Consistent descriptions of metal–ligand bonds and spin-crossover in inorganic chemistry

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

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

Predicting spin states of iron porphyrins with DFT methods including crystal packing effects and thermodynamic corrections

Accurate computational treatment of spin states for transition metal complexes, exemplified by iron porphyrins, lies at the heart of quantum bioinorganic chemistry, but at the same time represents a great challenge for approximate density functional theory (DFT) methods, which are predominantly used. Here, the accuracy of DFT methods for spin-state splittings in iron porphyrin is assessed by probing the ability to correctly predict the ground states for six FeIII or FeII complexes experimentally characterized in solid state. For each case, molecular and periodic DFT calculations are employed to quantify the effect of porphyrin side substituents and the crystal packing effect (CPE) on the spin-state splitting. It is proposed to partition the total CPE into additive components, the direct and structural one, the importance of which is shown to significantly vary from case to case. By knowing the substituent effect, the CPE, and the Gibbs free energy thermodynamic correction from calculations, one can employ the experimental ground-state information in order to derive a quantitative constraint on the electronic energy difference for a simplified (porphin) model of the experimentally characterized metalloporphyrin. The constraints derived in such a way-in the form of single or double inequalities-are used to assess the accuracy of dispersion-corrected DFT methods for 6 spin-state splittings of [FeIII(P)(2-MeIm)2]+, [FeIII(P)(2-MeIm)]+, [FeII(P)(THF)2] and [FeII(P)] models (where P is porphin, 2-MeIm is 2-methylimidazole, THF is tetrahydrofuran). These data constitute the new benchmark set of spin states for crystalline iron porphyrins (SSCIP6). The highest accuracy is obtained in the case of double-hybrid functionals (B2PLYP-D3, DSD-PBEB95-D3), whereas hybrid functionals, especially those with reduced admixture of the exact exchange (B3LYP*-D3, TPSSh-D3), are found to considerably overstabilize the intermediate spin state, leading to incorrect ground-state prediction in FeIII porphyrins. The present approach, which can be generalized to other transition metal complexes, is not only useful in method benchmarking, but also sheds light on the interpretations of experimental data for metalloporphyrins, which are important models to understand the electronic properties of heme proteins.

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.

Spin-Flip via Subtle Electronic Perturbation in Axially Ligated Diiron(III) Porphyrin Dimer

Spin state switching in the metal center is a crucial phenomenon in many enzymatic reactions in biology. The spin state alteration, a critical step in cytochrome P450 catalysis, is driven most likely through a weak perturbation upon substrate binding in the enzyme, which is still not well clarified. In the current work, the spin state transition of iron(III) from high to intermediate via an admixed state is observed upon a subtle electronic perturbation to the sulphonate moieties coordinated axially to a diiron(III)porphyrin dimer. While electron-donating substituents stabilize the high-spin state of iron(III), strongly electron-withdrawing groups stabilize an intermediate-spin state, whereas the moderate electron-withdrawing nature of axial ligands resulted in an admixed state. Confirmation of the molecular structures and their spin states have been made utilizing single-crystal X-ray structure analysis, Mössbauer, magnetic, EPR, and 1H NMR spectroscopic investigations. The position of the signals of the porphyrin macrocycle in the paramagnetic 1H NMR is found to be very characteristic of the spin state of the iron center in solution. The Curie plot for the pure high-spin complexes shows the signals' temperature dependency in line with the Curie law. Conversely, the pure intermediate-spin state of iron exhibits an anti-Curie temperature dependence, whereas the admixed-spin state of iron displays significant curvature of the lines in the Curie plot. An extensive DFT analysis displays a linear dependence between the energy difference between dx 2 - y 2 ${{_{x{^{2}}- y{^{2}}}}}$ and dz 2 ${{_{z{^{2}}}}}$ orbital versus Fe-Npor distance for the complexes reported here. Furthermore, a strong linear correlation between the Fe-O distance and the spin density over the oxygen atom, as well as the Fe-Npor distance for the complexes, has been observed. Thus, a slight electronic perturbation at the axial ligand of the diheme resulted in a large change in the electronic structures with a spin-flip. This is at par with the metalloenzymes, which employ minute perturbations around the periphery of the active sites, leading to spin state transitions.

