Hn (n = 4, 6, 8) Clusters: What are the Rules?

The structure, bonding, and properties of a series of atypical pentanuclear nickel hydride clusters supported by electron-rich iPr3P of the type [(iPr3P)Ni]5Hn (n = 4, 6, 8; H4, H6, H8) and their anionic models where iPr3P are substituted by H- (H4', H6', H8') were investigated by density functional theory (DFT) calculations. All clusters were calculated to adopt a similar square pyramidal core geometry. Calculations indicate singlet ground states with small singlet-triplet gaps for H4 and H6, similar to previously reported experimental values. Molecular orbital theory description clusters were investigated using the simplified model complexes [HNi]5Hn5- (n = 4, 6, 8; H4', H6', H8'). The results show that there are three skeletal electron pairs (SEPs) in H4'. The addition of two molecules of H2 to form H6' and H8' results in the partial or full occupation of two degenerate MOs (e* set) that give two SEPs and one SEP, respectively. Indeed, the occupation of these low-lying weakly antibonding orbitals governs the multielectron chemistry available for these clusters and plays a role in their unique reactivity.

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.

Perspective from a Hubbard U-density corrected scheme towards a spin crossover-mediated change in gas affinity

By employing a recently proposed Hubbard U density-corrected scheme within density functional theory, we provide design principles towards the design of materials exhibiting a spin crossover-assisted gas release. Small molecular fragments are used as case study to identify two main mechanisms behind the change in binding energy upon spin transitions. The feasibility of the proposed mechanism in porous crystals is assessed by correlating the change in binding energy of CO2, CO, N2, and H2, upon spin crossover, with the adiabatic energy difference associated with the spin state change of the square-planar metal in Hofmann-type clathrates (M = Fe, Mn, Ni). A few promising cases are identified for the adsorption of intermediate ligand field strength molecules such as N2 and H2. The latter stands out as the most original result as the strong interaction in low spin, as expected from a Kubas mechanism, results in a large change in binding energy. This work provides a general perspective towards the engineering of open-metal site frameworks exhibiting local environments designed to have a spin crossover upon adsorption of specific gas molecules.

Spin state and magnetic coupling in polynuclear Ni(II) complexes from density functional theory: is there an optimal amount of Fock exchange?

Reliable prediction of the ground-state spin and magnetic coupling constants in transition-metal complexes is a well-known challenge for density functional theory (DFT). One popular strategy for addressing this long-standing issue involves the modification of the fraction of Fock exchange in a hybrid functional. Here we explore the viability of this approach using three polynuclear metal-organic complexes based on a Ni4O4 cubane motif, having different ground state spin values (S = 0, 2, 4) owing to the use of different ligands. We systematically search for an optimum fraction of Fock exchange, across various global, range-separated, and double hybrid functionals. We find that for all functionals tested, at best there only exists a very narrow range of Fock exchange fractions which results in a correct prediction of the ground-state spin for all three complexes. The useful range is functional dependent, but general trends can be identified. Typically, at least two similar systems must be used in order to determine both an upper and lower limit of the optimal range. This is likely owing to conflicting demands of minimizing delocalization errors, which typically requires a higher percentage of Fock exchange, and addressing static correlation, which typically requires a lower one. Furthermore, we find that within the optimal range of Fock exchange, the sign and relative magnitude of Ni-Ni magnetic coupling constants are reasonably well reproduced, but there is still room for quantitative improvement in the prediction. Thus, the prediction of spin state and magnetic coupling in polynuclear complexes remains an ongoing challenge for DFT.

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.

Controlling Spin Crossover in a Family of Dinuclear Fe(III) Complexes via the Bis(catecholate) Bridging Ligand

