Metal and ligand hyperfine couplings in transition metal complexes: The effect of spin–orbit coupling as studied by coupled perturbed Kohn–Sham theory

Electron-Spin Relaxation in Boron-Doped Graphene Nanoribbons

Boron-doped graphene nanoribbons are promising platforms for developing organic materials with magnetic properties. Boron dopants can be used to create localized magnetic states in nanoribbons with tunable interactions. Controlling the coherence times of these magnetic states is the very first step in designing materials for quantum computation or information storage. In this work, we address the connection between the relaxation time and the position of the dopants for a series of boron-doped graphene nanofragments. We combine Redfield theory and ab initio calculations of magnetic properties to unveil the mechanism that governs spin relaxation in solution. We demonstrate that relaxation times can be in the order of 1 ms for the selected graphene nanofragments. A detailed analysis of the relaxation mechanism reveals that the spin decoherence is fundamentally driven by fluctuations of the spin-orbit coupling, and the hyperfine interaction facilitated by the thermal motion of the graphene nanofragments. The close connection between relaxation time, hyperfine interaction and the spin-orbit coupling offers the perspective of designing attractive materials with long-lived spin states.

A perspective on the future of quantum chemical software: the example of the ORCA program package

The field of computational chemistry has made an impressive impact on contemporary chemical research. In order to carry out computational studies on actual systems, sophisticated software is required in form of large-scale quantum chemical program packages. Given the enormous diversity and complexity of the methods that need to be implementation in such packages, it is evident that these software pieces are very large (millions of code lines) and extremely complex. Most of the packages in widespread use by the computational chemistry community have had a development history of decades. Given the rapid progress in the hardware and a lack of resources (time, workforce, money), it is not possible to keep redesigning these program packages from scratch in order to keep up with the ever more quickly shifting hardware landscape. In this perspective, some aspects of the multitude of challenges that the developer community faces are discussed. While the task at hand - to ensure that quantum chemical program packages can keep evolving and make best use of the available hardware - is daunting, there are also new evolving opportunities. The problems and potential cures are discussed with the example of the ORCA package that has been developed in our research group.

First-principles study on structural stabilities, mechanical properties, and biaxial strain-induced superconductivity in Janus MoWC monolayer

The unique attributes of hydrophilicity, expansive surface groups, remarkable flexibility, and superior conductivity converge in MXene, a pioneering 2D material. Owing to MXene's exceptional properties, diverse strategies have been explored to enhance its characteristics. Janus MXene and stress-strain response considerations represent the primary avenues of interest today. In this study, we investigated the Janus MXene structure under biaxial stress using first-principles calculations. The most stable configuration of Janus MoWC MXene identified in our analysis exhibits an atomic arrangement known as the hexagonal (2H) phase. Subsequently, we examined the mechanical and electronic properties of 2H-MoWC when subjected to biaxial strain. Our findings indicate that the 2H phase of Janus MoWC MXene demonstrates superior strength compared to the tetragonal (1T) phase. Analysis of the ELF of the 2H-MoWC structure unveiled that the robust C-C bond within the material is the underlying factor enabling the 2H phase to withstand a maximum of 9% tensile strain. Furthermore, we demonstrate that 2H-MoWC is a superconductor with the superconducting temperature (Tc) of 1.6 K, and the superconductivity of 2H phase can be enhanced by biaxial strain with the Tc reaching 7 K. This study offers comprehensive insights into the properties of Janus MoWC monolayer under biaxial stress, positioning it as a promising candidate for 2D straintronic applications.

Coordination of dissolved transition metals in pristine battery electrolyte solutions determined by NMR and EPR spectroscopy

The solvation of dissolved transition metal ions in lithium-ion battery electrolytes is not well-characterised experimentally, although it is important for battery degradation mechanisms governed by metal dissolution, deposition, and reactivity in solution. This work identifies the coordinating species in the Mn2+ and Ni2+ solvation spheres in LiPF6/LiTFSI-carbonate electrolyte solutions by examining the electron-nuclear spin interactions, which are probed by pulsed EPR and paramagnetic NMR spectroscopy. These techniques investigate solvation in frozen electrolytes and in the liquid state at ambient temperature, respectively, also probing the bound states and dynamics of the complexes involving the ions. Mn2+ and Ni2+ are shown to primarily coordinate to ethylene carbonate (EC) in the first coordination sphere, while PF6- is found primarily in the second coordination sphere, although a degree of contact ion pairing does appear to occur, particularly in electrolytes with low EC concentrations. NMR results suggest that Mn2+ coordinates more strongly to PF6- than to TFSI-, while the opposite is true for Ni2+. This work provides a framework to experimentally determine the coordination spheres of paramagnetic metals in battery electrolyte solutions.

Delving into theoretical and computational considerations for accurate calculation of chemical shifts in paramagnetic transition metal systems using quantum chemical methods

The chemical shielding tensor for a paramagnetic system has been derived from the macroscopically observed magnetization using the perturbation theory. An approach to calculate the paramagnetic chemical shifts in transition metal systems based on the spin-only magnetic susceptibility directly evaluated from the ab initio Hilbert space of the electronic Zeeman Hamiltonian has been discussed. Computationally, several advantages are associated with this approach: (a) it includes the state-specific paramagnetic Curie (first-order) and Van Vleck (second-order) contributions of the paramagnetic ion to the paramagnetic chemical shifts; (b) thus it avoids the system-specific modeling and evaluating effectively in terms of the electron paramagnetic resonance (EPR) spin Hamiltonian parameters of the magnetic moment of the paramagnetic ion formulated previously; (c) it can be utilized both in the point-dipole (PD) approximation (in the long-range) and with the quantum chemical (QC) method based the hyperfine tensors (in the short-range). Additionally, we have examined the predictive performance of various density functional theory (DFT) functionals of different families and commonly used core-augmented basis sets for nuclear magnetic resonance (NMR) chemical shifts. A selection of transition metal ion complexes with and without first-order orbital contributions, namely the [M(AcPyOx)3(BPh)]+ complexes of M = Mn2+, Ni2+ and Co2+ ions and CoTp2 complex and their reported NMR chemical shifts are studied from QC methods for illustration.

