Validation of Exchange−Correlation Functionals for Spin States of Iron Complexes

Improving Predictions of Spin-Crossover Complex Properties through DFT Calculations with a Local Hybrid Functional

We conducted a study on the performance of the local hybrid exchange-correlation functional PBE0r for a set of 95 experimentally characterized iron spin-crossover (SCO) complexes [Vennelakanti, V.; J. Chem. Phys. 2023, 159, 024120]. The PBE0r functional is a variant of PBE0 where the exchange correction is restricted to on-site terms formulated on the basis of local orbitals. We determine the free parameters of the PBE0r functional against the experimental data and other hybrid functionals. With a Hartree-Fock (HF) exchange factor of 4%, the PBE0r functional accurately reproduces the electronic and free-energy trends predicted in prior DFT studies for these 95 complexes by using the B3LYP functional. Larger values of HF exchange stabilize high-spin states. The PBE0r-predicted bond lengths tend to exceed the experimental bond lengths, although bond lengths are less sensitive to HF exchange than in global hybrids. The predicted SCO transition temperatures T1/2 from PBE0r correlate moderately with the experimental transition temperatures, showing a slight improvement compared to the previous modB3LYP-predicted T1/2. This study suggests that the PBE0r functional is computationally cost-effective and offers the possibility of simulating larger complexes with accuracy comparable to global hybrid functionals, provided the HF-exchange parameter is carefully optimized.

Low-spin to low-spin valence tautomeric transition in cobalt bis-dioxolenes

Cobalt dioxolenes are a well-known class of switchable coordination compounds showing intramolecular electron transfer, which is always accompanied by a spin state change at the cobalt center. Here, we present the first example of thermally switchable cobalt bis-dioxolenes where intramolecular electron transfer seems to take place, but the spin state change is suppressed. This leads to the detection of thermal transition between a common ls-CoIII(SQ˙-)(Cat2-) and an extremely rare ls-CoII(SQ˙-)2 electronic state (hs - high-spin, ls - low-spin, SQ˙- - benzosemiquinonate(1-) radical and Cat2- - catecholate(2-)). Parallel to the present work, a similar work but on cobalt mono-dioxolenes has just appeared (Chem. Eur. J., 2023, 29, e202300091), suggesting thermal transition between ls-CoIII(Cat2-) and ls-CoII(SQ˙-) electronic states.

Photoredox matching of earth-abundant photosensitizers with hydrogen evolving catalysts by first-principles predictions

Photoredox properties of several earth-abundant light-harvesting transition metal complexes in combination with cobalt-based proton reduction catalysts have been investigated computationally to assess the fundamental viability of different photocatalytic systems of current experimental interest. Density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations using several GGA (BP86, BLYP), hybrid-GGA (B3LYP, B3LYP*), hybrid meta-GGA (M06, TPSSh), and range-separated hybrid (ωB97X, CAM-B3LYP) functionals were used to calculate relevant ground and excited state reduction potentials for photosensitizers, catalysts, and sacrificial electron donors. Linear energy correction factors for the DFT/TD-DFT results that provide the best agreement with available experimental reference results were determined in order to provide more accurate predictions. Among the selection of functionals, the B3LYP* and TPSSh sets of correction parameters were determined to give the best redox potentials and excited states energies, ΔEexc, with errors of ∼0.2 eV. Linear corrections for both reduction and oxidation processes significantly improve the predictions for all the redox pairs. In particular, for TPSSh and B3LYP*, the calculated errors decrease by more than 0.5 V against experimental values for catalyst reduction potentials, photosensitizer oxidation potentials, and electron donor oxidation potentials. Energy-corrected TPSSh results were finally used to predict the energetics of complete photocatalytic cycles for the light-driven activation of selected proton reduction cobalt catalysts. These predictions demonstrate the broader usefulness of the adopted approach to systematically predict full photocycle behavior for first-row transition metal photosensitizer-catalyst combinations more broadly.