Spin crossover (SCO) complexes can reversibly switch between low spin (LS) and high spin (HS) states, affording possible applications in sensing, displays, and molecular electronics. Dinuclear SCO complexes with access to [LS-LS], [LS-HS], and [HS-HS] states may offer increased levels of functionality. The nature of the SCO interconversion in dinuclear complexes is influenced by the local electronic environment. We report the synthesis and characterization of [{FeIII(tpa)}2spiro](PF6)2 (1), [{FeIII(tpa)}2Br4spiro](PF6)2 (2), and [{FeIII(tpa)}2thea](PF6)2 (3) (tpa = tris(2-pyridylmethyl)amine, spiroH4 = 3,3,3',3'-tetramethyl-1,1'-spirobi(indan)-5,5',6,6'-tetraol, Br4spiroH4 = 3,3,3',3'-tetramethyl-1,1'-spirobi(indan)-4,4',7,7'-tetrabromo-5,5',6,6'-tetraol, theaH4 = 2,3,6,7-tetrahydroxy-9,10-dimethyl-9,10-dihydro-9,10-ethanoanthracene), utilizing non-conjugated bis(catecholate) bridging ligands. In the solid state, magnetic and structural analysis shows that 1 remains in the [HS-HS] state, while 2 and 3 undergo a partial SCO interconversion upon cooling from room temperature involving the mixed [LS-HS] state. In solution, all complexes undergo SCO from [HS-HS] at room temperature, via [LS-HS] to mixtures including [LS-LS] at 77 K, with the extent of SCO increasing in the order 1 < 2 < 3. Gas phase density functional theory calculations suggest a [LS-LS] ground state for all complexes, with the [LS-HS] and [HS-HS] states successively destabilized. The relative energy separations indicate that ligand field strength increases following spiro4- < Br4spiro4- < thea4-, consistent with solid-state magnetic and EPR behavior. All three complexes show stabilization of the [LS-HS] state in relation to the midpoint energy between [LS-LS] and [HS-HS]. The relative stability of the [LS-HS] state increases with increasing ligand field strength of the bis(catecholate) bridging ligand in the order 1 < 2 < 3. The bromo substituents of Br4spiro4- increase the ligand field strength relative to spiro4-, while the stronger ligand field provided by thea4- arises from extension of the overlapping π-orbital system across the two catecholate units. This study highlights how SCO behavior in dinuclear complexes can be modulated by the bridging ligand, providing useful insights for the design of molecules that can be interconverted between more than two states.

Transition Temperature for Spin-Crossover Materials with the Mean Value Ensemble Hubbard-U Correction

Calculation of transition temperatures T1/2 for thermally driven spin-crossover in condensed phases is challenging, even with sophisticated state-of-the-art density functional approximations. The first issue is the accuracy of the adiabatic crossover energy difference ΔEHL between the low- and high-spin states of the bistable metal-organic complexes. The other is the proper inclusion of entropic contributions to the Gibbs free energy from the electronic and vibrational degrees of freedom. We discuss the effects of treatments of both contributions upon the calculation of thermochemical properties for a set of 20 spin-crossover materials using a Hubbard-U correction obtained from a reference ensemble spin-state. The U values obtained from a simplest bimolecular representation may overcorrect, somewhat, the ΔEHL values, hence giving somewhat excessive reduction of the T1/2 results with respect to their U = 0 values in the crystalline phase. We discuss the origins of the discrepancies by analyzing different sources of uncertainties. By use of a first-coordination-sphere approximation and the assumption that vibrational contributions from the outermost atoms in a metal-organic complex are similar in both low- and high-spin states, we achieve T1/2 results with the low-cost, widely used PBE generalized gradient density functional approximation comparable to those from the more costly, more sophisticated r2SCAN meta-generalized gradient approximation. The procedure is promising for use in high-throughput materials screening, because it combines rather low computational effort requirements with freedom from user manipulation of parameters.

Comparative Density Functional Theory Study of Magnetic Exchange Couplings in Dinuclear Transition-Metal Complexes

Multicenter transition-metal complexes (MCTMs) with magnetically interacting ions have been proposed as components for information-processing devices and storage units. For any practical application of MCTMs as magnetic units, it is crucial to characterize their magnetic behavior, and in particular, the isotropic magnetic exchange coupling, J, between its magnetic centers. Due to the large size of typical MCTMs, density functional theory is the only practical electronic structure method for evaluating the J coupling. Here, we assess the accuracy of different density functional approximations for predicting the magnetic couplings of eight dinuclear transition-metal complexes, including five dimanganese, two dicopper, and one divanadium with known reliable experimental J couplings spanning from ferromagnetic to strong antiferromagnetic. The density functionals considered include global hybrid functionals which mix semilocal density functional approximations and exact exchange with a fixed admixing parameter, six local hybrid functionals where the admixing parameters are extended to be spatially dependent, the SCAN and r2SCAN meta-generalized gradient approximations (GGAs), and two widely used GGAs. We found that global hybrids tested in this work have a tendency to over-correct the error in magnetic coupling parameters from the Perdew-Burke-Ernzerhof (PBE) GGA as seen for manganese complexes. The performance of local hybrid density functionals shows no improvement in terms of bias and is scattered without a clear trend, suggesting that more efforts are needed for the extension from global to local hybrid density functionals for this particular property. The SCAN and r2SCAN meta-GGAs are found to perform as well as benchmark global hybrids on most tested complexes. We further analyze the charge density redistribution of meta-GGAs as well as global and local hybrid density functionals with respect to that of PBE, in connection to the self-interaction error or delocalization error.

