Iron(II) and Iron(III) Spin Crossover: Toward an Optimal Density Functional

Chelate Complexes of 3d Transition Metal Ions─A Challenge for Electronic-Structure Methods?

Different electronic-structure methods were assessed for their ability to predict two important properties of the industrially relevant chelating agent nitrilotriacetic acid (NTA): its selectivity with respect to six different first-row transition metal ions and the spin-state energetics of its complex with Fe(III). The investigated methods encompassed density functional theory (DFT), the random phase approximation (RPA), coupled cluster (CC) theory, and the auxiliary-field quantum Monte Carlo (AFQMC) method, as well as the complete active space self-consistent field (CASSCF) method and the respective on-top methods: second-order N-electron valence state perturbation theory (NEVPT2) and multiconfiguration pair-density functional theory (MC-PDFT). Different strategies for selecting active spaces were explored, and the density matrix renormalization group (DMRG) approach was used to solve the largest active spaces. Despite somewhat ambiguous multi-reference diagnostics, most methods gave relatively good agreement with experimental data for the chemical reactions connected to the selectivity, which only involved transition-metal complexes in their high-spin state. CC methods yielded the highest accuracy followed by range-separated DFT and AFQMC. We discussed in detail that even higher accuracies can be obtained with NEVPT2, under the prerequisite that consistent active spaces along the entire chemical reaction can be selected, which was not the case for reactions involving Fe(III). A bigger challenge for electronic-structure methods was the prediction of the spin-state energetics, which additionally involved lower spin states that exhibited larger multi-reference diagnostics. Conceptually different, typically accurate methods ranging from CC theory via DMRG-NEVPT2 in combination with large active spaces to AFQMC agreed well that the high-spin state is energetically significantly favored over the other spin states. This was in contrast to most DFT functionals and RPA which yielded a smaller stabilization and some common DFT functionals and MC-PDFT even predicting the low-spin state to be energetically most favorable.

Fano resonance in molecular junctions of spin crossover complexes

In this paper, we introduce a novel molecular switch paradigm that integrates spin crossover complexes with the Fano resonance effect. Specifically, by performing density-functional theory calculations, the feasibility of achieving Fano resonance using spin crossover complexes is demonstrated in our designed molecular junctions using the complex {Fe[H2B(pz)2]2[Bp(bipy)]} [pz = 1-pyrazolyl, Bp(bipy) = bis(phenylethynyl)(2,2'-bipyridine)]. It is further revealed that the Fano resonance, particularly the Fano dip, is most prominent in the junction with cobalt tips among all the schemes, together with the spin-filtering effect. Most importantly, this junction of cobalt tips is able to exhibit three distinct conductance states, which are controlled by the modulation of Fano resonance due to the spin-state transition of the complex and the applied gate voltage. Such a molecular switch paradigm holds potential for applications in logic gates, memory units, sensors, thermoelectrics, and beyond.

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.

Benchmarking Density Functional Theory Methods for Metalloenzyme Reactions: The Introduction of the MME55 Set

We present a new benchmark set of metalloenzyme model reaction energies and barrier heights that we call MME55. The set contains 10 different enzymes, representing eight transition metals, both open and closed shell systems, and system sizes of up to 116 atoms. We use four DLPNO-CCSD(T)-based approaches to calculate reference values against which we then benchmark the performance of a range of density functional approximations with and without dispersion corrections. Dispersion corrections improve the results across the board, and triple-ζ basis sets provide the best balance of efficiency and accuracy. Jacob's ladder is reproduced for the whole set based on averaged mean absolute (percent) deviations, with the double hybrids SOS0-PBE0-2-D3(BJ) and revDOD-PBEP86-D4 standing out as the most accurate methods for the MME55 set. The range-separated hybrids ωB97M-V and ωB97X-V also perform well here and can be recommended as a reliable compromise between accuracy and efficiency; they have already been shown to be robust across many other types of chemical problems, as well. Despite the popularity of B3LYP in computational enzymology, it is not a strong performer on our benchmark set, and we discourage its use for enzyme energetics.

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.