Synthesis, Characterization, and Single-Crystal X-ray Structures of Refractory Metal Compounds as Precursors for the Single-Source Chemical Vapor Deposition of Metal Nitrides

The chemical vapor deposition of refractory metal nitrides requires volatile precursors and has previously been achieved by using metal complexes containing a variety of imide ligands. Recently, the 1,4-di-tert-butyl-1,3-diazabutadiene (DAD) adduct of bis(tert-butylimide)dichloridemolybdenum(VI) was shown to be an excellent precursor for the single-source CVD of Mo2N thin films. Leveraging the success of this work, we prepared chromium and tungsten compounds with the same framework. Additionally, the framework has been modified slightly to allow the isolation of mono(tert-butylimide)trichloride complexes of vanadium, niobium, tantalum, and molybdenum(V) to extend the search for new vapor-phase precursors. These compounds were all fully characterized using the standard methods of multinuclear magnetic resonance spectroscopy, combustion analysis, and single-crystal X-ray diffraction. Their thermal properties were determined by using thermogravimetric analysis and differential scanning colorimetry to assess their utility as vapor-phase precursors. Finally, preliminary deposition studies were carried out to investigate their potential as single-source CVD precursors.

Artificial Neural Network-Based Density Functional Approach for Adiabatic Energy Differences in Transition Metal Complexes

During the past decades, approximate Kohn-Sham density functional theory schemes have garnered many successes in computational chemistry and physics, yet the performance in the prediction of spin state energetics is often unsatisfactory. By means of a machine learning approach, an enhanced exchange and correlation functional is developed to describe adiabatic energy differences in transition metal complexes. The functional is based on the computationally efficient revision of the regularized, strongly constrained, and appropriately normed functional and improved by an artificial neural network correction trained over a small data set of electronic densities, atomization energies, and/or spin state energetics. The training process, performed using a bioinspired nongradient-based approach adapted for this work from the particle swarm optimization, is analyzed and discussed extensively. The resulting machine learned meta-generalized gradient approximation functional is shown to outperform most known density functionals in the prediction of adiabatic energy differences for a diverse set of transition metal complexes with varying local coordinations and metal choices.

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

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

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

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

Molecular and Electronic Structures of Macrocyclic Compounds Formed at Template Synthesis in the M(II)-Thiocarbohydrazide-Diacetyl Triple Systems: A Quantum-Chemical Analysis by DFT Methods

Using density functional theory (DFT) B3PW91/TZVP, M06/TZVP, and OPBE/TZVP chemistry models and the Gaussian09 program, a quantum-chemical calculation of geometric and thermodynamic parameters of Ni(II), Cu(II), and Zn(II) macrotetracyclic chelates, with (NNNN)-coordination of ligand donor centers arising during template synthesis between the indicated ions of 3d elements, thiocarbohydrazide H₂N-HN-C(=S)-NH-NH₂ and diacetyl Me-C(=O)-C(=O)-Me, in gelatin-immobilized matrix implants was performed. The key bond lengths and bond angles in these coordination compounds are provided, and it is noted that in all these complexes the MN₄ chelate sites, the grouping of N₄ atoms bonded to the M atom, and the five-membered and six-membered metal chelate rings are practically coplanar. NBO analysis of these compounds was carried out, on the basis of which it was shown that all these complexes, in full accordance with theoretical expectations, are low-spin complexes. The standard thermodynamic characteristics of the template reactions for the formation of the above complexes are also presented. Good agreement between the data obtained using the above DFT levels is noted.

Heteroligand Iron(V) Complexes Containing Porphyrazine, trans-Di[benzo]porphyrazine or Tetra[benzo]porphyrazine, Oxo and Fluoro Ligands: DFT Quantum-Chemical Study

By using quantum chemical calculation data obtained by the DFT method with the B3PW91/TZVP and OPBE/TZVP levels, the possibility of the existence of three Fe(V) complexes, each of which contains in the inner coordination sphere porphyrazine/trans-di[benzo]porphyrazine/tetra[benzo]porphyrazine (phthalocyanine), oxygen (O^2-) and fluorine (F^-) ions, was shown. Key geometric parameters of the molecular structure of these heteroligand complexes are given; it is noted that FeN4 chelate nodes, and all metal-chelate and non-chelate cycles in each of these compounds, are practically planar with the deviation from coplanarity, as a rule, by no more than 0.5°. Furthermore, the bond angles between two nitrogen atoms and an Fe atom are equal to 90°, or less than this by no more than 0.1°, while the bond angles between donor atoms N, Fe, and O or F, in most cases, albeit insignificantly, differ from this value. Nevertheless, the bond angles formed by Fe, O and F atoms are exactly 180°. It is shown that good agreement occurs between the structural data obtained using the above two versions of the DFT method. NBO analysis data for these complexes are presented; it is noted that, according to both DFT methods used, the ground state of the each of three complexes under consideration may be a spin quartet or spin doublet. Additionally, standard thermodynamic parameters of formation (standard enthalpy ∆_fH⁰, entropy S⁰ and Gibbs's energy ∆_fG⁰) for the macrocyclic compounds under consideration are calculated.