How complex-surface interactions modulate the spin transition of Fe(II) SCO complexes supported on metallic surfaces?

The deposition of a prototypical spin-crossover [Fe(phen)2(NCS)2] complex on Au(111), Cu(111) and Ag(111) surfaces has been investigated by means of periodic DFT+U calculations, with the aim of understanding how different metallic surfaces affect the spin state switching. Our results show that adsorption is metal- and spin-dependent, with different preferred adsorption sites for the different surfaces and spin states. For the three considered surfaces adsorption energies are larger in the LS state than in the HS one, which increases the transition enthalpy by 58.7 kJ mol-1 for Cu(111), 14.6 kJ mol-1 for Au(111) and 9.6 kJ mol-1 for Ag(111) with respect to the free molecule. There is a clear correlation between this effect and the extent of the complex-surface interaction, which can be established from adsorption energies, surface-complex distances and charge density difference plots as: Cu(111) > Au(111) > Ag(111). Therefore, a stronger interaction with the surface produces a larger energy difference between two spin states, making the spin transition less probable to occur. Finally, our calculations show that it would be possible to probe the spin-state of the deposited molecules from the STM images, in line with the recent experimental results.

All-electron APW+lo calculation of magnetic molecules with the SIRIUS domain-specific package

We report APW+lo (augmented plane wave plus local orbital) density functional theory (DFT) calculations of large molecular systems using the domain specific SIRIUS multi-functional DFT package. The APW and FLAPW (full potential linearized APW) task and data parallelism options and the advanced eigen-system solver provided by SIRIUS can be exploited for performance gains in ground state Kohn-Sham calculations on large systems. This approach is distinct from our prior use of SIRIUS as a library backend to another APW+lo or FLAPW code. We benchmark the code and demonstrate performance on several magnetic molecule and metal organic framework systems. We show that the SIRIUS package in itself is capable of handling systems as large as a several hundred atoms in the unit cell without having to make technical choices that result in the loss of accuracy with respect to that needed for the study of magnetic systems.

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.

Computational demonstration of isomer- and spin-state-dependent charge transport in molecular junctions composed of charge-neutral iron(II) spin-crossover complexes

Chemistry offers a multitude of opportunities towards harnessing functional molecular materials with application propensity. One emerging area of interest is molecular spintronics, in which charge and spin degrees of freedom have been used to achieve power-efficient device architectures. Herein, we show that, with the aid of state-of-the-art quantum chemical calculations on designer molecular junctions, the conductance and spin filtering capabilities are molecular structure-dependent. As inferred from the calculations, structural control over the transport can be achieved by changing the position of the thiomethyl (SMe) anchoring groups for Au(111) electrodes in a set of isomeric 2,2'-bipyridine-based metal coordinating ligand entities L1 and L2. The computational studies on heteroleptic iron(II) coordination complexes (1 and 2) composed of L1 and L2 reveal that switching the spin-state of the iron(II) centers, from the low-spin (LS) to high-spin (HS) state, by means of an external electric field stimulus, could, in theory, be performed. Such switching, known as spin-crossover (SCO), renders charge transport through single-molecule junctions of 1 and 2 spin-state-dependent, and the HS junctions are more conductive than the LS junctions for both complexes. Additionally, the LS and HS junctions based on complex 1 are more conductive than those featuring complex 2. Moreover, it is predicted that the spin filtering efficiency (SFE) of the HS junctions strongly depends on the bridging complex geometry, with 1 showing a voltage-dependent SFE, whereas 2 exhibits an SFE of practically 100% over all the studied voltage range. To be pragmatic towards applications, the ligands L1 and L2 and complex 1 have been successfully synthesized, and the spin-state switching propensity of 1 in the bulk state has been elucidated. The results shown in this study might lead to the synthesis and characterization of isomeric SCO complexes with tuneable spin-state switching and charge transport properties.