Rational Design of a Phosphorus-Centered Disbiradical

Phosphorus-centered disbiradicals, in which the radical sites exist as individual spin doublets with weak spin-spin interaction have not been known so far. Starting from monoradicals of the type [⋅P(μ-NTer)2 P-R], we have now succeeded in linking two such monoradical phosphorus centers by appropriate choice of a linker. To this end, biradical [⋅P(μ-NTer)2 P⋅] (1) was treated with 1,6-dibromohexane, affording the brominated species {Br[P(μ-NTer)]2 }2 C6 H12 (3). Subsequent reduction with KC8 led to the formation of the disbiradical {⋅[P(μ-NTer)]2 }2 C6 H12 (4) featuring a large distance between the radical phosphorus sites in the solid state and formally the highest biradical character observed in a P-centered biradical so far, approaching 100 %. EPR spectroscopy revealed a three-line signal in solution with a considerably larger exchange interaction than would be expected from the molecular structure of the single crystal. Quantum chemical calculations revealed a highly dynamic conformational space; thus, the two radical sites can approach each other with a much smaller distance in solution. Further reduction of 4 resulted in the formation of a potassium salt featuring the first structurally characterized P-centered distonic radical anion (5- ). Moreover, 4 could be used in small molecule activation.

Reversible Dioxygen Binding to Co(II) Complexes with Noninnocent Ligands

A series of mononuclear Co(II) complexes with noninnocent (redox-active) ligands are prepared that exhibit metal-ligand cooperativity during the reversible binding of O2. The complexes have the general formula, [CoII(LS,N)(TpR2)] (R = Me, Ph), where LS,N is a bidentate o-aminothiophenolate and TpR2 is a hydrotris(pyrazol-1-yl)borate scorpionate with R-substituents at the 3- and 5-positions. Exposure to O2 at room temperature results in one-electron oxidation and deprotonation of LS,N. The oxidized derivatives possess substantial "singlet diradical" character arising from antiferromagnetic coupling between an iminothiosemiquinonate (ITSQ•-) ligand radical and a low-spin Co(II) ion. The [CoII(TpMe2)(X2ITSQ)] complexes, where X = H or tBu, coordinate O2 reversibly at reduced temperatures to provide Co/O2 adducts. The O2 binding reactions closely resemble those previously reported by our group (Kumar et al., J. Am. Chem. Soc. 2019,141, 10984-10987) for the related complexes [CoII(TpMe2)(tBu2SQ)] and [CoII(TpMe2)(tBu2ISQ)], where tBu2(I)SQ represents 4,6-di-tert-butyl-(2-imino)semiquinonate radicals. In each case, the oxygenation reaction proceeds via the addition of O2 to both the cobalt ion and the ligand radical, generating metallocyclic cobalt(III)-alkylperoxo structures. Thermodynamic measurements elucidate the relationship between O2 affinity and redox potentials of the (imino)(thio)semiquinonate radicals, as well as energetic differences between these reactions and conventional metal-based oxygenations. The results highlight the utility and versatility of noninnocent ligands in the design of O2-absorbing compounds.

Dioxygen Activation and Mandelate Decarboxylation by Iron(II) Complexes of N4 Ligands: Evidence for Dioxygen-Derived Intermediates from Cobalt Analogues

The isolation, characterization, and dioxygen reactivity of monomeric [(TPA)M^II(mandelate)]⁺ (M = Fe, 1; Co, 3) and dimeric [(BPMEN)₂M^II₂(μ-mandelate)₂]²⁺ (M = Fe, 2; Co, 4) (TPA = tris(2-pyridylmethyl)amine and BPMEN = N¹,N²-dimethyl-N¹,N²-bis(pyridin-2-yl-methyl)ethane-1,2-diamine) complexes are reported. The iron(II)- and cobalt(II)-mandelate complexes react with dioxygen to afford benzaldehyde and benzoic acid in a 1:1 ratio. In the reactions, one oxygen atom from dioxygen is incorporated into benzoic acid, but benzaldehyde does not derive any oxygen atom from dioxygen. While no O₂-derived intermediate is observed with the iron(II)-mandelate complexes, the analogous cobalt(II) complexes react with dioxygen at a low temperature (-80 °C) to generate the corresponding cobalt(III)-superoxo species (S), a key intermediate implicated in the initiation of mandelate decarboxylation. At -20 °C, the cobalt(II)-mandelate complexes bind dioxygen reversibly leading to the formation of μ-1,2-peroxo-dicobalt(III)-mandelate species (P). The geometric and electronic structures of the O₂-derived intermediates (S and P) have been established by computational studies. The intermediates S and P upon treatment with a protic acid undergo decarboxylation to afford benzaldehyde (50%) with a concomitant formation of the corresponding μ-1,2-peroxo-μ-mandelate-dicobalt(III) (P1) species. The crystal structure of a peroxide species isolated from the cobalt(II)-carboxylate complex [(TPA)Co^II(MPA)]⁺ (5) (MPA = 2-methoxyphenylacetate) supports the composition of P1. The observations of the dioxygen-derived intermediates from cobalt complexes and their electronic structure analyses not only provide information about the nature of active species involved in the decarboxylation of mandelate but also shed light on the mechanistic pathway of two-electron versus four-electron reduction of dioxygen.

Electron correlation and vibrational effects in predictions of paramagnetic NMR shifts

Electronic structure calculations are fundamentally important for the interpretation of nuclear magnetic resonance (NMR) spectra from paramagnetic systems that include organometallic and inorganic compounds, catalysts, or metal-binding sites in proteins. Prediction of induced paramagnetic NMR shifts requires knowledge of electron paramagnetic resonance (EPR) parameters: the electronic g tensor, zero-field splitting D tensor, and hyperfine A tensor. The isotropic part of A, called the hyperfine coupling constant (HFCC), is one of the most troublesome properties for quantum chemistry calculations. Yet, even relatively small errors in calculations of HFCC tend to propagate into large errors in the predicted NMR shifts. The poor quality of A tensors that are currently calculated using density functional theory (DFT) constitutes a bottleneck in improving the reliability of interpretation of the NMR spectra from paramagnetic systems. In this work, electron correlation effects in calculations of HFCCs with a hierarchy of ab initio methods were assessed, and the applicability of different levels of DFT approximations and the coupled cluster singles and doubles (CCSD) method was tested. These assessments were performed for the set of selected test systems comprising an organic radical, and complexes with transition metal and rare-earth ions, for which experimental data are available. Severe deficiencies of DFT were revealed but the CCSD method was able to deliver good agreement with experimental data for all systems considered, however, at substantial computational costs. We proposed a more computationally tractable alternative, where the A was computed with the coupled cluster theory exploiting locality of electron correlation. This alternative is based on the domain-based local pair natural orbital coupled cluster singles and doubles (DLPNO-CCSD) method. In this way the robustness and reliability of the coupled cluster theory were incorporated into the modern formalism for the prediction of induced paramagnetic NMR shifts, and became applicable to systems of chemical interest. This approach was verified for the bis(cyclopentadienyl)vanadium(II) complex (Cp₂V; vanadocene), and the metal-binding site of the Zn²⁺ → Co²⁺ substituted superoxide dismutase (SOD) metalloprotein. Excellent agreement with experimental NMR shifts was achieved, which represented a substantial improvement over previous theoretical attempts. The effects of vibrational corrections to orbital shielding and hyperfine tensor were evaluated and discussed within the second-order vibrational perturbation theory (VPT2) framework.