Spin effect on redox acceleration and regioselectivity in Fe-catalyzed alkyne hydrosilylation

Iron catalysts are ideal transition metal catalysts because of the Earths abundant, cheap, biocompatible features of iron salts. Iron catalysts often have unique open-shell structures that easily undergo spin crossover in chemical transformations, a feature rarely found in noble metal catalysts. Unfortunately, little is known currently about how the open-shell structure and spin crossover affect the reactivity and selectivity of iron catalysts, which makes the development of iron catalysts a low efficient trial-and-error program. In this paper, a combination of experiments and theoretical calculations revealed that the iron-catalyzed hydrosilylation of alkynes is typical spin-crossover catalysis. Deep insight into the electronic structures of a set of well-defined open-shell active formal Fe(0) catalysts revealed that the spin-delocalization between the iron center and the 1,10-phenanthroline ligand effectively regulates the iron center's spin and oxidation state to meet the opposite electrostatic requirements of oxidative addition and reductive elimination, respectively, and the spin crossover is essential for this electron transfer process. The triplet transition state was essential for achieving high regioselectivity through tuning the nonbonding interactions. These findings provide an important reference for understanding the effect of catalyst spin state on reaction. It is inspiring for the development of iron catalysts and other Earth-abundant metal catalysts, especially from the point of view of ligand development.

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.

Chemically accurate singlet-triplet gaps of organic chromophores and linear acenes by the random phase approximation and σ-functionals

Predicting the energy differences between different spin-states is challenging for many widely used ab initio electronic structure methods. We here assess the ability of the direct random phase approximation (dRPA), dRPA plus two different screened second-order exchange (SOX) corrections, and σ-functionals to predict adiabatic singlet-triplet gaps. With mean absolute deviations of below 0.1 eV to experimental reference values, independent of the Kohn-Sham starting point, dRPA and σ-functionals accurately predict singlet-triplet gaps of 18 organic chromophores. The addition of SOX corrections to dRPA considerably worsens agreement with experiment, adding to the mounting evidence that dRPA+SOX methods are not generally applicable beyond-RPA methods. Also for a series of linear acene chains with up to ten fused rings, dRPA, and σ-functionals are in excellent agreement with coupled-cluster single double triple reference data. In agreement with advanced multi-reference methods, dRPA@PBE and σ-functional@PBE predict a singlet ground state for all chain lengths, while dRPA@PBE0 and σ-functional@PBE0 predict a triplet ground state for longer acenes. Our work shows dRPA and σ-functionals to be reliable methods for calculating singlet-triplet gaps in aromatic molecules.

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.

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.

Environmental Control of the Magnetic Behavior of Transition Metal Complexes: Density Functional Theory Study of Zeolite Y Embedded Complexes [M(bpy)3]2+@Y (M = Fe2+, Co2+)

Using the supramolecular approach developed for the study of the guest-host interactions in the zeolite Y encapsulated [Fe(bpy)₃]²⁺ compound: [Fe(bpy)₃]²⁺@Y (bpy = 2,2'-bipyridine) [Vargas et al., J. Chem. Theory Comput. 2009, 5, 97-115], we apply density functional theory (DFT) to the study of the influence of zeolite Y encapsulation on the structural and energetic properties of [Co(bpy)₃]²⁺ in the low-spin (LS) and high-spin (HS) states, while revisiting [Fe(bpy)₃]²⁺@Y. Although the accurate prediction of the HS-LS energy difference ΔE_HL^el remains challenging for current DFT methods, they give accurate estimates of its variation Δ(ΔE_HL^el) in a series of complexes of a given transition metal ion. Therefore, denoting [M(bpy)₃]²⁺@Y_SM as the supramolecular model of the inclusion compounds, the values of ΔE_HL^el for the bpy complexes in the gas phase and in the supercage of zeolite Y were determined by combining the DFT estimates of Δ(ΔE_HL^el) in the series {[M(NCH)₆]²⁺, [M(bpy)₃]²⁺, and [M(bpy)₃]²⁺@Y_SM}, with accurate CCSD(T) estimates of ΔE_HL^el in the benchmark complexes [M(NCH)₆]²⁺ (M = Fe, Co) [Lawson Daku et al., J. Chem. Theory Comput., 2012, 8, 4216-4231]. Generalized gradient approximations as well as global and range-separated hybrids were employed. In order to better account for the key role of dispersion, they were also augmented with the semiempirical D2, D3BJ, and D3BJM dispersion corrections when available. The use of the D3BJ and D3BJM corrections led to similar results, and this is only with the use of the D2 scheme that (i) the free and encapsulated [Fe(bpy)₃]²⁺ are correctly predicted as LS species and that (ii) the encapsulation of both complexes translates into a destabilization of their HS state with respect to their LS state. The increase of the HS-LS energy difference is smaller for [Co(bpy)₃]²⁺ than [Fe(bpy)₃]²⁺ because the HS-LS molecular volume difference ΔV_HL in [Co(bpy)₃]²⁺ is ∼50% smaller than in [Fe(bpy)₃]²⁺. Periodic DFT calculations performed on crystalline [M(bpy)₃]²⁺@Y show that the employed [M(bpy)₃]²⁺@Y_SM supramolecular model allows the influence of encapsulation on the geometry and the spin-state energetics of [M(bpy)₃]²⁺ (M = Fe, Co) to be quantitatively captured.