Mean Value Ensemble Hubbard-U Correction for Spin-Crossover Molecules

High-throughput searches for spin-crossover molecules require Hubbard-U corrections to common density functional exchange-correlation (XC) approximations. However, the U_eff values obtained from linear response or based on previous studies overcorrect the spin-crossover energies. We demonstrate that employing a linearly mixed ensemble average spin state as the reference configuration for the linear response calculation of U_eff resolves this issue. Validation on a commonly used set of spin-crossover complexes shows that these ensemble U_eff values consistently are smaller than those calculated directly on a pure spin state, irrespective of whether that be low- or high-spin. Adiabatic crossover energies using this methodology for a generalized gradient approximation XC functional are closer to the expected target energy range than with conventional U_eff values. Based on the observation that the U_eff correction is similar for different complexes that share transition metals with the same oxidation state, we devise a set of recommended averaged U_eff values for high-throughput calculations.

Negative Differential Resistance in Spin-Crossover Molecular Devices

We demonstrate, based on low-temperature scanning tunneling microscopy (STM) and spectroscopy, a pronounced negative differential resistance (NDR) in spin-crossover (SCO) molecular devices, where a Fe^II SCO molecule is deposited on surfaces. The STM measurements reveal that the NDR is robust with respect to substrate materials, temperature, and the number of SCO layers. This indicates that the NDR is intrinsically related to the electronic structure of the SCO molecule. Experimental results are supported by density functional theory (DFT) with nonequilibrium Green's function (NEGF) calculations and a generic theoretical model. While the DFT+NEGF calculations reproduce NDR for a special atomically sharp STM tip, the effect is attributed to the energy-dependent tip density of states rather than the molecule itself. We, therefore, propose a Coulomb blockade model involving three molecular orbitals with very different spatial localization as suggested by the molecular electronic structure.

Redox-Programmable Spin-Crossover Behaviors in a Cationic Framework

Metal-organic frameworks (MOFs) provide versatile platforms to construct multi-responsive materials. Herein, by introducing the neutral tetradentate ligand and the linear dicyanoaurate(I) anion, we reported a rare cationic MOF [Fe^II(TPB){Au^I(CN)₂}]I·4H₂O·4DMF (TPB = 1,2,4,5-tetra(pyridin-4-yl)benzene) with hysteretic spin-crossover (SCO) behavior near room temperature. This hybrid framework with an open metal site (Au^I) exhibits redox-programmable capability toward dihalogen molecules. By means of post-synthetic modification, all the linear [Au^I(CN)₂]^- linkers can be oxidized to square planar [Au^III(CN)₂X₂]^- units, which results in the hysteretic SCO behaviors switching from one-step to two-step for Br₂ and three-step for I₂. More importantly, the stepwise SCO behaviors can go back to one-step via the reduction by l-ascorbic acid (AA). Periodic DFT calculations using various SCAN-type exchange-correlation functionals have been employed to rationalize the experimental data. Hence, these results demonstrate for the first time that switchable one-/two-/three-stepped SCO dynamics can be manipulated by chemical redox reactions, which opens a new perspective for multi-responsive molecular switches.

Spin transitions in ferric catecholate complexes mediated by outer-sphere counteranions

A family of ionic ferric catecholate complexes 1-4 bearing a disubstituted 3,6-di-tert-butyl-catecholate ligand (3,6-DBCatH₂) and tetradentate tris(2-pyridylmethyl)amine (TPA) was prepared and its spin transitions were investigated. Variation of the outer-sphere counteranions (PF₆, BPh₄, ClO₄, BF₄) is accompanied by changes in the magnetic behavior of the compounds under consideration. The crystal structures of complexes 1, 3 and 4 were determined by single crystal X-ray diffraction analysis at 100 K and 293 K. The complexes were characterized by the occurrence of a thermally induced spin-crossover process in the solid state with different degrees of completeness, which was confirmed by the comprehensive spectroscopic investigation (EPR, magnetic susceptibility, Mössbauer, and XAS) of the isolated compounds. Complex 4 containing BF₄ anions was found to demonstrate valence tautomeric transition along with spin-crossover. This finding makes compound 4 the first salt-like mononuclear ferric catecholate complex exhibiting valence tautomerism.