Radical Reactivity of the Biradical [⋅P(μ-NTer)2 P⋅] and Isolation of a Persistent Phosphorus-Cantered Monoradical [⋅P(μ-NTer)2 P-Et]

The activation of C-Br bonds in various bromoalkanes by the biradical [⋅P(μ-NTer)2 P⋅] (1) (Ter=2,6-bis-(2,4,6-trimethylphenyl)-phenyl) is reported, yielding trans-addition products of the type [Br-P(μ-NTer)2 P-R] (2), so-called 1,3-substituted cyclo-1,3-diphospha-2,4-diazanes. This addition reaction, which represents a new easy approach to asymmetrically substituted cyclo-1,3-diphospha-2,4-diazanes, was investigated mechanistically by different spectroscopic methods (NMR, EPR, IR, Raman); the results suggested a stepwise radical reaction mechanism, as evidenced by the in-situ detection of the phosphorus-centered monoradical [⋅P(μ-NTer)2 P-R].< To provide further evidence for the radical mechanism, [⋅P(μ-NTer)2 P-Et] (3Et⋅) was synthesized directly by reduction of the bromoethane addition product [Br-P(μ-NTer)2 P-Et] (2 a) with magnesium, resulting in the formation of the persistent phosphorus-centered monoradical [⋅P(μ-NTer)2 P-Et], which could be isolated and fully characterized, including single-crystal X-ray diffraction. Comparison of the EPR spectrum of the radical intermediate in the addition reaction with that of the synthesized new [⋅P(μ-NTer)2 P-Et] radical clearly proves the existence of radicals over the course of the reaction of biradical [⋅P(μ-NTer)2 P⋅] (1) with bromoethane. Extensive DFT and coupled cluster calculations corroborate the experimental data for a radical mechanism in the reaction of biradical [⋅P(μ-NTer)2 P⋅] with EtBr. In the field of hetero-cyclobutane-1,3-diyls, the demonstration of a stepwise radical reaction represents a new aspect and closes the gap between P-centered biradicals and P-centered monoradicals in terms of radical reactivity.

Electronic and Optical Properties of Eu2+-Activated Narrow-Band Phosphors for Phosphor-Converted Light-Emitting Diode Applications: Insights from a Theoretical Spectroscopy Perspective

In this work, we present a computational protocol that is able to predict the experimental absorption and emission spectral shapes of Eu²⁺-doped phosphors. The protocol is based on time-dependent density functional theory and operates in conjunction with an excited-state dynamics approach. It is demonstrated that across the study set consisting of representative examples of nitride, oxo-nitride, and oxide Eu²⁺-doped phosphors, the energy distribution and the band shape of the emission spectrum are related to the nature of the 4f–5d transitions that are probed in the absorption process. Since the 4f orbitals are very nearly nonbonding, the decisive quantity is the covalency of the 5d acceptor orbitals that become populated in the electronically excited state that leads to emission. The stronger the (anti) bonding interaction between the lanthanide and the ligands is in the excited state, the larger will be the excited state distortion. Consequently, the corresponding emission will get broader due to the vibronic progression that is induced by the structural distortion. In addition, the energy separation of the absorption bands that are dominated by states with valence 4f–5d and a metal to ligand charge transfer character defines a measure for the thermal quenching of the studied Eu²⁺-doped phosphors. Based on this analysis, simple descriptors are identified that show a strong correlation with the energy position and bandwidth of the experimental emission bands without the need for elaborate calculations. Overall, we believe that this study serves as an important reference for designing new Eu²⁺-doped phosphors with desired photoluminescence properties.

Theoretical analysis of the long-distance limit of NMR chemical shieldings

After some years of controversy, it was recently demonstrated how to obtain the correct long-distance limit [point-dipole approximation (PDA)] of pseudo-contact nuclear magnetic resonance chemical shifts from rigorous first-principles quantum mechanics [Lang et al., J. Phys. Chem. Lett. 11, 8735 (2020)]. This result confirmed the classical Kurland-McGarvey theory. In the present contribution, we elaborate on these results. In particular, we provide a detailed derivation of the PDA both from the Van den Heuvel-Soncini equation for the chemical shielding tensor and from a spin Hamiltonian approximation. Furthermore, we discuss in detail the PDA within the approximate density functional theory and Hartree-Fock theories. In our previous work, we assumed a relatively crude effective nuclear charge approximation for the spin-orbit coupling operator. Here, we overcome this assumption by demonstrating that the derivation is also possible within the fully relativistic Dirac equation and even without the assumption of a specific form for the Hamiltonian. Crucial ingredients for the general derivation are a Hamiltonian that respects gauge invariance, the multipolar gauge, and functional derivatives of the Hamiltonian, where it is possible to identify the first functional derivative with the electron number current density operator. The present work forms an important foundation for future extensions of the Kurland-McGarvey theory beyond the PDA, including induced magnetic quadrupole and higher moments to describe the magnetic hyperfine field.

Copper(II) Complexes of Pyridine-2,6-dicarboxamide Ligands with High SOD Activity

Copper(II) complexes of pyridine-based ligands functionalized with alanine (PydiAla) and tyrosine (PydiTyr) moieties have been synthesized as novel superoxide dismutase mimics. The complexes were characterized by pH-potentiometric, spectroscopic (UV-vis, circular dichroism, mass spectrometry, electron paramagnetic resonance spectroscopy), computational (DFT), and X-ray diffraction methods. Both ligands form high stability copper(II) complexes via the (Npy,N-,N-) donor set supported by the binding of the carboxylate pendant arms. Although the coordination mode is the same for the two systems, the tyrosine containing counterpart exhibits increased copper(II) binding affinity, which is most likely due to the presence of the aromatic moiety of the side chains. Both copper(II) complexes are capable of binding N-methylimidazole, and the formation of the corresponding ternary species was observed at physiological pH. The binary and ternary copper(II) complexes exhibit high SOD activity. The PydiTyr complex exhibits about 1 order of magnitude higher activity than the PydiAla complex. This is probably due to the presence of the phenolic OH group in the former species, which promotes the binding of the superoxide anion radical to the metal center. The results serve as a basis for designing highly efficient copper(II) mimics for medical and practical applications.