Quasi-Restricted Orbital Description of the Copper(I) Photoredox Catalytic Cycle

In this computational study, the electronic structure changes along the oxidative and reductive quenching cycles of a homoleptic and a heteroleptic prototype Cu(I) photoredox catalyst, namely [Cu(dmp)2]+ (dmp = 2,9-dimethyl-1,10-phenanthroline) and [Cu(phen)(POP)]+ (POP = bis[2-(diphenylphosphino)phenyl]ether) are scrutinized and characterized using quasi-restricted orbitals (QRO), electron density differences and spin densities. After validating our density functional theory-based computational protocol, the equilibrium geometries and wavefunctions (using QROs and atom/fragment compositions) of the four states involved in photoredox cycle (S0, T1, Dox and Dred) are systematically and thoroughly described. The formal ground and excited state ligand- and metal-centered redox events are substantiated by the QRO description of the open-shell triplet 3MLCT (d9L-1), Dox (d9L0) and Dred (d10L-1) species and the corresponding structural changes, e.g., flattening distortion, shortening/elongation of Cu-N/Cu-P bonds, are rationalized in terms of the underlying electronic structure transformations. Amongst others, we reveal the molecular-scale delocalization of the ligand-centered radical in the a 3MLCT (d9L-1) and Dred (d9L-1) states of homoleptic [Cu(dmp)2]+ and its localization to the redox-active phenanthroline ligand in the case of heteroleptic [Cu(phen)(POP)]+.

Trend in light-induced excited-state spin trapping in Fe(II)-based spin crossover systems

A computational study of the light-induced excited spin-state trapping (LIESST) in a number of Fe(II) spin crossover complexes, coordinated by monodentate, bidentate and multidentate ligands is carried out, with the goal to uncover the trend in the low temperature relaxation rate. A nine order of magnitude change in low temperature relaxation rate is observed among the complexes. The trend is rationalized in terms of the change in metal-ligand covalency, numerically estimated by the crystal orbital Hamiltonian population, thus influencing the back donation or delocalization of the electrons from the low-lying Fe(II)-centered molecular orbital to the empty low-lying ligand-centered π* antibonding molecular orbitals.

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

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

Performance Enhancement of APW+lo Calculations by Simplest Separation of Concerns

Full-potential linearized augmented plane wave (LAPW) and APW plus local orbital (APW+lo) codes differ widely in both their user interfaces and in capabilities for calculations and analysis beyond their common central task of all-electron solution of the Kohn–Sham equations. However, that common central task opens a possible route to performance enhancement, namely to offload the basic LAPW/APW+lo algorithms to a library optimized purely for that purpose. To explore that opportunity, we have interfaced the Exciting-Plus (“EP”) LAPW/APW+lo DFT code with the highly optimized SIRIUS multi-functional DFT package. This simplest realization of the separation of concerns approach yields substantial performance over the base EP code via additional task parallelism without significant change in the EP source code or user interface. We provide benchmarks of the interfaced code against the original EP using small bulk systems, and demonstrate performance on a spin-crossover molecule and magnetic molecule that are of size and complexity at the margins of the capability of the EP code itself.

Ionization Energies and Redox Potentials of Hydrated Transition Metal Ions: Evaluation of Domain-Based Local Pair Natural Orbital Coupled Cluster Approaches

Hydrated transition metal ions are prototypical systems that can be used to model properties of transition metals in complex chemical environments. These seemingly simple systems present challenges for computational chemistry and are thus crucial in evaluations of quantum chemical methods for spin-state and redox energetics. In this work, we explore the applicability of the domain-based pair natural orbital implementation of coupled cluster (DLPNO-CC) theory to the calculation of ionization energies and redox potentials for hydrated ions of all first transition row (3d) metals in the 2+/3+ oxidation states, in connection with various solvation approaches. In terms of model definition, we investigate the construction of a minimally explicitly hydrated quantum cluster with a first and second hydration layer. We report on the convergence with respect to the coupled cluster expansion and the PNO space, as well as on the role of perturbative triple excitations. A recent implementation of the conductor-like polarizable continuum model (CPCM) for the DLPNO-CC approach is employed to determine self-consistent redox potentials at the coupled cluster level. Our results establish conditions for the convergence of DLPNO-CCSD(T) energetics and stress the absolute necessity to explicitly consider the second solvation sphere even when CPCM is used. The achievable accuracy for redox potentials of a practical DLPNO-based approach is, on average, 0.13 V. Furthermore, multilayer approaches that combine a higher-level DLPNO-CCSD(T) description of the first solvation sphere with a lower-level description of the second solvation layer are investigated. The present work establishes optimal and transferable methodological choices for employing DLPNO-based coupled cluster theory, the associated CPCM implementation, and cost-efficient multilayer derivatives of the approach for open-shell transition metal systems in complex environments.