DFT Method Used for Prediction of Molecular and Electronic Structures of Mn(VI) Macrocyclic Complexes with Porhyrazine/Phthalocyanine and Two Oxo Ligands

By using the data of the DFT quantum chemical calculation in the OPBE/TZVP and B3PW91/TZVP levels, the possibility of the existence of a manganese(VI) heteroligand complex containing porphyrazine or its tetra[benzo] derivative (phthalocyanine) and two oxygen (O^2-) ligands, which is still unknown for this element, is shown. The parameters of the molecular structure, multiplicity of the ground state, NBO analysis data and standard thermodynamic parameters (enthalpy ΔH⁰_f, entropy S⁰_f and Gibbs's energy ΔG⁰_f of formation) of each of these metal macrocyclic compounds are presented. Additionally, it is noted that, based on the totality of structural data obtained by the above versions of the DFT method, the existence of a similar complex of manganese with di[benzo] derivative of porhyrazine and two oxygen (O^2-) ligands seems doubtful.

One-electron self-interaction error and its relationship to geometry and higher orbital occupation

Density Functional Theory (DFT) sees prominent use in computational chemistry and physics; however, problems due to the self-interaction error (SIE) pose additional challenges to obtaining qualitatively correct results. As an unphysical energy an electron exerts on itself, the SIE impacts most practical DFT calculations. We conduct an in-depth analysis of the one-electron SIE in which we replicate delocalization effects for simple geometries. We present a simple visualization of such effects, which may help in future qualitative analysis of the one-electron SIE. By increasing the number of nuclei in a linear arrangement, the SIE increases dramatically. We also show how molecular shape impacts the SIE. Two- and three-dimensional shapes show an even greater SIE stemming mainly from the exchange functional with some error compensation from the one-electron error, which we previously defined [D. R. Lonsdale and L. Goerigk, Phys. Chem. Chem. Phys. 22, 15805 (2020)]. Most tested geometries are affected by the functional error, while some suffer from the density error. For the latter, we establish a potential connection with electrons being unequally delocalized by the DFT methods. We also show how the SIE increases if electrons occupy higher-lying atomic orbitals; seemingly one-electron SIE free methods in a ground are no longer SIE free in excited states, which is an important insight for some popular, non-empirical density functional approximations (DFAs). We conclude that the erratic behavior of the SIE in even the simplest geometries shows that robust DFAs are needed. Our test systems can be used as a future benchmark or contribute toward DFT development.

Electron Correlation in the Iron(II) Porphyrin by Natural Orbital Functional Approximations

The relative stability of the singlet, triplet, and quintet spin states of iron(II) porphyrin (FeP) represents a challenging problem for electronic structure methods. While it is currently accepted that the ground state is a triplet, multiconfigurational wave function-based methods predict a quintet, and density functional approximations vary between triplet and quintet states, leading to a prediction that highly depends on the features of the method employed. The recently proposed Global Natural Orbital Functional (GNOF) aims to provide a balanced treatment between static and dynamic correlation, and together with the previous Piris Natural Orbital Functionals (PNOFs), allowed us to explore the importance of each type of correlation in the stability order of the states of FeP with a method that conserves the spin of the system. It is noteworthy that GNOF correlates all electrons in all available orbitals for a given basis set; in the case of the FeP with a double-ζ basis set as used in this work, this means that GNOF can properly correlate 186 electrons in 465 orbitals, significantly increasing the sizes of systems amenable to multiconfigurational treatment. Results show that PNOF5, PNOF7s, and PNOF7 predict the quintet to have a lower energy than the triplet state; however, the addition of dynamic correlation via second-order Møller-Plesset corrections (NOF-MP2) turns the triplet state to be lower than the quintet state, a prediction also reproduced by GNOF that incorporates much more dynamic correlation than its predecessors.