Direct Benzene Hydroxylation with Dioxygen Induced by Copper Complexes: Uncovering the Active Species by DFT Calculations

The direct oxidation of benzene into phenol using molecular oxygen at very mild temperatures can be promoted in the presence of the copper complex Tp^Br3Cu(NCMe) in the homogeneous phase in the presence of ascorbic acid as the source of protons and electrons. The stoichiometric nature, relative to copper, of this transformation prompted a thorough DFT study in order to understand the reaction pathway. As a result, the dinuclear species Tp^Br3Cu^II(μ-O^•)(μ-OH)Cu^IITp^Br3 is proposed as the relevant structure which is responsible for activating the arene C–H bond leading to phenol formation.

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.

One-Step versus Two-Step Valence Tautomeric Transitions in Tetraoxolene-Bridged Dinuclear Cobalt Compounds

The syntheses of valence tautomeric compounds with multistep transitions using new redox-active ligands are the long-term goal of the field of bistable materials. The redox-active tetraoxolene ligand, 2,7-di-tert-butylpyrene-4,5,9,10-tetraone (pyrene^Q-Q), is now developed to synthesize a pair of dinuclear compounds {[CoL₂]₂(pyrene^Sq-Sq)}[Co(CO)₄]₂·xCH₂Cl₂·2C₆H₅CH₃ (1, x = 2, L = 1,10-phenanthroline, phen; 2, x = 1.5, L = 2,2'-bipyridine, bpy). Variable-temperature magnetic susceptibilities and single-crystal X-ray diffraction measurements indicate a partial one-step valence tautomeric transition for 1 and a rare two-step valence tautomeric transition for 2, respectively. DFT calculation results are consistent with the experimental data, revealing the correlation between thermodynamic parameters and the one-step/two-step valence tautomeric behaviors.

Structural and theoretical insights into solvent effects in an iron(III) SCO complex

Alcohol effects in a series of iron(III) spin crossover complexes [Fe(qsal-Cl)2]NO3·ROH (R = Me 1, Et 2, 1-Pr 3) are explored. Despite the solvents differing from each other by only...

Accurate calculation of spin-state energy gaps in Fe(III) spin-crossover systems using density functional methods

Fe(III) complexes are receiving ever-increasing attention as spin crossover (SCO) systems because they are usually air stable, as opposed to Fe(II) complexes, which are prone to oxidation. Here, we present the first systematic study exclusively devoted to assess the accuracy of several exchange-correlation functionals when it comes to predicting the energy gap between the high-spin (S = 5/2) and the low-spin (S = 1/2) states of Fe(III) complexes. Using a dataset of 24 different Fe(III) hexacoordinated complexes, it is demonstrated that the B3LYP* functional is an excellent choice not only for predicting spin-state energy gaps for Fe(III) complexes undergoing spin-transitions but also for discriminating Fe(III) complexes that are either low- or high-spin in the whole range of temperatures. Our benchmark study has led to the identification of a very versatile Fe(III) compound whose SCO properties can be engineered upon changing a single axial ligand. Overall, this work demonstrates that B3LYP* is a reliable functional for screening new spin-crossover systems with tailored properties.

Computational Study of CO2 Reduction Catalyzed by Iron(I) Complex at Different Spin States: Cooperativity of Hydrogen Bonding and Auxiliary Group Effect

To explore alternative approaches to the CO₂ reduction to formate and provide an insight into the spin state effect on the CO₂ reduction, we theoretically designed a kind of low-valence iron(I) model complex, whose doublet, quartet, and sextet states are denoted as ² Fe(I), ⁴ Fe(I), and ⁶ Fe(I), respectively. This complex is featured with an iron(I) center, which bonds to a 1,2-ethanediamine (en) and a 2-hydroxy-biphenyl group. Reaction mechanisms for the CO₂ reduction to formate catalyzed by this iron(I) model complex were explored using density functional theory (DFT) computations. Studies showed that the univalent iron(I) compound can efficiently fix and activate a CO₂ molecule, whereas its oxidized forms with trivalent iron(III) or bivalent iron(II) cannot activate CO₂. For the iron(I) compound, it was found that the lowest spin state ² Fe(I) is the most favorable for the CO₂ reduction as the reactions barriers involving ² Fe(I), ⁴ Fe(I), and ⁶ Fe(I) are 25.6, 37.2, and 35.9 kcal/mol, respectively. Yet, a photosensitizer-free visible-light-mediated high-low spin shift from ⁴ Fe(I) and ⁶ Fe(I) to ² Fe(I) is likely through the reverse intersystem crossing (RIC) because the ⁴ Fe(I) and ⁶ Fe(I) compounds have strong absorption in the visible-light range. Notably, the synergistic interaction between the hydrogen bonding from the auxiliary hydroxyl group in the 2-hydroxy-biphenyl moiety to CO₂ and an intermediate five-membered ring promotes the proton transfer, leading to the formation of the -COOH moiety from CO₂ and the Fe-O bond. With the addition of H₂, one H₂ molecule is split by the Fe-O bond and thus serves as H atom sources for both the CO₂ reduction and the recovery of the auxiliary hydroxyl group. The present theoretical study provides a novel solution for the challenging CO₂ reduction, which calls for further experimental verifications.