Iron(II) complexes of 2,6-bis(imidazo[1,2-a]pyridin-2-yl)pyridine and related ligands with annelated distal heterocyclic donors

Following a published synthesis of 2,6-bis(imidazo[1,2-a]pyridin-2-yl)pyridine (L1), treatment of α,α'-dibromo-2,6-diacetylpyridine with 2 equiv. 2-aminopyrimidine or 2-aminoquinoline in refluxing acetonitrile respectively gives 2,6-bis(imidazo[1,2-a]pyrimidin-2-yl)pyridine (L2) and 2,6-bis(imidazo[1,2-a]quinolin-2-yl)pyridine (L3). Solvated crystals of [Fe(L1)2][BF4]2 (1[BF4]2) and [Fe(L2)2][BF4]2 (2[BF4]2) are mostly high-spin, although one solvate of 1[BF4]2 undergoes thermal spin-crossover on cooling. The iron coordination geometry is consistently distorted in crystals of 2[BF4]2 which may reflect the influence of intramolecular, inter-ligand N⋯π interactions on the molecular conformation. Only 1 : 1 Fe : L3 complexes were observed in solution, or isolated in the solid state; a crystal structure of [FeBr(py)2L3]Br·0.5H2O (py = pyridine) is presented. A solvate crystal structure of high-spin [Fe(L4)2][BF4]2 (L4 = 2,6-di{quinolin-2-yl}pyridine; 4[BF4]2) is also described, which exhibits a highly distorted six-coordinate geometry with a helical ligand conformation. The iron(II) complexes are high-spin in solution at room temperature, but 1[BF4]2 and 2[BF4]2 undergo thermal spin-crossover equilibria on cooling. All the compounds exhibit a ligand-based emission in solution at room temperature. Gas phase DFT calculations mostly reproduce the spin state properties of the complexes, but show small anomalies attributed to intramolecular, inter-ligand dispersion interactions in the sterically crowded 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.

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.

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.

Insights into the deviation from piecewise linearity in transition metal complexes from supervised machine learning models

Virtual high-throughput screening (VHTS) and machine learning (ML) with density functional theory (DFT) suffer from inaccuracies from the underlying density functional approximation (DFA). Many of these inaccuracies can be traced to the lack of derivative discontinuity that leads to a curvature in the energy with electron addition or removal. Over a dataset of nearly one thousand transition metal complexes typical of VHTS applications, we computed and analyzed the average curvature (i.e., deviation from piecewise linearity) for 23 density functional approximations spanning multiple rungs of "Jacob's ladder". While we observe the expected dependence of the curvatures on Hartree-Fock exchange, we note limited correlation of curvature values between different rungs of "Jacob's ladder". We train ML models (i.e., artificial neural networks or ANNs) to predict the curvature and the associated frontier orbital energies for each of these 23 functionals and then interpret differences in curvature among the different DFAs through analysis of the ML models. Notably, we observe spin to play a much more important role in determining the curvature of range-separated and double hybrids in comparison to semi-local functionals, explaining why curvature values are weakly correlated between these and other families of functionals. Over a space of 187.2k hypothetical compounds, we use our ANNs to pinpoint DFAs for which representative transition metal complexes have near-zero curvature with low uncertainty, demonstrating an approach to accelerate screening of complexes with targeted optical gaps.

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.

Di-Iron(II) [2+2] Helicates of Bis-(Dipyrazolylpyridine) Ligands: The Influence of the Ligand Linker Group on Spin State Properties

Four bis[2-{pyrazol-1-yl}-6-{pyrazol-3-yl}pyridine] ligands have been synthesized, with butane-1,4-diyl (L¹ ), pyrid-2,6-diyl (L² ), benzene-1,2-dimethylenyl (L³ ) and propane-1,3-diyl (L⁴ ) linkers between the tridentate metal-binding domains. L¹ and L² form [Fe₂ (μ-L)₂ ]X₄ (X^- =BF₄ ^- or ClO₄ ^- ) helicate complexes when treated with the appropriate iron(II) precursor. Solvate crystals of [Fe₂ (μ-L¹ )₂ ][BF₄ ]₄ exhibit three different helicate conformations, which differ in the torsions of their butanediyl linker groups. The solvates exhibit gradual thermal spin-crossover, with examples of stepwise switching and partial spin-crossover to a low-temperature mixed-spin form. Salts of [Fe₂ (μ-L² )₂ ]⁴⁺ are high-spin, which reflects their highly twisted iron coordination geometry. The composition and dynamics of assembly structures formed by iron(II) with L¹ -L³ vary with the ligand linker group, by mass spectrometry and ¹ H NMR spectroscopy. Gas-phase DFT calculations imply the butanediyl linker conformation in [Fe₂ (μ-L¹ )₂ ]⁴⁺ influences its spin state properties, but show anomalies attributed to intramolecular electrostatic repulsion between the iron atoms.