Computational Investigation of the Metal and Ligand Substitution Effects on the Structure and Electronic States of the Phosphoranimide Tetramer Complexes of Cu(I), Ni(I), Co(I), and Fe(I)

The structurally unique saddle-shaped paramagnetic tetrametallic clusters of Co(I) and Ni(I) with phosphoranimide ligands have been synthesized and proposed as catalyst precursors. The analogous Cu(I) nanocluster is planar and diamagnetic. These notable variations in geometry and ground electronic states indicate that the effect of metal and ligand substituents on the structure and electronic properties of these complexes requires investigation. We present a computational study of a series of these novel homoleptic complexes containing Co(I), Ni(I), and Cu(I) as well as Fe(I) coordinated to phosphoranimides with electron-donating and withdrawing substituents, conducted at the relativistic density functional theory level using ZORA-PBE/TZP. The optimized structures of the saddle-shaped Co(I) and Ni(I) and planar Cu(I) tetramers with linear N-M-N coordination are validated with respect to X-ray diffraction determinations. The ground-state analysis indicates that Cu(I) complexes are diamagnetic, whereas Ni(I) and Co(I) complexes are in high-spin states, in agreement with magnetic susceptibility measurements. The computational results show that Fe(I) complexes are saddle shaped and high spin. The Co(I) complex is stabilized by a metal macrocycle distortion from square to diamond, as elucidated from its Walsh diagram. The effects of metals and ligand substituents on the ground electronic state, metal center coordination environment, and energy of the complexes are investigated. The bulky tertiary butyl substituent causes the largest saddle-shape distortion of the tetramer marcocycle, which partially offsets its electron-donating effect. Macrocycle distortions with N-M-N site angles ranging from obtuse to alternating obtuse reflex are correlated with the increasing number of unpaired electrons. The phenyl-substituted complexes are expected to have the highest reactivity toward electrophiles. Understanding the interplay between structural and electronic parameters is intended to guide the development of synthetic cooperative systems for multielectron redox reactions, models of biological systems, and molecular magnets.

Bioinorganic Chemistry of Zinc in Relation to the Immune System

Zinc is well-known to have a central role in human inflammation and immunity and is itself an anti-inflammatory and antiviral agent. Despite its massively documented role in such processes, the underlying chemistry of zinc in relation to specific proteins and pathways of the immune system has not received much focus. This short review provides an overview of this topic, with emphasis on the structures of key proteins, zinc coordination chemistry, and probable mechanisms involved in zinc-based immunity, with some focus points for future chemical and biological research.

Precision Biotransformation of Emerging Pollutants by Human Cytochrome P450 Using Computational-Experimental Synergy: A Case Study of Tris(1,3-dichloro-2-propyl) Phosphate

Precision biotransformation is an envisioned strategy offering detailed insights into biotransformation pathways in real environmental settings using experimentally guided high-accuracy quantum chemistry. Emerging pollutants, whose metabolites are easily overlooked but may cause idiosyncratic toxicity, are important targets of such a strategy. We demonstrate here that complex metabolic reactions of tris(1,3-dichloro-2-propyl) phosphate (TDCIPP) catalyzed by human CYP450 enzymes can be mapped via a three-step synergy strategy: (i) screening the possible metabolites via high-throughout (moderate-accuracy) computations; (ii) analyzing the proposed metabolites in vitro by human liver microsomes and recombinant human CYP450 enzymes; and (iii) rationalizing the experimental data via precise mechanisms using high-level targeted computations. Through the bilateral dialogues from qualitative to semi-quantitative to quantitative levels, we show how TDCIPP metabolism especially by CYP3A4 generates bis(1,3-dichloro-2-propyl) phosphate (BDCIPP) as an O-dealkylation metabolite and bis(1,3-dichloro-2-propyl) 3-chloro-1-hydroxy-2-propyl phosphate (alcohol_β-dehalogen) as a dehalogenation/reduction metabolite via the initial rate-determining H-abstraction from αC- and βC-positions. The relative yield ratio [dehalogenation/reduction]/[O-dealkylation] is derived from the relative barriers of H-abstraction at the βC- and αC-positions by CYP3A4, estimated as 0.002 to 0.23, viz., an in vitro measured ratio of 0.04. Importantly, alcohol_β-dehalogen formation points to a new mechanism involving successive oxidation and reduction functions of CYP450, with its precursor aldehyde_β-dehalogen being a key intermediate detected by trapping assays and rationalized by computations. We conclude that the proposed three-step synergy strategy may meet the increasing challenge of elucidating biotransformation mechanisms of substantial synthesized organic compounds in the future.