From the Physicochemical Characteristic of Novel Hesperetin Hydrazone to Its In Vitro Antimicrobial Aspects

Microorganisms are able to give rise to biofilm formation on food matrixes and along food industry infrastructures or medical equipment. This growth may be reduced by the application of molecules preventing bacterial adhesion on these surfaces. A new Schiff base ligand, derivative of hesperetin, HABH (2-amino-N'-(2,3-dihydro-5,7-dihydroxy-2-(3-hydroxy-4-methoxyphenyl)chromen-4-ylidene)benzohydrazide), and its copper complex, CuHABH [CuLH₂(OAc)], were designed, synthesized and analyzed in terms of their structure and physicochemical properties, and tested as antibacterial agents. Their structures both in a solid state and in solution were established using several methods: FT-IR, ¹H NMR, ¹³C NMR, UV-Vis, FAB MS, EPR, ESI-MS and potentiometry. Coordination binding of the copper(II) complex dominating at the physiological pH region in the solution was found to be the same as that detected in the solid state. Furthermore, the interaction between the HABH and CuHABH with calf-thymus DNA (CT-DNA) were investigated. These interactions were tracked by UV-Vis, CD (circular dichroism) and spectrofluorimetry. The results indicate a stronger interaction of the CuHABH with the CT-DNA than the HABH. It can be assumed that the nature of the interactions is of the intercalating type, but in the high concentration range, the complex can bind to the DNA externally to phosphate residues or to a minor/major groove. The prepared compounds possess antibacterial and antibiofilm activities against Gram-positive and Gram-negative bacteria. Their antagonistic activity depends on the factor-strain test system. The glass was selected as a model surface for the experiments on antibiofilm activity. The adhesion of bacterial cells to the glass surface in the presence of the compounds was traced by luminometry and the best antiadhesive action against both bacterial strains was detected for the CuHABH complex. This molecule may play a crucial role in disrupting exopolymers (DNA/proteins) in biofilm formation and can be used to prevent bacterial adhesion especially on glass equipment.

Analysis of reduced paramagnetic shifts as an effective tool in NMR spectroscopy

A recently introduced concept of reduced paramagnetic shifts (RPS) in NMR spectroscopy is applied here to a series of paramagnetic complexes with different metal ions, such as iron(II), iron(III) and cobalt(II), in different coordination environments of N-donor ligands, including a unique trigonal-prismatic geometry that is behind some record single-molecule magnet behaviours. A simple, almost visual analysis of the chemical shifts as a function of temperature, which is at the core of this approach, allows for a correct signal assignment and evaluation of the anisotropy of the magnetic susceptibility, the key indicator of a good single molecule magnet, that often cannot be done using traditional techniques rooted in quantum chemistry and NMR spectroscopy. The proposed approach thus emerged as a powerful alternative in deciphering the NMR spectra of paramagnetic compounds for applications in data processing and storage, magnetic resonance imaging and structural biology.

Unusual Slow Magnetic Relaxation in a Mononuclear Copper(II) Complex

A hexacoordinate Cu(II) complex with the {CuO4O’N} donor set shows an intermolecular π-πstacking owing to which a 1D-chain structure is formed. The DC magnetic data at low temperature is consistent...

Density functional theory calculations of copper-doped rutile crystals: Local structural, electronic, optical, and electron paramagnetic resonance properties

The local structural, electronic, optical, and electron paramagnetic resonance (EPR) properties are uniformly studied for Cu²⁺ -doped rutile (TiO₂ ) crystals by using the density functional theory (DFT) calculations. The local cation-oxygen bond lengths and planar bond angle, band gap, Mulliken charge and overlapping population, density of state (DOS), and UV-Vis absorption spectra are calculated for pure and copper-doped rutile. The smaller overlapping population of Cu-O bonds in the doped system than Ti-O bonds in pure rutile reflects weaker orbital admixtures or covalency of the former. Compared with pure rutile, Cu²⁺ doping leads to significant redshift of the UV-Vis absorption band and the narrow impurity band in visible and near-infrared regions arising from the Cu²⁺ d-d transitions and narrowing of the band gap by about 0.636 eV, possibly suggesting enhancement of visible light activity. The Cu dopant induces a spin magnetic moment of 0.74 μB for the doped rutile. The calculated UV-Vis absorption spectra and spin Hamiltonian parameters for copper-doped rutile show reasonable agreement with the experimental data and some improvement related to the previous perturbation formula calculations. Present systematic studies would be helpful to understand the mechanisms of the enhancement in the optical and magnetic properties of this material with transition-metal (especially Cu²⁺ ) dopants.

Introducing the penicillamine moiety into a metallopeptide mimicking the NiSOD enzyme: electronic and kinetic effects

The novel NiSOD related metallopeptide incorporates penicillamine moiety in the active center which alters both the electronic and kinetic features.

Low-Spin Cyanide Complexes of 3-Mercaptopropionic Acid Dioxygenase (MDO) Reveal the Impact of Outer-Sphere SHY-Motif Residues

3-Mercaptopropionic acid (3MPA) dioxygenase (MDO) is a non-heme Fe(II)/O2-dependent oxygenase that catalyzes the oxidation of thiol-substrates to yield the corresponding sulfinic acid. Hydrogen-bonding interactions between the Fe-site and a conserved set of three outer-sphere residues (Ser-His-Tyr) play an important catalytic role in the mechanism of this enzyme. Collectively referred to as the SHY-motif, the functional role of these residues remains poorly understood. Here, catalytically inactive Fe(III)-MDO precomplexed with 3MPA was titrated with cyanide to yield a low-spin (S = 1/2) (3MPA/CN)-bound ternary complex (referred to as 1C). UV-visible and electron paramagnetic resonance (EPR) spectroscopy were used to monitor the binding of 3MPA and cyanide. Comparisons of results obtained from SHY-motif variants (H157N and Y159F) were performed to investigate specific H-bonding interactions. For the wild-type enzyme, the binding of 3MPA- and cyanide to the enzymatic Fe-site is selective and results in a homogeneous ternary complex. However, this selectivity is lost for the Y159F variant, suggesting that H-bonding interactions contributed from Tyr159 gate ligand coordination at the Fe-site. Significantly, the g-values for the low-spin ferric site are diagnostic of the directionality of Tyr159 H-bond donation. Computational models coupled with CASSCF/NEVPT2-calculated g-values were used to verify that a major shift in the central g-value (g2) displayed between wild-type and SHY variants could be attributed to the loss of Tyr159 H-bond donation to the Fe-bound cyanide. Applied to native cosubstrate, this H-bond donation provides a means to stabilize Fe-bound dioxygen and potentially explains the attenuated (∼15-fold) rate of catalytic turnover previously reported for MDO SHY-motif variants.