First crystal structure of an Fe(III) anionic complex based on a pyruvic acid thiosemicarbazone ligand with Li+: synthesis, features of magnetic behavior and theoretical analysis

The iron(III) anionic complex based on a pyruvic acid thiosemicarbazone ligand with the lithium cation Li[Fe^III(thpy)₂]·3H₂O (1) has been synthesized and characterized by FTIR spectroscopy, powder and single crystal X-ray diffraction, direct current magnetic susceptibility measurements, and ⁵⁷Fe Mössbauer spectroscopy. Moreover, the molecular structure of the [Fe(thpy)₂]^- anion has been determined for the first time. The [Fe(thpy)₂]^- units in the triclinic P1̄ lattice of 1 are assembled into layers parallel to the bc plane. The Li⁺ cations and water molecules are located between the layers and the structure is stabilized by hydrogen bonding. The [Fe(thpy)₂]^- anions form interconnected dimer pairs through hydrogen bonds and short contacts with Fe⋯Fe separation of 6.7861(4) Å. According to dc magnetic measurements, compound 1 demonstrates an incipient spin-crossover transition from the LS (S = 1/2) to the HS (S = 5/2) state above 250 K. The Bleaney-Bowers equation for a model of an isolated LS dimer with a mean-field correction was applied to fit the experimental data of magnetic susceptibility dependence on temperature in the temperature range of 2-250 K. The intra-dimer J₁ = -1.79(1) K and inter-dimer J₂ = -0.24(3) K antiferromagnetic coupling constants were defined. The analysis of the ⁵⁷Fe Mössbauer spectra at 80 K and 296 K confirms the presence of the shortened distances between the iron nuclei. Moreover, the influence of the lithium cation on the stabilization of the LS state was shown for the [Fe(thpy)₂]^- anion. BS-DFT calculations for the optimized structure of two isolated [Fe(thpy)₂]^- anions also correctly predict a weak exchange J₁(calc) = -0.92 K. DFT calculations revealed the OPBE (GGA-type) functional that correctly predicts the spin-crossover transition for the iron(III) thpy compounds. Besides, the effect of the N₂O₄, N₂S₂O₂, and N₂Se₂O₂ coordination environments on the energy stabilization of the LS state of iron(III) anionic thpy complexes was noted as well.

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.

Redox-active ligands as a challenge for electronic structure methods

To improve the catalytic activity of 3d transition metal catalysts, redox-active ligands are a promising tool. These ligands influence the oxidation state of the metal center as well as the ground spin-state and make the experimental determination of both properties challenging. Therefore, first-principles calculations, in particular employing density functional theory with a proper choice of exchange-correlation (xc) functional, are crucial. Common xc functionals were tested on a simple class of metal complexes: homoleptic, octahedral tris(diimine) iron(II) complexes. The spin-state energy splittings for most of these complexes showed the expected linear dependence on the amount of exact exchange included in the xc functionals. Even though varying redox-activity affects the electronic structure of the complexes considerably, the sensitivity of the spin-state energetics to the exact exchange admixture is surprisingly small. For iron(II) complexes with highly redox-active ligands and for a broad range of ligands in the reduced tris(diimine) iron(I) complexes, self-consistent field convergence to local minima was observed, which differ from the global minimum in the redox state of the ligand. This may also result in convergence to a molecular structure that corresponds to an energetically higher-lying local minimum. One criterion to detect such behavior is a change in the sign of the slope for the dependence of the spin-state energy splittings on the amount of exact exchange. We discuss possible protocols for dealing with such artifacts in cases in which a large number of calculations makes checking by hand unfeasible.