On the Use of Normalized Metrics for Density Sensitivity Analysis in DFT

In the past years, there has been a discussion about how the errors in density functional theory might be related to errors in the self-consistent densities obtained from different density functional approximations. This, in turn, brings up the discussion about the different ways in which we can measure such errors and develop metrics that assess the sensitivity of calculated energies to changes in the density. It is important to realize that there cannot be a unique metric in order to look at this density sensitivity, simultaneously needing size-extensive and size-intensive metrics. In this study, we report two metrics that are widely applicable to any density functional approximation. We also show how they can be used to classify different chemical systems of interest with respect to their sensitivity to small variations in the density.

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.

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.

Probing the generality of spin crossover complex T½vs. ligand 15N NMR chemical shift correlations: towards predictable tuning

A study of 6 families (42 members) demonstrates that within a family the easily calculated 15N-NMR values of ligands enable predictable tuning of T1/2 in the corresponding complexes, except for 2 families with weakly influencing meta-substituents.

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

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

Dioxygen Binding to all 3d, 4d, and 5d Transition Metals from Coupled-Cluster Theory

Understanding how transition metals bind and activate dioxygen (O₂ ) is limited by experimental and theoretical uncertainties, making accurate quantum mechanical descriptors of interest. Here we report coupled-cluster CCSD(T) energies with large basis sets and vibrational and relativistic corrections for 160 3d, 4d, and 5d metal-O₂ systems. We define four reaction energies (120 in total for the 30 metals) that quantify O-O activation and reveal linear relationships between metal-oxygen and O-O binding energies. The CCSD(T) data can be combined with thermochemical cycles to estimate chemisorption and physisorption energies for each metal from metal oxide embedding energies, in good correlation with atomization enthalpies (R² =0.75). Spin-geometry variations can break the linearities, of interest to circumventing the Sabatier principle. Pt, Pd, Co, and Fe form a distinct group with the weakest O₂ binding. R² up to 0.84 between surface adsorption energies and our energies for MO₂ systems indicate relevance also to real catalytic systems.

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.

Assessment of the SCAN Functional for Spin-State Energies in Spin-Crossover Systems

The strongly constrained and appropriately normed (SCAN) functional has been tested toward the calculation of spin-state energy differences in a data set of 20 spin-crossover (SCO) systems, ranging from d⁴ to d⁷. Results show that the SCAN functional is able to correctly predict the low-spin state as the ground state for all systems, and the energy window provided by the calculations falls in the approximate range of energies that will allow for SCO to occur. Moreover, the SCAN functional can be used in periodic boundary condition calculations, accounting for the effect of collective crystal vibrations and counterions in the thermochemistry of the spin transition. Our results validate this functional as a potential method for in silico screening of new SCO systems at both, molecular and crystal-packed levels.

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

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

Detailed Pair Natural Orbital-Based Coupled Cluster Studies of Spin Crossover Energetics

In this work, a detailed study of spin-state splittings in three spin crossover model compounds with DLPNO-CCSD(T) is presented. The performance in comparison to canonical CCSD(T) is assessed in detail. It was found that spin-state splittings with chemical accuracy, compared to the canonical results, are achieved when the full iterative triples (T1) scheme and TightPNO settings are applied and relativistic effects are taken into account. Having established the level of accuracy that can be reached relative to the canonical results, we have undertaken a detailed basis set study in the second part of the study. The slow convergence of the results of correlated calculations with respect to basis set extension is particularly acute for spin-state splittings for reasons discussed in detail in this Article. In fact, for some of the studied systems, 5Z basis sets are necessary in order to come close to the basis set limit that is estimated here by basis set extrapolation. Finally, the results of the present work are compared to available literature. In general, acceptable agreement with previous CCSD(T) results is found, although notable deviations stemming from differences in methodology and basis sets are noted. It is noted that the published CASPT2 numbers are far away from the extrapolated CCSD(T) numbers. In addition, dynamic quantum Monte Carlo results differ by several tens of kcal/mol from the CCSD(T) numbers. A comparison to DFT results produced with a range of popular density functionals shows the expected scattering of results and showcases the difficulty of applying DFT to spin-state energies.

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.