Iron-Catalyzed Olefin Metathesis: Recent Theoretical and Experimental Advances

The "metathesis reaction" is a straightforward and often metal-catalyzed chemical reaction that transforms two hydrocarbon molecules to two new hydrocarbons by exchange of molecular fragments. Alkane, alkene and alkyne metathesis have become an important tool in synthetic chemistry and have provided access to complex organic structures. Since the discovery of industrial olefin metathesis in the 1960s, many modifications have been reported; thus, increasing scope and improving reaction selectivity. Olefin metathesis catalysts based on high-valent group six elements or Ru(IV) have been developed and improved through ligand modifications. In addition, significant effort was invested to realize olefin metathesis with a non-toxic, bio-compatible and one of the most abundant elements in the earth's crust; namely, iron. First evidences suggest that low-valent Fe(II) complexes are active in olefin metathesis. Although the latter has not been unambiguously established, this review summarizes the key advances in the field and aims to guide through the challenges.

Novel porphyrazine derivative – 2,3,5,7,8,10,12,13,15,17,18,20-dodecaazaporphin and its complexes with M(II) ions of 3d-elements: DFT quantum-chemical modeling

Using three different versions of the density functional theory (DFT) – B3PW91/TZVP, M06/TZVP and OPBE/TZVP chemical models, the calculation of the molecular structures of (6666) macrocyclic complexes of 3d-elements (M) with a novel (NNNN)-donor macrocyclic ligand, 2,3,5,7,8,10,12,13,15,17,18,20-dodecaazaporphin (H2L), was carried out. The values of the most important bond lengths, bond and non-bond angles in these metal complexes were presented. The standard enthalpy, entropy, and Gibbs energy of formation of these compounds were also calculated. It was noted that according to the data of the above chemical models, [MnL], [FeL], [CoL], [NiL], and [CuL] complexes with this novel ligand have a flat MN4 chelate node and a planar structure as a whole, while the [TiL], [VL], [CrL] and [ZnL] complexes have a non-coplanar MN4 chelate node. Moreover, all 6-membered rings in each of these metal chelates are identical to each other (both in terms of the sum of the bond angles included in them and in their assortment); adjoining 5-membered cycles for the majority of M are also identical to each other (non-identity is noted only in the cases M = Ti, Mn, as well as for the original 2,3,5,7,8,10,12,13,15,17,18,20-dodecaazaporphin). A good agreement was also noted between similar parameters calculated by various DFT methods, both qualitatively and quantitatively.

Accurate computed singlet-triplet energy differences for cobalt systems: implication for two-state reactivity

Accurate singlet-triplet energy differences for cobalt and rhodium complexes were calculated by using several wave function methods, such as MRCISD, CASPT2, CCSD(T) and BCCD(T). Relaxed energy differences were obtained by considering the singlet and triplet complexes, each at the minimum of their potential energy surfaces. Active spaces for multireference calculations were carefully checked to provide accurate results. The considered systems are built by increasing progressively the first coordination sphere around the metal. We included in our set two CpCoX complexes (Cp = cyclopentadienyl, X = alkenyl ligand), which have been suggested as intermediates in cycloaddition reactions. Indeed, cobalt systems have been used for more than a decade as active species in this kind of transformations, for which a two-state reactivity has been proposed. Most of the considered systems display a triplet ground state. However, in the case of a reaction intermediate, while a triplet ground state was predicted on the basis of Density Functional Theory results, our calculations suggest a singlet ground state. This stems from the competition between the exchange term (stabilising the triplet) and the accessibility of an intramolecular coordination (stabilising the singlet). This finding has an impact on the general mechanism of the cycloaddition reaction. Analogous rhodium systems were also studied and, as expected, they have a larger tendency to electron pairing than cobalt species.

Twelve-Nitrogen-Atom Cyclic Structure Stabilized by 3d-Element Atoms: Quantum Chemical Modeling

Using various versions of density functional theory (DFT), DFT M06/TZVP, DFT B3PW91/TZVP, DFT OPBE/TZVP, and, partially, the MP2 method, the possibility of the existence of 3d-element (M) compounds with nitrogen having unusual M: nitrogen ratio 1:12, unknown for these elements at the present, was shown. Structural parameter data were presented. It was shown that all MN4 groupings have tetragonal-pyramidal structure. It was noted that the bond lengths formed by nitrogen atoms and an M atom were equal to each other only in the case of M = Ti, V, Cr and Co, whereas for other Ms, they were slightly different; moreover, the bond angles formed by nitrogen atoms and an M atom were equal to 90.0°, or practically did not differ from this value. Thermodynamic parameters, NBO analysis data and HOMO/LUMO images for this compound were also presented. Good agreement between the calculated data obtained using the above three quantum chemical methods was also noted.