Spin-State Splittings in 3d Transition-Metal Complexes Revisited: Toward a Reliable Theory Benchmark

A new composite method for the calculation of spin-crossover energies in 3d transition-metal complexes based on multireference methods is presented. The method reduces to MRCISD+Q at the complete-basis-set (CBS) level for atomic ions, for which it gives excitation energies with a mean absolute error of only ca. 0.01 eV. For molecular complexes, the CASPT2+δMRCI composite approach corresponds to a CASPT2/CBS calculation augmented by a high-level MRCISD+Q-CASPT2 correction with a smaller ligand basis set. For a set of [Fe(He)6]n+ test complexes, the approach reproduces full MRCISD+Q/CBS results to within better than 0.04 eV, without depending on any arbitrary IPEA shifts. The high-quality CASPT2+δMRCI method has then been applied to a series of 3d transition-metal hexaqua complexes in aqueous solution, augmented by an elaborate 3D-RISM-SCF solvent treatment of the underlying structures. It provides unprecedented agreement with experiment for the lowest-lying vertical spin-flip excitation energies, except for the Fe³⁺ system. Closer examination of the latter case provides strong evidence that the observed lowest-energy excitation at 1.56 eV, which has been used frequently for evaluating quantum-chemical methods, does not arise from the iron(III) hexaqua complex in solution, but from its singly deprotonated counterpart, [Fe(H2O)5OH]2+.

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.

Spin-crossover Fe(ii) complexes on a surface: a mixture of low-spin and high-spin molecules at low temperature from quantum-chemistry calculations

The deposition of a 2D monolayer of an Fe(ii) SCO complex on Au(111) is studied by quantum chemistry calculations. The results indicate that there exists thermodynamic and kinetic factors favoring the presence of the mixed HS/LS state at low temperature.

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.

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.

Machine learning to tame divergent density functional approximations: a new path to consensus materials design principles

Virtual high-throughput screening (VHTS) with density functional theory (DFT) and machine-learning (ML)-acceleration is essential in rapid materials discovery. By necessity, efficient DFT-based workflows are carried out with a single density functional approximation (DFA). Nevertheless, properties evaluated with different DFAs can be expected to disagree for cases with challenging electronic structure (e.g., open-shell transition-metal complexes, TMCs) for which rapid screening is most needed and accurate benchmarks are often unavailable. To quantify the effect of DFA bias, we introduce an approach to rapidly obtain property predictions from 23 representative DFAs spanning multiple families, “rungs” (e.g., semi-local to double hybrid) and basis sets on over 2000 TMCs. Although computed property values (e.g., spin state splitting and frontier orbital gap) differ by DFA, high linear correlations persist across all DFAs. We train independent ML models for each DFA and observe convergent trends in feature importance, providing DFA-invariant, universal design rules. We devise a strategy to train artificial neural network (ANN) models informed by all 23 DFAs and use them to predict properties (e.g., spin-splitting energy) of over 187k TMCs. By requiring consensus of the ANN-predicted DFA properties, we improve correspondence of computational lead compounds with literature-mined, experimental compounds over the typically employed single-DFA approach.

Machine learning (ML)-based feature analysis reveals universal design rules regardless of density functional choices. Using the consensus among multiple functionals, we identify robust lead complexes in ML-accelerated chemical discovery.

Structures and Spin States of Iron(II) Complexes of Isomeric 2,6-Di(1,2,3-triazolyl)pyridine Ligands