A Persistent Phosphanyl-Substituted Thioketyl Radical Anion

Alkali metal salts, M⁺[Ter(iPr)P−C(=S)−P(iPr)₂S]^.− (M=Na, K; 2_M; Ter=2,6‐bis‐(2,4,6‐trimethylphenyl)phenyl) containing a room‐temperature‐stable thioketyl radical anion were obtained by reduction of the thioketone precursor, Ter(iPr)P−C(=S)−P(iPr)₂S (1), with alkali metals (Na, K). Single‐crystal X‐ray studies as well as EPR spectroscopy revealed the unequivocal existence of a thioketyl radical anion in the solid state and in solution, respectively. The computed Mulliken spin density within 2_M is mainly located at the sulfur (49 %) and the carbonyl carbon (33 %) atoms. Upon adding [2.2.2]‐cryptand to the radical species 2_K to minimize the interionic interaction, an activation reaction was observed, yielding a potassium salt with a phosphanyl thioether based anion, [K(crypt)]⁺[Ter(iPr)P−C(−S‐iPr)−P(iPr)₂S]⁻ (3) as the product of an intermolecular shift of an iPr group from a second anion. The products were fully characterized and application of the radical anion as a reducing agent was demonstrated.

Interaction of the potent antitumoral compounds Casiopeinas® with blood serum and cellular bioligands

Casiopeinas® are among the few Cu^II compounds patented for their antitumor activity, but their mode of action has not been fully elucidated yet. One of them, Cas II-gly, is formed by 4,7-dimethyl-1,10-phenanthroline (Me₂phen) and glycinato (Gly). In blood and cells, Cas II-gly can keep its identity or form mixed species with serum or cytosol bioligands (bL or cL) with composition Cu^II-Me₂phen-bL/cL, Cu^II-Gly-bL/cL, or Cu^II-bL/cL. In this study, the binding of Cas II-gly with low molecular mass bioligands of blood serum (citric, L-lactic acid, and L-histidine) and cytosol (reduced glutathione (GSH), reduced nicotinamide adenine dinucleotide (NADH), adenosine triphosphate (ATP), and l-ascorbic acid) was examined through the application of instrumental (ElectroSpray Ionization-Mass Spectrometry and Electron Paramagnetic Resonance) and computational (Density Functional Theory) methods. The results indicated that mixed species Cu^II-Me₂phen-bL/cL are formed, with the bioligands replacing glycinato. The formation of these adducts may participate in the copper transport toward the target organs and facilitate the cellular uptake or, in constrast, preclude it. In the systems with GSH, NADH and L-ascorbate, a redox reaction occurs with the partial oxidation of cL to the corresponding oxidized form (GSSG, NAD⁺ and dehydroascorbate) which interact with Cu^II. Formed Cu^I ion does not give complexation reactions with reduced or oxidized form of bioligands for its 'soft' character and low affinity for oxygen and nitrogen donors compared to Cu^II. However, Cu^I could promote Fenton-like reactions with production of reactive oxygen species (ROS) related to the antitumor activity of Casiopeinas®.

17O-EPR determination of the structure and dynamics of copper single-metal sites in zeolites

The bonding of copper ions to lattice oxygens dictates the activity and selectivity of copper exchanged zeolites. By ¹⁷O isotopic labelling of the zeolite framework, in conjunction with advanced EPR methodologies and DFT modelling, we determine the local structure of single site Cu^II species, we quantify the covalency of the metal-framework bond and we assess how this scenario is modified by the presence of solvating H₂¹⁶O or H₂¹⁷O molecules. This enables to follow the migration of Cu^II species as a function of hydration conditions, providing evidence for a reversible transfer pathway within the zeolite cage as a function of the water pressure. The results presented in this paper establish ¹⁷O EPR as a versatile tool for characterizing metal-oxide interactions in open-shell systems.

Oxo versus Sulfido Coordination at Tungsten: A Spectroscopic and Correlated Ab Initio Electronic Structure Study

The tungsten ion that resides at the active site of a unique class of enzymes only found in esoteric hyperthermophilic archaea bacteria is known to possess at least one terminal chalcogenide ligand. The identity of this as either an oxo or sulfido (or both) is difficult to ascertain from structural studies; therefore, small-molecule analogues are developed to calibrate and substantiate spectroscopic signatures obtained from native proteins. The electronic structures of Tp*WECl₂ (E = O, S; Tp* = hydrotris(3,5-dimethylpyrazol-1-yl)borate) have been scrutinized using electronic, electron paramagnetic resonance (EPR), and X-ray absorption spectroscopy to assess the impact of terminal chalcogen on the adjacent cis chloride ligands. Examination at the Cl K-edge provides a direct probe of the bonding and therein lability of these chloride ligands, and in conjunction with density functional theoretical and multireference calculations reveals greater bond covalency in Tp*WOCl₂ compared to Tp*WSCl₂. The computational model and electronic structure assignment are corroborated by the reproduction of spin-Hamiltonian parameters, whose magnitude is dominated by the sizeable spin-orbit coupling of tungsten.

A High-Resolution View of the Coordination Environment in a Paramagnetic Metalloprotein from its Magnetic Properties

Metalloproteins constitute a significant fraction of the proteome of all organisms and their characterization is critical for both basic sciences and biomedical applications. A large portion of metalloproteins bind paramagnetic metal ions, and paramagnetic NMR spectroscopy has been widely used in their structural characterization. However, the signals of nuclei in the immediate vicinity of the metal center are often broadened beyond detection. In this work, we show that it is possible to determine the coordination environment of the paramagnetic metal in the protein at a resolution inaccessible to other techniques. Taking the structure of a diamagnetic analogue as a starting point, a geometry optimization is carried out by fitting the pseudocontact shifts obtained from first principles quantum chemical calculations to the experimental ones.