DFT Quantum-chemical prediction of molecular structure of iron(VI) macrocyclic complex with phthalocyanine and two oxo ligands

The possibility of the existence of the unknown iron complex containing phthalocyanine and two oxygen atoms in the inner coordination sphere was predicted using DFT quantum chemical calculation (OPBE/TZVP and B3PW91/TZVP levels). The structural parameters, the ground state multiplicity, the NBO analysis results, and the standard thermodynamic parameters for complex formation (standard enthalpy [Formula: see text], entropy [Formula: see text] and Gibbs’s energy [Formula: see text] are represented.

FCIQMC-Tailored Distinguishable Cluster Approach: Open-Shell Systems

A recently proposed tailored approach based on the distinguishable cluster method and the stochastic FCI solver, FCIQMC [J. Chem. Theory Comput. 2020, 16, 5621], is extended to open-shell molecular systems. The method is employed to calculate spin gaps of various Fe(II) complexes, including a Fe(II) porphyrin model system. Both distinguishable cluster and fully relaxed CASSCF natural orbitals were used in this work as reference for the subsequent tailored distinguishable cluster calculations. The distinguishable cluster natural orbitals occupation numbers were also used as an aid to the selection of the active space. The effect of the active space sizes and of the explicit correlation correction (F12) onto the predicted spin gaps is investigated. The tailored distinguishable cluster with singles and doubles yields consistently more accurate results compared to the tailored coupled cluster with singles and doubles.

New heteroligand complex of cobalt with phthalocyanine, oxo and fluoro ligands: DFT consideration

Based on the results of a quantum chemical calculation using the DFT method in the OPBE/TZVP and B3PW91/TZVP levels, the possibility of the existence of a cobalt heteroligand complex containing in the inner coordination sphere tetra[benzo]derivative of porphyrazine (phthalocyanine), oxide (O[Formula: see text] and fluoride (F[Formula: see text] ions, with possible oxidation state of Co(V) that is non-characteristic for the given 3[Formula: see text]-element, has been shown. The data on the structural parameters, multiplicity of the ground state, NBO analysis data and standard thermodynamic parameters of formation (standard enthalpy [Formula: see text], entropy [Formula: see text] and Gibbs’s energy [Formula: see text] for the indicated complex have been presented. At the same time, it has been noted that the porphyrazine itself as well as di[benzo]porphyrazine, do not form such metalcomplexes.

Nickel macrocyclic complexes with porphyrazine and some [benzo]substituted, oxo and fluoro ligands: DFT analysis

By using quantum chemical calculation data obtained by the DFT method with the OPBE/TZVP and B3PW91/TZVP levels, the principal possibility of the existence of three heteroligand complexes of nickel, each of which was shown to contain in the inner coordination sphere either porphyrazine or di[benzo]- and tetra[benzo]porphyrazine, oxygen (O[Formula: see text] and fluorine (F[Formula: see text] ions. The data on the geometric parameters of the molecular structure of these complexes are presented; which shows that NiN4 chelate nodes, all metal-chelate and non-chelate cycles in each of these complexes, are strictly planar. The bond angles between two donor nitrogen atoms and a nickel atom are equal to 90[Formula: see text], while the bond angles between donor atoms N, Ni, and O or F, in most cases, albeit insignificantly, differ from this value. Nevertheless, the bond angles formed by Ni, O and F atoms are exactly 180[Formula: see text]. NBO analysis data for these complexes are presented; it was noted that the ground state of all these complexes was a spin doublet. It has been shown that a good agreement between the data obtained using the above two versions of the DFT method occurs. Also, standard thermodynamic parameters of formation (standard enthalpy [Formula: see text], entropy [Formula: see text] and Gibbs’s energy [Formula: see text] for the macrocyclic compounds under consideration were calculated.

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.