Transition Metal Spin-State Energetics by MC-PDFT with High Local Exchange

The energetics of the spin states of transition metal complexes have been explored with a variety of electronic structure methods, but the calculations require a compromise between accuracy and affordability. In this work, the spin splittings of several iron complexes are studied with multiconfiguration pair-density functional theory (MC-PDFT). The results are compared to previously published results obtained by complete active space second-order perturbation theory (CASPT2) and CASPT2 with coupled-cluster semicore correlation (CASPT2/CC). In contrast to CASPT2's systematic overstabilization of high-spin states with respect to the CASPT2/CC reference, MC-PDFT with the tPBE on-top functional understabilizes high-spin states. This systematic understabilization is largely corrected by revising the exchange and correlation contributions to the on-top functional using the high local-exchange approximation (tPBE-HLE). Moreover, tPBE-HLE correctly predicts the spin of the ground state in most cases, while CASPT2 incorrectly predicts high-spin ground states in all cases. This is encouraging for practical work because tPBE and tPBE-HLE are faster than CASPT2 by a factor of 50 even in a moderately sized example.

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.

Improving the Light-Induced Spin Transition Efficiency in Ni(II)-Based Macrocyclic-Ligand Complexes

The structural stability and photoabsorption properties of Ni(II)-based metal-organic complexes with octahedral coordination having different planar ligand ring structures were investigated employing density functional theory (DFT) and its time-dependent extension (TD-DFT) considering the M06 exchange-correlation functional and the Def2-TZVP basis set. The results showed that the molecular composition of different planar cyclic ligand structures had significant influences on the structural stability and photoabsorption properties of metal-organic complexes. Only those planar ligands that contained aromatic rings met the basic criteria (thermal stability, structural reversibility, and appropriate excitation frequency domain) for light-induced excited spin state trapping, but their spin transition efficiencies were very different. While, in all three aromatic cases, the singlet electronic excitations induced charge distribution that could help in the singlet-to-triplet spin transition, and triplet excitations, which could assist in the backward (triplet-to-singlet) spin transition, was found only for one complex.

Stable Surfaces That Bind Too Tightly: Can Range-Separated Hybrids or DFT+U Improve Paradoxical Descriptions of Surface Chemistry?

Approximate, semilocal density functional theory (DFT) suffers from delocalization error that can lead to a paradoxical model of catalytic surfaces that both overbind adsorbates yet are also too stable. We investigate the effect of two widely applied approaches for delocalization error correction, (i) affordable DFT+U (i.e., semilocal DFT augmented with a Hubbard U) and (ii) hybrid functionals with an admixture of Hartree-Fock (HF) exchange, on surface and adsorbate energies across a range of rutile transition metal oxides widely studied for their promise as water-splitting catalysts. We observe strongly row- and period-dependent trends with DFT+U, which increases surface formation energies only in early transition metals (e.g., Ti and V) and decreases adsorbate energies only in later transition metals (e.g., Ir and Pt). Both global and local hybrids destabilize surfaces and reduce adsorbate binding across the periodic table, in agreement with higher-level reference calculations. Density analysis reveals why hybrid functionals correct both quantities, whereas DFT+U does not. We recommend local, range-separated hybrids for the accurate modeling of catalysis in transition metal oxides at only a modest increase in computational cost over semilocal DFT.

The Role of Vibrational Anharmonicity in the Computational Study of Thermal Spin Crossover

Spin crossover in transition metal complexes can be studied in great detail with computational chemistry. Over the years, the understanding has grown that the relative stability of high-spin (HS) versus low-spin (LS) states is a subtle balance of many factors that all need to be taken into account for a reliable description. Among the different contributions, the zero-point energy (ZPE) and the entropy play key roles. These quantities are usually calculated assuming a harmonic oscillator model for the molecular vibrations. We investigated the impact of including anharmonic corrections on the ZPE and the entropy and indirectly on the critical temperature of spin crossover. As test systems, we used a set of ten Fe(II) complexes and one Fe(III) complex, covering different coordination modes (mono-, bi-, and tri-dentate ligands), decreasing coordination number upon spin crossover, coordination by second- and third-row atoms, and changes in the oxidation state. The results show that the anharmonicity has a measurable effect, but it is in general rather small, and tendencies are not easily recognized. As a conclusion, we put forward that for high precision results, one should be aware of the anharmonic effects, but as long as computational chemistry is still struggling with other larger factors like the influence of the environment and the accurate determination of the electronic energy difference between HS and LS, the anharmonicity of the vibrational modes is a minor concern.

Ironing out pyoverdine's chromophore structure: serendipity or design?