Iron(II) complex salts of 2,6-di(1,2,3-triazol-1-yl)pyridine (L¹) are unexpectedly unstable in undried solvent. This is explained by the isolation of [Fe(L¹)₄(H₂O)₂][ClO₄]₂ and [Fe(NCS)₂(L¹)₂(H₂O)₂]·L¹, containing L¹ bound as a monodentate ligand rather than in the expected tridentate fashion. These complexes associate into 4⁴ grid structures through O-H···N hydrogen bonding; a solvate of a related 4⁴ coordination framework, catena-[Cu(μ-L¹)₂(H₂O)₂][BF₄]₂, is also presented. The isomeric ligands 2,6-di(1,2,3-triazol-2-yl)pyridine (L²) and 2,6-di(1H-1,2,3-triazol-4-yl)pyridine (L³) bind to iron(II) in a more typical tridentate fashion. Solvates of [Fe(L³)₂][ClO₄]₂ are low-spin and diamagnetic in the solid state and in solution, while [Fe(L²)₂][ClO₄]₂ and [Co(L³)₂][BF₄]₂ are fully high-spin. Treatment of L³ with methyl iodide affords 2,6-di(2-methyl-1,2,3-triazol-4-yl)pyridine (L⁴) and 2-(1-methyl-1,2,3-triazol-4-yl)-6-(2-methyl-1,2,3-triazol-4-yl)pyridine (L⁵). While salts of [Fe(L⁵)₂]²⁺ are low-spin in the solid state, [Fe(L⁴)₂][ClO₄]₂·H₂O is high-spin, and [Fe(L⁴)₂][ClO₄]₂·3MeNO₂ exhibits a hysteretic spin transition to 50% completeness at T_1/2 = 128 K (ΔT_1/2 = 6 K). This transition proceeds via a symmetry-breaking phase transition to an unusual low-temperature phase containing three unique cation sites with high-spin, low-spin, and 1:1 mixed-spin populations. The unusual distribution of the spin states in the low-temperature phase reflects "spin-state frustration" of the mixed-spin cation site by an equal number of high-spin and low-spin nearest neighbors. Gas-phase density functional theory calculations reproduce the spin-state preferences of these and some related complexes. These highlight the interplay between the σ-basicity and π-acidity of the heterocyclic donors in this ligand type, which have opposing influences on the molecular ligand field. The Brønsted basicities of L¹-L³ are very sensitive to the linkage isomerism of their triazolyl donors, which explains why their iron complex spin states show more variation than the better-known iron(II)/2,6-dipyrazolylpyridine system.

Replacing hybrid density functional theory: motivation and recent advances

Density functional theory (DFT) is the most widely-used electronic structure approximation across chemistry, physics, and materials science. Every year, thousands of papers report hybrid DFT simulations of chemical structures, mechanisms, and spectra. Unfortunately, hybrid DFT's accuracy is ultimately limited by tradeoffs between over-delocalization and under-binding. This review summarizes these tradeoffs, and introduces six modern attempts to go beyond them while maintaining hybrid DFT's relatively low computational cost: DFT+U, self-interaction corrections, localized orbital scaling corrections, local hybrid functionals, real-space nondynamical correlation, and our rung-3.5 approach. The review concludes with practical suggestions for DFT users to identify and mitigate these tradeoffs' impact on their simulations.

Enhanced Ammonia Oxidation Catalysis by a Low-Spin Iron Complex Featuring Cis Coordination Sites

The goal of using ammonia as a solar fuel motivates the development of selective ammonia oxidation (AO) catalysts for fuel cell applications. Herein, we describe Fe-mediated AO electrocatalysis with [(bpyPy₂Me)Fe(MeCN)₂]²⁺, exhibiting the highest turnover number (TON) reported to date for a molecular system. To improve on our recent report of a related iron AO electrocatalyst, [(TPA)Fe(MeCN)₂]²⁺ (TON of 16), the present [(bpyPy₂Me)Fe(MeCN)₂]²⁺ system (TON of 149) features a stronger-field, more rigid auxiliary ligand that maintains cis-labile sites and a dominant low-spin population at the Fe(II) state. The latter is posited to mitigate demetalation and hence catalyst degradation by the presence of a large excess of ammonia under the catalytic conditions. Additionally, the [(bpyPy₂Me)Fe(MeCN)₂]²⁺ system exhibits a substantially faster AO rate (ca. 50×) at significantly lower (∼250 mV) applied bias compared to [(TPA)Fe(MeCN)₂]²⁺. Electrochemical data are consistent with an initial E₁ net H-atom abstraction step that furnishes the cis amide/ammine complex [(bpyPy₂Me)Fe(NH₂)(NH₃)]²⁺, followed by the onset of catalysis at E₂. Theoretical calculations suggest the possibility of N-N bond formation via multiple thermodynamically plausible pathways, including both reductive elimination and ammonia nucleophilic attack. In sum, this study underscores that Fe, an earth-abundant metal, is a promising metal for further development in metal-mediated AO catalysis by molecular systems.