Effect of Oriented Electric Fields on Biologically Relevant Iron-Sulfur Clusters: Tuning Redox Reactivity for Catalysis

Enzyme-based iron-sulfur clusters, exemplified in families such as hydrogenases, nitrogenases, and radical S-adenosylmethionine enzymes, feature in many essential biological processes. The functionality of biological iron-sulfur clusters extends beyond simple electron transfer, relying primarily on the redox activity of the clusters, with a remarkable diversity for different enzymes. The active-site structure and the electrostatic environment in which the cluster resides direct this redox reactivity. Oriented electric fields in enzymatic active sites can be significantly strong, and understanding the extent of their effect on iron-sulfur cluster reactivity can inform first steps toward rationally engineering their reactivity. An extensive systematic density functional theory-based screening approach using OPBE/TZP has afforded a simple electric field-effect representation. The results demonstrate that the orientation of an external electric field of strength 28.8 MV cm^-1 at the center of the cluster can have a significant effect on its relative stability in the order of 35 kJ mol^-1. This shows clear implications for the reactivity of iron-sulfur clusters in enzymes. The results also demonstrate that the orientation of the electric field can alter the most stable broken-symmetry state, which further has implications on the directionality of initiated electron-transfer reactions. These insights open the path for manipulating the enzymatic redox reactivity of iron-sulfur cluster-containing enzymes by rationally engineering oriented electric fields within the enzymes.

Catalytic properties of the ferryl ion in the solid state: a computational review

This review summarises the last findings in the emerging field of heterogeneous catalytic oxidation of light alkanes by ferryl species supported on solid-state systems such as the conversion of methane into methanol by FeO-MOF74.

Quantum-Chemical Consideration of Al2M2 Tetranuclear Metal Clusters (M-3d-Element): Molecular/Electronic Structures and Thermodynamics

Quantum-chemical calculation of most important parameters of molecular and electronic structures of tetra-nuclear (pd) metal clusters having Al₂M₂ composition, where M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, or Zn (bond lengths, bond and torsion angles), and HOMO and LUMO of these compounds by means of DFT OPBE/QZVP method, have been carried out. It has been found that, for each of these metal clusters, an existence of rather large amount of structural isomers different substantially in their total energy, occurs. It has been noticed that molecular structures of metal clusters of the given type differ significantly between them in terms of geometric parameters, as well as in geometric form, wherein the most stable modifications of metal clusters considered are similar between themselves in geometric form. In addition, the standard thermodynamic parameters of formation of metal clusters considered here, and namely standard enthalpy Δ_fH⁰(298 K), entropy S_f⁰(298 K), and Gibbs’ energy Δ_fG⁰(298 K) of formation for these metal clusters, were calculated.

Copper macrocyclic complex with trans-di[benzo]-porphyrazine and two oxo ligands: DFT quantum-chemical design

Based on the results of a quantum chemical calculation using the DFT method in the OPBE/TZVP and B3PW91/TZVP, the possibility of the existence of a copper heteroligand complex with trans-di[benzo]derivative of 3,7,11,15-tetraazaporphine (trans-di[benzo]porphyrazine) and two oxygen (O[Formula: see text] ions that is still unknown for this element was shown. In addition, the data on the structural parameters, the multiplicity of the ground state, NBO analysis and standard thermodynamic parameters of formation (standard enthalpy [Formula: see text], entropy [Formula: see text] and Gibbs’s energy [Formula: see text] for this complex are presented.

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

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

Computational Discovery of Transition-metal Complexes: From High-throughput Screening to Machine Learning

Transition-metal complexes are attractive targets for the design of catalysts and functional materials. The behavior of the metal-organic bond, while very tunable for achieving target properties, is challenging to predict and necessitates searching a wide and complex space to identify needles in haystacks for target applications. This review will focus on the techniques that make high-throughput search of transition-metal chemical space feasible for the discovery of complexes with desirable properties. The review will cover the development, promise, and limitations of "traditional" computational chemistry (i.e., force field, semiempirical, and density functional theory methods) as it pertains to data generation for inorganic molecular discovery. The review will also discuss the opportunities and limitations in leveraging experimental data sources. We will focus on how advances in statistical modeling, artificial intelligence, multiobjective optimization, and automation accelerate discovery of lead compounds and design rules. The overall objective of this review is to showcase how bringing together advances from diverse areas of computational chemistry and computer science have enabled the rapid uncovering of structure-property relationships in transition-metal chemistry. We aim to highlight how unique considerations in motifs of metal-organic bonding (e.g., variable spin and oxidation state, and bonding strength/nature) set them and their discovery apart from more commonly considered organic molecules. We will also highlight how uncertainty and relative data scarcity in transition-metal chemistry motivate specific developments in machine learning representations, model training, and in computational chemistry. Finally, we will conclude with an outlook of areas of opportunity for the accelerated discovery of transition-metal complexes.