Converged Structural and Spectroscopic Properties for Refined QM/MM Models of Azurin

Blue copper proteins continue to challenge experiment and theory with their electronic structure and spectroscopic properties that respond sensitively to the coordination environment of the copper ion. In this work, we report state-of-the art electronic structure studies for geometric and spectroscopic properties of the archetypal "Type I" copper protein azurin in its Cu(II) state. A hybrid quantum mechanics/molecular mechanics (QM/MM) approach is used, employing both density functional theory (DFT) and coupled cluster with singles, doubles, and perturbative triples (CCSD(T)) methods for the QM region, the latter method making use of the domain-based local pair natural orbital (DLPNO) approach. Models of increasing QM size are employed to investigate the convergence of critical geometric parameters. It is shown that convergence is slow and that a large QM region is critical for reproducing the short experimental Cu-SCys112 distance. The study of structural convergence is followed by investigation of spectroscopic parameters using both DFT and DLPNO-CC methods and comparing these to the experimental spectrum using simulations. The results allow us to examine for the first time the distribution of spin densities and hyperfine coupling constants at the coupled cluster level, leading us to revisit the experimental assignment of the 33S hyperfine splitting. The wavefunction-based approach to obtain spin-dependent properties of open-shell systems demonstrated here for the case of azurin is transferable and applicable to a large array of bioinorganic systems.

A method to calculate the NMR spectra of paramagnetic species using thermalized electronic relaxation

For paramagnetic species, it has been long understood that the hyperfine interaction between the unpaired electrons and the nucleus results in a nuclear magnetic resonance (NMR) peak that is shifted by a paramagnetic shift, rather than split by the coupling, due to an averaging of the electronic magnetic moment caused by electronic relaxation that is fast in comparison to the hyperfine coupling constant. However, although this feature of paramagnetic NMR has formed the basis of all theories of the paramagnetic shift, the precise theory and mechanism of the electronic relaxation required to predict this result has never been discussed, nor has the assertion been tested. In this paper, we show that the standard semi-classical Redfield theory of relaxation fails to predict a paramagnetic shift, as does any attempt to correct for the semi-classical theory using modifications such as the inhomogeneous master equation or Levitt-di Bari thermalization. In fact, only the recently-introduced Lindbladian theory of relaxation in magnetic resonance [J.Magn.Reson., 310, 106645 (2019)] is able to correctly predict the paramagnetic shift tensor and relaxation-induced linewidth in pNMR. Furthermore, this new formalism is able to predict the NMR spectra of paramagnetic species outside the high-temperature and weak-order limits, and is therefore also applicable to dynamic nuclear polarization. The formalism is tested by simulations of five case studies, which include Fermi-contact and spin-dipolar hyperfine couplings, g-anisotropy, zero-field splitting, high and low temperatures, and fast and slow electronic relaxation.

Quantum dynamics of Mn2+ in dimethylammonium magnesium formate

Dimethylammonium magnesium formate, [(CH₃)₂NH₂][Mg(HCOO)₃] or DMAMgF, is a model used to study high temperature hybrid perovskite-like dielectrics. This compound displays an order-disorder phase transition at about 260 K. Using multifrequency electron spin resonance in continuous wave and pulsed modes, we herein present the quantum dynamics of the Mn²⁺ ion probe in DMAMgF. In the high temperature paraelectric phase, we observe a large distribution of the zero field splitting that is attributed to the high local disorder and further supported by density functional theory computations. In the low temperature ferroelastic phase, a single structure phase is detected and shown to contain two magnetic structures. The complex electron paramagnetic resonance signals were identified by means of the Rabi oscillation method combined with the crystal field kernel density estimation.

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.

A Quantum Chemistry View on Two Archetypical Paramagnetic Pentacoordinate Nickel(II) Complexes Offers a Fresh Look on Their NMR Spectra

Quantum chemical methods for calculating paramagnetic NMR observables are becoming increasingly accessible and are being included in the inorganic chemistry practice. Here, we test the performance of these methods in the prediction of proton hyperfine shifts of two archetypical high-spin pentacoordinate nickel(II) complexes (NiSAL-MeDPT and NiSAL-HDPT), which, for a variety of reasons, turned out to be perfectly suited to challenge the predictions to the finest level of detail. For NiSAL-MeDPT, new NMR experiments yield an assignment that perfectly matches the calculations. The slightly different hyperfine shifts from the two “halves” of the molecules related by a pseudo-C₂ axis, which are experimentally divided into two well-defined spin systems, are also straightforwardly distinguished by the calculations. In the case of NiSAL-HDPT, for which no X-ray structure is available, the quality of the calculations allowed us to refine its structure using as a starting template the structure of NiSAL-MeDPT.

State-of-the-art quantum chemical methods and paramagnetism-tailored NMR experiments provide a deep insight on the relation between the spectra and the electronic structure for two paramagnetic pentacoordinate nickel(II) complexes.

Ligand Field Inversion as a Mechanism to Gate Bioorganometallic Reactivity: Investigating a Biochemical Model of Acetyl CoA Synthase Using Spectroscopy and Computation

The biological global carbon cycle is largely regulated through microbial nickel enzymes, including carbon monoxide dehydrogenase (CODH), acetyl coenzyme A synthase (ACS), and methyl coenzyme M reductase (MCR). These systems are suggested to utilize organometallic intermediates during catalysis, though characterization of these species has remained challenging. We have established a mutant of nickel-substituted azurin as a scaffold upon which to develop protein-based models of enzymatic intermediates, including the organometallic states of ACS. In this work, we report the comprehensive investigation of the S = 1/2 Ni-CO and Ni-CH₃ states using pulsed EPR spectroscopy and computational techniques. While the Ni-CO state shows conventional metal-ligand interactions and a classical ligand field, the Ni-CH₃ hyperfine interactions between the methyl protons and the nickel indicate a closer distance than would be expected for an anionic methyl ligand. Structural analysis instead suggests a near-planar methyl ligand that can be best described as cationic. Consistent with this conclusion, the frontier molecular orbitals of the Ni-CH₃ species indicate a ligand-centered LUMO, with a d⁹ population on the metal center, rather than the d⁷ population expected for a typical metal-alkyl species generated by oxidative addition. Collectively, these data support the presence of an inverted ligand field configuration for the Ni-CH₃ Az species, in which the lowest unoccupied orbital is centered on the ligands rather than the more electropositive metal. These analyses provide the first evidence for an inverted ligand field within a biological system. The functional relevance of the electronic structures of both the Ni-CO and Ni-CH₃ species are discussed in the context of native ACS, and an inverted ligand field is proposed as a mechanism by which to gate reactivity both within ACS and in other thiolate-containing metalloenzymes.