Zeolites at the Molecular Level: What Can Be Learned from Molecular Modeling

This review puts the development of molecular modeling methods in the context of their applications to zeolitic active sites. We attempt to highlight the utmost necessity of close cooperation between theory and experiment, resulting both in advances in computational methods and in progress in experimental techniques.

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 energetics of metallocenes: How do best wave function and density functional theory results compare with the experimental data?

We benchmark the accuracy of quantum-chemical methods, including wave function theory methods [coupled cluster theory at the CCSD(T) level, multiconfigurational perturbation-theory (CASPT2, NEVPT2) and internally contracted multireference configuration interaction (MRCI)] and 30 density functional theory (DFT) approximations, in reproducing the spin-state splittings of metallocenes. The reference values of the electronic energy differences are derived from the experimental spin-crossover enthalpy for manganocene and the spectral data of singlet-triplet transitions for ruthenocene, ferrocene, and cobaltocenium. For ferrocene and cobaltocenium we revise the previous experimental interpretations regarding the lowest triplet energy; our argument is based on the comparison with the lowest singlet excitation energy and herein reported, carefully determined absorption spectrum of ferrocene. When deriving vertical energies from the experimental band maxima, we go beyond the routine vertical energy approximation by introducing vibronic corrections based on simulated vibrational envelopes. The benchmarking result confirms the high accuracy of the CCSD(T) method (in particular, for UCCSD(T) based on Hartree-Fock orbitals we find for our dataset: maximum error 0.12 eV, weighted mean absolute error 0.07 eV, weighted mean signed error 0.01 eV). The high accuracy of the single-reference method is corroborated by the analysis of a multiconfigurational character of the complete active space wave function for the triplet state of ferrocene. On the DFT side, our results confirm the non-universality problem with approximate functionals. The present study is an important step toward establishing an extensive and representative benchmark set of experiment-derived spin-state energetics for transition metal complexes.

A Review of Density Functional Models for the Description of Fe(II) Spin-Crossover Complexes

Spin-crossover (SCO) materials have for more than 30 years stood out for their vast application potential in memory, sensing and display devices. To reach magnetic multistability conditions, the high-spin (HS) and low-spin (LS) states have to be carefully balanced by ligand field stabilization and spin-pairing energies. Both effects could be effectively modelled by electronic structure theory, if the description would be accurate enough to describe these concurrent influences to within a few kJ/mol. Such a milestone would allow for the in silico-driven development of SCO complexes. However, so far, the ab initio simulation of such systems has been dominated by general gradient approximation density functional calculations. The latter can only provide the right answer for the wrong reasons, given that the LS states are grossly over-stabilized. In this contribution, we explore different venues for the parameterization of hybrid functionals. A fitting set is provided on the basis of explicitly correlated coupled cluster calculations, with single- and multi-dimensional fitting approaches being tested to selected classes of hybrid functionals (hybrid, range-separated, and local hybrid). Promising agreement to benchmark data is found for a rescaled PBE0 hybrid functional and a local version thereof, with a discussion of different atomic exchange factors.

Spin-inversion mechanisms in O2 binding to a model heme compound: A perspective from nonadiabatic wave packet calculations

Spin-inversion dynamics in O₂ binding to a model heme complex, which consisted of Fe(II)-porphyrin and imidazole, were studied using nonadiabatic wave packet dynamics calculations. We considered three active nuclear degrees of freedom in the dynamics, including the motions along the Fe-O distance, Fe-O-O angle, and Fe out-of-plane distance. Spin-free potential energy surfaces for the singlet, triplet, quintet, and septet states were developed using density functional theory calculations, and spin-orbit coupling elements were obtained from CASSCF-level electronic structure calculations. The spin-inversion mainly occurred between the singlet state and one of the triplet states due to large spin-orbit couplings and the contributions of other states were extremely small. The present quantum dynamics calculations suggested that the narrow crossing region model plays a dominant role in the O₂ binding dynamics. In addition, the one-dimensional Landau-Zener model underestimated the nonadiabatic transition probability.