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.

Experimental and Computational Insight into the Mechanism of NO Binding to Ferric Microperoxidase. The Likely Role of Tautomerization to Account for the pH Dependence

According to the current paradigm, the metal-hydroxo bond in a six-coordinate porphyrin complex is believed to be significantly less reactive in ligand substitution than the analogous metal-aqua bond, due to a much higher strength of the former bond. Here, we report kinetic studies for nitric oxide (NO) binding to a heme-protein model, acetylated microperoxidase-11 (AcMP-11), that challenge this paradigm. In the studied pH range 7.4-12.6, ferric AcMP-11 exists in three acid-base forms, assigned in the literature as [(AcMP-11)Fe^III(H₂O)(HisH)] (1), [(AcMP-11)Fe^III(OH)(HisH)] (2), and [(AcMP-11)Fe^III(OH)(His^-)] (3). From the pH dependence of the second-order rate constant for NO binding (k_on), we determined individual rate constants characterizing forms 1-3, revealing only a ca. 10-fold decrease in the NO binding rate on going from 1 (k_on⁽¹⁾ = 3.8 × 10⁶ M^-1 s^-1) to 2 (k_on⁽²⁾ = 4.0 × 10⁵ M^-1 s^-1) and the inertness of 3. These findings lead to the abandonment of the dissociatively activated mechanism, in which the reaction rate can be directly correlated with the Fe-OH bond energy, as the mechanistic explanation for the process with regard to 2. The reactivity of 2 is accounted for through the existence of a tautomeric equilibrium between the major [(AcMP-11)Fe^III(OH)(HisH)] (2a) and minor [(AcMP-11)Fe^III(H₂O)(His^-)] (2b) species, of which the second one is assigned as the NO binding target due to its labile Fe-OH₂ bond. The proposed mechanism is further substantiated by quantum-chemical calculations, which confirmed both the significant labilization of the Fe-OH₂ bond in the [(AcMP-11)Fe^III(H₂O)(His^-)] tautomer and the feasibility of the tautomer formation, especially after introducing empirical corrections to the computed relative acidities of the H₂O and HisH ligands based on the experimental pK_a values. It is shown that the "effective lability" of the axial ligand (OH^-/H₂O) in 2 may be comparable to the lability of the H₂O ligand in 1.

Fe(phen)2(NCS)2 on Al(100): influence of AlN layer on spin crossover barrier

We study how a nitride layer affects spin crossover (SCO) in a single Fe(phen)₂(NCS)₂ (Fephen) molecule adsorbed on the Al(100) surface using ab initio calculations. The Coulomb correlation of the open-shell 3d electrons has been considered using a Hubbard-U correction within different exchange-correlation approximations, including the van der Waals density functional. We determine the SCO energy barrier by computing the minimum energy path between the high-spin (HS) and low-spin (LS) states via direct constraint relaxations. It is shown that the HS-LS energy difference is slightly increased once deposited on Al(100), and thus LS states tend to be stabilized, as usually observed on metallic substrates. The oxidation of metallic Al to aluminum ions in the AlN layer promotes molecular adsorption, while it decreases HS-LS splitting, making Fephen switchable between its two spin states. Due to enhanced molecule-substrate bonding, the SCO barrier height is considerably increased, which may promote cooperativity. This effect is consistent with the AlN facilitated charge transfer at the interface that results from a reduction in surface work function. Our findings reveal the crucial role that surface electronic structure plays in maintaining spin bistability of the molecular adsorbate.