Unexpected radical mechanism in a [4+1] cycloaddition reaction

The mechanism of the cheletropic reaction of monoimines with PPh₃via unexpected radical intermediates resulting in oxazaphospholes has been discussed based on EPR, UV-vis and DFT calculations.

Integrated experimental/computational approaches to characterize the systems formed by vanadium with proteins and enzymes

An integrated instrumental/computational approach to characterize metallodrug–protein adducts at the molecular level is reviewed. A series of applications are described, focusing on potential vanadium drugs with a generalization to other metals.

Estimating the accuracy of calculated electron paramagnetic resonance hyperfine couplings for a lytic polysaccharide monooxygenase

Lytic polysaccharide monooxygenases (LPMOs) are enzymes that bind polysaccharides followed by an (oxidative) disruption of the polysaccharide surface, thereby boosting depolymerization. The binding process between the LPMO catalytic domain and polysaccharide is key to the mechanism and establishing structure-function relationships for this binding is therefore crucial. The hyperfine coupling constants (HFCs) from EPR spectroscopy have proven useful for this purpose. Unfortunately, EPR does not provide direct structural data and therefore the experimental EPR parameters have to be supported with parameters calculated with density functional theory. Yet, calculated HFCs are extremely sensitive to the employed computational setup. Using the LPMO Ls(AA9)A catalytic domain, we here quantify the importance of several choices in the computational setup, ranging from the use of specialized basis, the underlying structures, and the employed exchange-correlation functional. We show that specialized basis sets are an absolute necessity, and also that care has to be taken in the optimization of the underlying structure: only by allowing large parts of the protein around the active site to structurally relax could we obtain results that uniformly reproduced experimental trends. We compare our results to previously published X-ray structures and experimental HFCs for Ls(AA9)A as well as to recent experimental/theoretical results for another (AA10) family of LPMOs.

Dimethyl sulfoxide as a strongly coordinating solvent: 3′,4′-dihydroxyflavone-Cu(II)-DMSO system case study

Dimethyl sulfoxide (DMSO) is an aprotic organic solvent widely used in laboratory practice due to its ability to dissolve both polar and nonpolar compounds. However, DMSO is also commonly known as a strongly coordinating solvent, especially towards transition metal containing complexes. In this study, estimation of the coordination ability of DMSO towards the Cu(II) ion was attempted, employing a model system composed of 3′,4′-dihydroxyflavone-Cu(II) complex in the presence of explicit DMSO molecules, using the density functional theory (DFT). Nature of the Cu-DMSO chemical interaction (i.e. Cu-O bonding) was studied within the framework of quantum theory of atoms in molecules (QTAIM). Impact of DMSO coordination on the charge and spin distribution at Cu(II) ion was inspected using Mulliken population and QTAIM analysis.

Comparison of Density Functional and Correlated Wave Function Methods for the Prediction of Cu(II) Hyperfine Coupling Constants

The reliable prediction of Cu(II) hyperfine coupling constants remains a challenge for quantum chemistry. Until recently only density functional theory (DFT) could target this property for systems of realistic size. However, wave function based methods become increasingly applicable. In the present work, we define a large set of Cu(II) complexes with experimentally known hyperfine coupling constants and use it to investigate the performance of modern quantum chemical methods for the prediction of this challenging spectroscopic parameter. DFT methods are evaluated against orbital‐optimized second‐order Møller‐Plesset (OO‐MP2) theory and coupled cluster calculations including singles and doubles excitations, driven by the domain‐based local pair natural orbital approach (DLPNO‐CCSD). Special attention is paid to the definition of a basis set that converges adequately toward the basis set limit for the given property for all methods considered in this study, and a specifically optimized basis set is proposed for this purpose. The results suggest that wave function based methods can supplant but do not outcompete DFT for the calculation of Cu(II) hyperfine coupling constants. Mainstream hybrid functionals such as B3PW91 remain on average the best choice.

Solution of a Puzzle: High-Level Quantum-Chemical Treatment of Pseudocontact Chemical Shifts Confirms Classic Semiempirical Theory

A recently popularized approach for the calculation of pseudocontact shifts (PCSs) based on first-principles quantum chemistry (QC) leads to different results than the classic "semiempirical" equation involving the susceptibility tensor. Studies that attempted a comparison of theory and experiment led to conflicting conclusions with respect to the preferred theoretical approach. In this Letter, we show that after inclusion of previously neglected terms in the full Hamiltonian, one can deduce the semiempirical equations from a rigorous QC-based treatment. It also turns out that in the long-distance limit, one can approximate the complete A tensor in terms of the g tensor. By means of Kohn-Sham density functional theory calculations, we numerically confirm the long-distance expression for the A tensor and the theoretically predicted scaling behavior of the different terms. Our derivation suggests a computational strategy in which one calculates the susceptibility tensor and inserts it into the classic equation for the PCS.

Hyperfine-Coupling Tensors from Projected Hartree-Fock Theory

We assess the calculation of hyperfine coupling (HFC) tensors by different variants of Projected Hartree-Fock (PHF) theory. For a set of small main-group S = 1/2 radicals (BO, CO⁺, CN, AlO, vinyl, methyl, ethynyl), spin-symmetry as well as complex-conjugation and point-group symmetry are first broken in a reference determinant, and then variationally restored, in the frame of the modern formulation of PHF theory. Historically, PHF theory was basically restricted to the restoration of spin symmetry from an unrestricted HF determinant (conserving S_z symmetry). This afforded unsatisfactory HFCs. We obtain far better results for isotropic (and anisotropic) HFCs when the variational energy is further lowered by working with generalized determinants that completely break spin symmetry, and when additional symmetries are used. Specifically, complex-conjugation projection recovers a substantial fraction of the dynamical correlation energy in small molecules, and the detailed equations for combined complex-conjugation, spin- and point-group projection in the density-matrix/diagonalization formulation of PHF theory are here reported for the first time. The compact representation of the PHF wave function allows for a straightforward evaluation of the spin-density matrix and of HFC tensors with little effort. The promising performance of PHF theory may motivate the application of post-PHF methods to the calculation of HFC tensors.