A DFT Study on FeI/FeII/FeIII Mechanism of the Cross-Coupling between Haloalkane and Aryl Grignard Reagent Catalyzed by Iron-SciOPP Complexes

To explore plausible reaction pathways of the cross-coupling reaction between a haloalkane and an aryl metal reagent catalyzed by an iron–phosphine complex, we examine the reaction of FeBrPh(SciOPP) 1 and bromocycloheptane employing density functional theory (DFT) calculations. Besides the cross-coupling, we also examined the competitive pathways of β-hydrogen elimination to give the corresponding alkene byproduct. The DFT study on the reaction pathways explains the cross-coupling selectivity over the elimination in terms of Fe^I/Fe^II/Fe^III mechanism which involves the generation of alkyl radical intermediates and their propagation in a chain reaction manner. The present study gives insight into the detailed molecular mechanic of the cross-coupling reaction and revises the Fe^II/Fe^II mechanisms previously proposed by us and others.

Spin Splitting Energy of Transition Metals: A New, More Affordable Wave Function Benchmark Method and Its Use to Test Density Functional Theory

Accurately predicting the spin splitting energy of chemical species is important for understanding their reactivity and magnetic properties, but it is very challenging, especially for molecules containing transition metals. One impediment to progress is the scarcity of accurate benchmark data. Here we report a set of calculations designed to yield reliable benchmarks for simple transition-metal complexes that can be used to test density functional methods that are affordable for large systems of more practical interest. Various wave function methods are tested against experiment for Fe²⁺, Fe³⁺, and Co³⁺, including CASSCF, CASPT2, CASPT3, MRCISD, MRCISD+Q, ACPF, AQCC, CCSD(T), and CASPT2/CCSD(T) and also a new method called CASPT2.5, which is performed by taking the average of the CASPT2 and CASPT3 energies. We find that MRCISD+Q, ACPF, and AQCC require smaller active spaces for good accuracy than are required by CASPT2 and CASPT3, and this aspect may be important for calculations on larger molecules; here we find that CASPT2.5 extrapolated to a complete basis set is the most suitable method-in terms of computational cost and in terms of accuracy on monatomic systems-and therefore we chose this method for molecular benchmarks. Then Kohn-Sham density functional calculations with 60 exchange-correlation functionals are tested for FeF₂, FeCl₂, and CoF₂. We find that MN15-L, M06-SX, and revM06 have very good agreement with CASPT2.5 benchmarks in terms of both the spin splitting energy and the optimized geometry for each spin state. In addition, we recommend def2-TZVP as the most suitable basis set to perform density functional calculations for molecular spin splitting energies; extra polarization functions in the basis set do not help to increase the accuracy of the spin splitting energy in KS calculations.

Using electronegativity and hardness to test density functionals

Density functional theory (DFT) is used in thousands of papers each year, yet lack of universality reduces DFT's predictive capacity, and functionals may produce energy-density imbalances. The absolute electronegativity (χ) and hardness (η) directly reflect the energy-density relationship via the chemical potential ∂E/∂N and we thus hypothesized that they probe universality. We studied χ and η for atoms Z = 1-36 using 50 diverse functionals covering all major classes. Very few functionals describe both χ and η well. η benefits from error cancellation, whereas χ is marred by error propagation from IP and EA; thus, almost all standard GGA and hybrid functionals display a plateau in the MAE at ∼0.2 eV-0.3 eV for η. In contrast, variable performance for χ indicates problems in describing the chemical potential by DFT. The accuracy and precision of a functional is far from linearly related, yet for a universal functional, we expect linearity. Popular functionals such as B3LYP, PBE, and revPBE perform poorly for both properties. Density sensitivity calculations indicate large density-derived errors as occupation of degenerate p- and d-orbitals causes "non-universality" and large dependency on exact exchange. Thus, we argue that performance for χ for the same systems is a hallmark of an important aspect of universality by probing ∂E/∂N. With this metric, B98, B97-1, PW6B95D3, MN-15, rev-TPSS, HSE06, and APFD are the most "universal" among the tested functionals. B98 and B97-1 are accurate for very diverse metal-ligand bonds, supporting that a balanced description of ∂E/∂N and ∂E²/∂N², via χ and η, is probably a first simple probe of universality.