A density functional theory study of Fe(II)/Fe(III) distribution in single layer green rust: a cluster approach

Green rust (GR) is a potentially important compound for the reduction of heavy metal and organic pollutants in subsurface environment because of its high Fe(II) content, but many details of the actual reaction mechanism are lacking. The reductive capacity distribution within GR is a key to understand how and where the redox reaction occurs and computational chemistry can provide more details about the electronic properties of green rust. We constructed three sizes of cluster models of single layer GR (i.e., without interlayer molecules or ions) and calculated the charge distribution of these structures using density functional theory. We found that the Fe(II) and Fe(III) are distributed unevenly in the single layer GR. Within a certain range of Fe(II)/Fe(III) ratios, the outer iron atoms behave more like Fe(III) and the inner iron atoms behave more like Fe(II). These findings indicate that the interior of GR is more reductive than the outer parts and will provide new information to understand the GR redox interactions.

Putting Density Functional Theory to the Test in Machine-Learning-Accelerated Materials Discovery

Accelerated discovery with machine learning (ML) has begun to provide the advances in efficiency needed to overcome the combinatorial challenge of computational materials design. Nevertheless, ML-accelerated discovery both inherits the biases of training data derived from density functional theory (DFT) and leads to many attempted calculations that are doomed to fail. Many compelling functional materials and catalytic processes involve strained chemical bonds, open-shell radicals and diradicals, or metal-organic bonds to open-shell transition-metal centers. Although promising targets, these materials present unique challenges for electronic structure methods and combinatorial challenges for their discovery. In this Perspective, we describe the advances needed in accuracy, efficiency, and approach beyond what is typical in conventional DFT-based ML workflows. These challenges have begun to be addressed through ML models trained to predict the results of multiple methods or the differences between them, enabling quantitative sensitivity analysis. For DFT to be trusted for a given data point in a high-throughput screen, it must pass a series of tests. ML models that predict the likelihood of calculation success and detect the presence of strong correlation will enable rapid diagnoses and adaptation strategies. These "decision engines" represent the first steps toward autonomous workflows that avoid the need for expert determination of the robustness of DFT-based materials discoveries.

Improved Spin-State Energy Differences of Fe(II) Molecular and Crystalline Complexes via the Hubbard U-Corrected Density

We recently showed that the DFT+U approach with a linear-response U yields adiabatic energy differences biased toward high spin [Mariano et al. J. Chem. Theory Comput. 2020, 16, 6755-6762]. Such bias is removed here by employing a density-corrected DFT approach where the PBE functional is evaluated on the Hubbard U-corrected density. The adiabatic energy differences of six Fe(II) molecular complexes computed using this approach, named PBE[U] here, are in excellent agreement with coupled cluster-corrected CASPT2 values for both weak- and strong-field ligands resulting in a mean absolute error (MAE) of 0.44 eV, smaller than that of the recently proposed Hartree-Fock density-corrected DFT (1.22 eV) and any other tested functional, including the best performer TPSSh (0.49 eV). We take advantage of the computational efficiency of this approach and compute the adiabatic energy differences of five molecular crystals using PBE[U] with periodic boundary conditions. The results show, again, an excellent agreement (MAE = 0.07 eV) with experimentally extracted values and a superior performance compared with the best performers M06-L (MAE = 0.08 eV) and TPSSh (MAE = 0.31 eV) computed on molecular fragments.

Computational exploration of heterometal substitution into the decaniobate framework, [Nb10O28]6

The factors governing the substitution of group 4B-12B metals into the decaniobate framework are explored using density functional theory in order to ascertain whether (1) recently isolated [MNb9O28]x- clusters are kinetic or thermodynamic products, (2) density functional theory is a sufficient level of theory to accurately predict substitution patterns in polyoxometalates where ion pairing and other effects may operate, and (3) it can be used to guide future synthetic efforts. Computations using restricted, unrestricted and open-shell density functional theory at PBE0/def2-tzvp were found to correctly predict substitution patterns in known clusters, and were subsequently used to calculate the relative energies of a large series of [MNb9O28]x- clusters, to reveal trends and suggest potential synthetic approaches. OPBE/def2-tzvp correctly predicted favoured spin states of known substituted decametalates.