Pyoverdines are Pseudomonas aeruginosa's primary siderophores. These molecules, composed of a fluorescent chromophore attached to a peptide chain of 6-14 amino acids, are synthesized by the bacterium to scavenge iron (essential to its survival and growth) from its environment. Hijacking the siderophore pathway to use pyoverdine-antibiotic compounds in a Trojan horse approach has shown promise but remains very challenging because of the synthetic efforts involved. Indeed, both possible approaches (grafting an antibiotic on pyoverdine harvested from Pseudomonas or designing a total synthesis route) are costly, time-consuming and low-yield tasks. Designing comparatively simple analogs featuring the salient properties of the original siderophore is thus crucial for the conception of novel antibiotics to fight bacterial resistance. In this work, we focus on the replacement of the pyoverdine chromophore, a major roadblock on the synthetic pathway. We propose three simpler analogs and evaluate their ability to complex iron and interact with the FpvA transporter using molecular modeling techniques. Based on these results, we discuss the role of the native chromophore's main features (polycyclicity, positive charge, flexibility) on pyoverdine's ability to bind iron and be recognized by membrane transporter FpvA and propose guidelines for the design of effective synthetic siderophores.

Spin Interconversion of Heme-Peroxo-Copper Complexes Facilitated by Intramolecular Hydrogen-Bonding Interactions

Synthetic peroxo-bridged high-spin (HS) heme-(μ-η2:η1-O22-)-Cu(L) complexes incorporating (as part of the copper ligand) intramolecular hydrogen-bond (H-bond) capabilities and/or steric effects are herein demonstrated to affect the complex's electronic and geometric structure, notably impacting the spin state. An H-bonding interaction with the peroxo core favors a low-spin (LS) heme-(μ-η1:η1-O22-)-Cu(L) structure, resulting in a reversible temperature-dependent interconversion of spin state (5 coordinate HS to 6 coordinate LS). The LS state dominates at low temperatures, even in the absence of a strong trans-axial heme ligand. Lewis base addition inhibits the H-bond facilitated spin interconversion by competition for the H-bond donor, illustrating the precise H-bonding interaction required to induce spin-crossover (SCO). Resonance Raman spectroscopy (rR) shows that the H-bonding pendant interacts with the bridging peroxide ligand to stabilize the LS but not the HS state. The H-bond (to the Cu-bound O atom) acts to weaken the O-O bond and strengthen the Fe-O bond, exhibiting ν(M-O) and ν(O-O) values comparable to analogous known LS complexes with a strong donating trans-axial ligand, 1,5-dicyclohexylimidazole, (DCHIm)heme-(μ-η1:η1-O22-)-Cu(L). Variable-temperature (-90 to -130 °C) UV-vis and 2H NMR spectroscopies confirm the SCO process and implicate the involvement of solvent binding. Examining a case of solvent binding without SCO, thermodynamic parameters were obtained from a van't Hoff analysis, accounting for its contribution in SCO. Taken together, these data provide evidence for the H-bond group facilitating a core geometry change and allowing solvent to bind, stabilizing a LS state. The rR data, complemented by DFT analysis, reveal a stronger H-bonding interaction with the peroxo core in the LS compared to the HS complexes, which enthalpically favors the LS state. These insights enhance our fundamental understanding of secondary coordination sphere influences in metalloenzymes.

The Metal Hydride Problem of Computational Chemistry: Origins and Consequences

Formation and breaking of metal-hydrogen bonds are central to many important catalytic processes such as transition-metal catalyzed ammonia synthesis, hydrogenation reactions, and water splitting, and thus, they require an adequate theoretical description. We studied a data set of all 30 M-H and 30 M⁺-H bonds of the 3d, 4d, and 5d transition series; 50 of these systems have experimentally known bond dissociation enthalpies (BDE). To probe both the limit of low and high coordination number, we also studied a data set of 19 ML _nH complexes. The BDEs were computed using Hartree-Fock (HF), MP2, CCSD, CCSD(T), and 10 diverse density functionals including local, GGA, hybrid GGA, meta hybrid, range-separated, and double hybrids. Our ten most important findings are as follows: (1) HF fails completely to describe the metal hydrogen bond due to its lack of static correlation; (2) this makes post-HF methods such as MP2 and even CCSD(T) perform worse than many density functionals; (3) DFT requires much more HF exchange (∼35% on average) to describe the pure M-H bonds than to describe other metal ligand bonds (0-20%); (4) we design a test to determine if self-interaction error (SIE) is important by correlating DFT errors against a one-electron SIE metric; (5) we show that SIE correlates directly with the DFT errors and thus causes most of the problem; (6) HF-DFT cannot handle these systems because the HF method is too pathological already at the density level; (7) instead, we define and apply a simple metric of electronic abnormality as the difference in PBE energy computed at the self-consistent PBE0 and SVWN densities, and this metric gives appropriate spread and effectively captures density-derived errors; (8) the low electronegativity of the metal enforces a diffuse hydride-like electron density, which make the metal hydrides primary examples of many-electron systems exhibiting SIE already at equilibrium geometries; (9) in the coordinatively saturated ML _nH systems, much less HF exchange is required; i.e., the HF exchange requirements vary drastically with coordination number. Accordingly, DFT is unbalanced for any catalytic process involving both M-H and M-L bonds and changing coordination numbers; (10) importantly, the range-separated and double-hybrid functionals CAM-B3LYP and B2PLYP alone perform well for both M-H and M-L systems and in both limits of low and high coordination number, and at least as well as CCSD(T). This lends hope to a balanced treatment of computational chemistry for all types of M-L bonds at variable coordination number, as required for real catalytic reactions.