Spin-inversion mechanisms in O2 binding to a model heme complex revisited by density function theory calculations

Spin-inversion mechanisms in O₂ binding to a model heme complex, consisting of Fe(II)-porphyrin and imidazole, were investigated using density-functional theory calculations. First, we applied the recently proposed mixed-spin Hamiltonian method to locate spin-inversion structures between different total spin multiplicities. Nine spin-inversion structures were successfully optimized for the singlet-triplet, singlet-quintet, triplet-quintet, and quintet-septet spin-inversion processes. We found that the singlet-triplet spin-inversion points are located around the potential energy surface region at short Fe-O distances, whereas the singlet-quintet and quintet-septet spin-inversion points are located at longer Fe-O distances. This suggests that both narrow and broad crossing models play roles in O₂ binding to the Fe-porphyrin complex. To further understand spin-inversion mechanisms, we performed on-the-fly Born-Oppenheimer molecular dynamics calculations. The reaction coordinates, which are correlated to the spin-inversion dynamics between different spin multiplicities, are also discussed.

Heteronuclear Iron(III)-Schiff Base Complexes with the Hexacyanidocobaltate(III) Anion: On the Quest To Understand the Governing Factors of Spin Crossover

Two heteronuclear compounds (1 and 2) containing three ferric centers linked in facial-like mode with the magnetically silent hexacyanidocobaltate(III) anion were prepared and studied. The structural investigation revealed that both compounds are tetranuclear complexes with molecular formulas of [{Fe(L1)NC}₃Co(CN)₃]·2CH₃OH·2.5CH₃CN (1) and [{Fe(L2)NC}₃Co(CN)₃]·2H₂O·1CH₃OH (2). The magnetic properties of both complexes are controlled by the molecular design of the corresponding pentadentate Schiff base anions L1^2- and L2^2-. While compound 2 with a symmetric ligand prepared from salicylaldehyde shows high-spin state properties, compound 1 containing the asymmetric ligand with naphthalene units either is low-spin in its solvated form or shows a gradual but hysteretic spin crossover event when desolvated. The magnetic behavior was analyzed with respect to the Ising-like model and spin Hamiltonian, respectively, and the results were confronted with ab initio calculations. Additionally, the influence of structural features, lattice solvent molecules, the distribution of electronic terms, and active orbitals on the spin state properties of reported complexes is discussed.

Controlling the Lifetime of the Triplet MLCT State in Fe(II) Polypyridyl Complexes through Ligand Modification

A computational study is presented in which two strategies of ligand modifications have been explored to invert the relative energy of the metal-to-ligand charge transfer (MLCT) and metal-centered (MC) state in Fe(II)-polypyridyl complexes. Replacing the bipyridines by stronger σ donors increases the ligand-field strength and pushes the MC state to higher energy, while the use of ligands with a larger π conjugation leads to lower MLCT energies.

Spin modification of iron(ii) complexes via covalent (dative) and dispersion guided non-covalent bonding with N-heterocyclic carbenes: DFT, DLPNO-CCSD(T) and MCSCF studies

Spin crossover from high spin Fe(ii)-phthalocyanine to low or intermediate spin via either dative covalent or non-covalent interaction by just varying the substituent using the same core ligand.

Large-scale comparison of 3d and 4d transition metal complexes illuminates the reduced effect of exchange on second-row spin-state energetics

The origin of distinct 3d vs. 4d transition metal complex sensitivity to exchange is explored over a large data set.

Appraising spin-state energetics in transition metal complexes using double-hybrid models: accountability of SOS0-PBESCAN0-2(a) as a promising paradigm

Through a comprehensive survey, reliable double-hybrid models have been validated and proposed for spin-state energetics in transition metal complexes.