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-chemical effects on intramolecular photoinduced charge transfer reactions in bisphenanthroline copper(i)-viologen dyad assemblies

Two covalently linked donor-acceptor copper phenanthroline complexes (C-A dyads) of interest for solar energy conversion/storage schemes, [Cu(i)(Rphen(OMV)2 4+)2]9+ = RC+A4 8+ with RC+ = [Cu(i)Rphen2]+ involving 2,9-methyl (R = Me) or 2,9-phenyl (R = Ph)-phenanthroline ligands that are 5,6-disubstituted by 4-(n-butoxy) linked methylviologen electron acceptor groups (A2+ = OMV2+), have been synthesized and investigated via quantum chemical calculations and nanosecond laser flash spectroscopy in 1,2-difluorobenzene/methanol (dfb/MeOH) mixtures. Upon photoexcitation, charge transfer (CT) states RC2+A+A3 6+ are formed in less than one ns and decay by charge recombination on a time scale of 6-45 ns. The CT lifetime of RC2+A+A3 6+ has a strong dependence on MeOH solvent fraction when R = Me, but is unaffected if R = Ph. This solvent effect is due to coordination of MeOH solvent in MeC+A4 8+ (i.e. exciplex formation) allowed by conformational flattening of the ligand sphere, which cannot occur in PhC+A4 8+ having bulkier Phphen ligand framework. Interestingly, the decay time of the CT state increases for both species at low magnetic fields with a maximum increase of ca. 30% at ca. 150 mT, then decreases as the field is increased up to 1500 mT, the highest field investigated. This magnetic field effect (MFE) is due to magnetic modulation of the spin dynamics interconverting 3CT and 1CT states. A quantitative modeling according to the radical pair mechanism involving ab initio multireference calculations of the complexes revealed that the spin process is dominated by the effect of Cu hyperfine coupling. The external magnetic field suppresses the hyperfine coupling induced spin state mixing thereby lengthening the CT decay time. This effect is counteracted by the field dependent processes of T0-S mixing through the Δg-mechanism and by a local mode spin-orbit mechanism. Further, the maximum MFE is limited by a finite rate of direct recombination of 3CT states and the spin-rotational mechanism of spin relaxation. This study provides a first comprehensive characterization of Cu(ii)-complex spin chemistry and highlights how spin chemistry can be used to manipulate solar energy harvesting and storage materials.

Decoherence in Molecular Electron Spin Qubits: Insights from Quantum Many-Body Simulations

Quantum states are described by wave functions whose phases cannot be directly measured but which play a vital role in quantum effects such as interference and entanglement. The loss of the relative phase information, termed decoherence, arises from the interactions between a quantum system and its environment. Decoherence is perhaps the biggest obstacle on the path to reliable quantum computing. Here we show that decoherence occurs even in an isolated molecule, although not all phase information is lost, via a theoretical study of a central electron spin qubit interacting with nearby nuclear spins in prototypical magnetic molecules. The residual coherence, which is molecule-dependent, provides a microscopic rationalization for the nuclear spin diffusion barrier proposed to explain experiments. The contribution of nearby molecules to the decoherence has a nontrivial dependence on separation, peaking at intermediate distances. Molecules that are far away affect only the long-time behavior. Because the residual coherence is simple to calculate and correlates well with the coherence time, it can be used as a descriptor for coherence in magnetic molecules. This work will help establish design principles for enhancing coherence in molecular spin qubits and serve to motivate further theoretical work.

Spectroscopic and Computational Comparisons of Thiolate-Ligated Ferric Nonheme Complexes to Cysteine Dioxygenase: Second-Sphere Effects on Substrate (Analogue) Positioning

Parallel spectroscopic and computational studies of iron(III) cysteine dioxygenase (CDO) and synthetic models are presented. The synthetic complexes utilize the ligand tris(4,5-diphenyl-1-methylimidazol-2-yl)phosphine (^Ph2TIP), which mimics the facial three-histidine triad of CDO and other thiol dioxygenases. In addition to the previously reported [Fe^II(CysOEt)(^Ph2TIP)]BPh₄ (1; CysOEt is the ethyl ester of anionic l-cysteine), the formation and crystallographic characterization of [Fe^II(2-MTS)(^Ph2TIP)]BPh₄ (2) is reported, where the methyl 2-thiosalicylate anion (2-MTS) resembles the substrate of 3-mercaptopropionate dioxygenase (MDO). One-electron chemical oxidation of 1 and 2 yields ferric species that bind cyanide and azide anions, which have been used as spectroscopic probes of O₂ binding in prior studies of Fe^III-CDO. The six-coordinate Fe^III-CN and Fe^III-N₃ adducts are examined with UV-vis absorption, electron paramagnetic resonance (EPR), and resonance Raman (rRaman) spectroscopies. In addition, UV-vis and rRaman studies of cysteine- and cyanide-bound Fe^III-CDO are reported for both the wild-type (WT) enzyme and C93G variant, which lacks the Cys-Tyr cross-link that is present in the second coordination sphere of the WT active site. Density functional theory (DFT) and ab initio calculations are employed to provide geometric and electronic structure descriptions of the synthetic and enzymatic Fe^III adducts. In particular, it is shown that the complete active space self-consistent field (CASSCF) method, in tandem with n-electron valence state second-order perturbation theory (NEVPT2), is capable of elucidating the structural basis of subtle shifts in EPR g values for low-spin Fe^III species.

First-Principles Calculation of Transition Metal Hyperfine Coupling Constants with the Strongly Constrained and Appropriately Normed (SCAN) Density Functional and its Hybrid Variants

Density functional theory (DFT) is used extensively for the first-principles calculation of hyperfine coupling constants in both main-group and transition metal systems. As with many other properties, the performance of DFT for hyperfine coupling constants is of variable quality, particularly for transition metal complexes, because it strongly depends on the nature of the chemical system and the type of approximation to the exchange-correlation functional. Recently, a meta-generalized-gradient approximation (mGGA) functional was proposed that obeys all known exact constraints for such a method, known as the Strongly Constrained and Appropriately Normed (SCAN) functional. In view of its theoretically superior formulation a benchmark set of complexes is used to assess the performance of SCAN for the challenging case of transition metal hyperfine coupling constants. In addition, two global hybrid versions of the functional, SCANh and SCAN0, are described and tested. The values computed with the new functionals are compared with experiment and with those of other DFT approximations. Although the original SCAN and the SCAN-based hybrids may offer improved hyperfine coupling constants for specific systems, no uniform improvement is observed. On the contrary, there are specific cases where the new functionals fail badly due to a flawed description of the underlying electronic structure. Therefore, despite these methodological advances, systematically accurate and system-independent prediction of transition metal hyperfine coupling constants with DFT remains an unmet challenge.