Benchmarking quantum chemistry methods for spin-state energetics of iron complexes against quantitative experimental data

The accuracy of relative spin-state energetics predicted by selected quantum chemistry methods: coupled cluster theory at the CCSD(T) level, multiconfigurational perturbation theory (CASPT2, NEVPT2), multireference configuration interaction at the MRCISD+Q level, and a number of DFT methods, is quantitatively evaluated by comparison with the experimental data of four octahedral iron complexes. The available experimental data, either spin-forbidden transition energies or spin crossover enthalpies, are corrected for relevant environmental effects in order to derive the quantitative benchmark set of iron spin-state energetics. Comparison of theory predictions with the resulting reference data: (1) validates the high accuracy of the CCSD(T) method, particularly when based on Kohn-Sham orbitals, giving the maximum error below 2 kcal mol-1 and the mean absolute error (MAE) below 1 kcal mol-1; (2) corroborates the tendency of CASPT2 to systematically overstabilize higher-spin states by up to 5.5 kcal mol-1; (3) confirms that the latter problem is partly remedied by the recently proposed CASPT2/CC approach [Phung et al., J. Chem. Theory Comput., 2018, 14, 2446-2455]; (4) demonstrates that NEVPT2 performs worse than CASPT2, by giving errors up to 7 kcal mol-1; (5) shows that the accuracy of MRCISD+Q spin-state energetics strongly depends on the size-consistency correction: the Davidson-Silver and Pople corrections perform best (MAE < 3 kcal mol-1), whereas the standard Davidson correction is not recommended (MAE of 7 kcal mol-1). Only a few DFT methods (including the best performing ones identified in this study: B2PLYP-D3 and OPBE) are able to provide a balanced description of the spin-state energetics for all four studied iron complexes simultaneously, corroborating the non-universality problem of approximate density functionals.

Local Energy Decomposition of Open-Shell Molecular Systems in the Domain-Based Local Pair Natural Orbital Coupled Cluster Framework

Local energy decomposition (LED) analysis decomposes the interaction energy between two fragments calculated at the domain-based local pair natural orbital CCSD(T) (DLPNO-CCSD(T)) level of theory into a series of chemically meaningful contributions and has found widespread applications in the study of noncovalent interactions. Herein, an extension of this scheme that allows for the analysis of interaction energies of open-shell molecular systems calculated at the UHF-DLPNO-CCSD(T) level is presented. The new scheme is illustrated through applications to the CH₂···X (X = He, Ne, Ar, Kr, and water) and heme···CO interactions in the low-lying singlet and triplet spin states. The results are used to discuss the mechanism that governs the change in the singlet–triplet energy gap of methylene and heme upon adduct formation.

High-temperature Spin Crossover of a Solvent-Free Iron(II) Complex with the Linear Hexadentate Ligand [Fe(L2-3-2Ph)](AsF6)2 (L2-3-2Ph = bis[N-(1-Phenyl-1H-1,2,3-triazol-4-yl)methylidene-2-aminoethyl]-1,3- propanediamine)

A novel mononuclear iron(II) complex with a linear hexadentate N6 ligand, containing two 1,2,3-triazole moieties, [Fe(L2-3-2Ph)](AsF6)2 (1), was synthesized (L2-3-2Ph = bis[N-(1-Phenyl-1H-1,2,3-triazol-4-yl)methylidene-2-aminoethyl]-1,3-propanediamine). Variable-temperature magnetic susceptibility measurements revealed a gradual one-step spin crossover (SCO) between the high-spin (HS, S = 2) and low-spin (LS, S = 0) states above room temperature (T1/2 = 468 K). The spin transition was further confirmed by differential scanning calorimetry (DSC). A single-crystal X-ray diffraction study showed that the complex was in the LS state (S = 0) at room temperature (296 K). In the crystal lattice, a three-dimensional (3D) supramolecular network was formed by intermolecular CH⋯ and – interactions of neighboring complex cations [Fe(L2-3-2Ph)]2+. AsF6− ions were located interstitially in the 3D network of complex cations, with no solvent-accessible voids. The crystal structure at 448 K (mixture of HS and LS species) was also successfully determined thanks to the thermal stability of the solvent-free crystal.

Contribution of substrate reorganization energies of electron transfer to laccase activity

Laccase substrate reorganization energies computed by DFT show that electronic structure changes of these substrates contribute to enzymatic proficiency.