Models of Molecular Structures of Hexa-Nuclear AlnFem Metal Clusters (n + m = 6): DFT Quantum-Chemical Design

By using the density functional theory (DFT) method at the OPBE/QZVP level, key parameters of molecular structures of six-atomic (heterobi)nuclear metal clusters with an Al_nFe_m composition (n + m = 6) (bond lengths, bond angles, and torsion (dihedral) angles) were calculated. It was found that each of these clusters exists in a large number of structural isomers that differ substantially in terms of their total energy. Furthermore, the molecular structures of these structural isomers significantly differ regarding the geometric parameters and geometric form. In addition, the most stable structural isomers of these metal clusters also differ rather considerably in terms of the geometric form.

Electronic and geometric structure effects on one-electron oxidation of first-row transition metals in the same ligand framework

Developing new transition metal catalysts requires understanding of how both metal and ligand properties determine reactivity. Since metal complexes bearing ligands of the Py5 family (2,6-bis-[(2-pyridyl)methyl]pyridine) have been employed in many fields in the past 20 years, we set out here to understand their redox properties by studying a series of base metal ions (M = Mn, Fe, Co, and Ni) within the Py5OH (pyridine-2,6-diylbis[di-(pyridin-2-yl)methanol]) variant. Both reduced (M^II) and the one-electron oxidized (M^III) species were carefully characterized using a combination of X-ray crystallography, X-ray absorption spectroscopy, cyclic voltammetry, and density-functional theory calculations. The observed metal-ligand interactions and electrochemical properties do not always follow consistent trends along the periodic table. We demonstrate that this observation cannot be explained by only considering orbital and geometric relaxation, and that spin multiplicity changes needed to be included into the DFT calculations to reproduce and understand these trends. In addition, exchange reactions of the sixth ligand coordinated to the metal, were analysed. Finally, by including published data of the extensively characterised Py5OMe (pyridine-2,6-diylbis[di-(pyridin-2-yl)methoxymethane])complexes, the special characteristics of the less common Py5OH ligand were extracted. This comparison highlights the non-innocent effect of the distal OH functionalization on the geometry, and consequently on the electronic structure of the metal complexes. Together, this gives a complete analysis of metal and ligand degrees of freedom for these base metal complexes, while also providing general insights into how to control electrochemical processes of transition metal complexes.

Unveiling the catalytic potential of the Fe(iv)oxo species for the oxidation of hydrocarbons in the solid state

We have investigated the three steps in the conversion of methane into methanol by Fe(iv)Ooxo species supported in MOF-74. We use ab initio MD and static approximations to predict the reaction barriers using enthalpy ΔH and free energy ΔG.

A Theoretical Assessment of Spin and Charge States in Binuclear Cobalt-Ruthenium Complexes: Implications for a Creutz-Taube Model Ion Separated by a C60-Derivative Bridging Ligand

We investigate the spin-state energetics and the role of ionic charges in the electronic configuration of binuclear complexes of the form [(NH₃)₅Co(py)-X-(py)Ru(NH₃)₅]^q+. In these compounds with q = 4-6, py = pyridine, and X = C≡C and C₆₀, the Co-Ru distance varies from ∼1.4 to ∼2.1 nm. We carry out a systematic electronic structure calculation using different exchange-correlation (xc) approaches within spin-density functional theory, which are largely employed to investigate the properties of a variety of coordination complexes. To evaluate the effects of spin states and type of spacer in the bridging ligand on the valence tautomerism between Co^2+/3+ and Ru^2+/3+, we examine in more detail the case of Creutz-Taube-type ions [(NH₃)₅Co(py)-X-(py)Ru(NH₃)₅]⁵⁺. Our analysis shows that the stabilization of low- and high-spin states critically depends on the total charge of the complex, type of X-bridged ligand, and employed xc approach to calculate the electron spin density. Importantly, the C₆₀-bridged group may result in a blockage of the valence tautomerism of the Creutz-Taube complex, inducing bistable charge configurations. Overall, our results also show that an adiabatic description in terms of the frontier molecular spin-orbitals for analyzing the distinct spin-charge states of these complexes may dramatically depend on the density-functional description.

DFT Quantum-Chemical Modeling Molecular Structures of Cobalt Macrocyclic Complexes with Porphyrazine or Its Benzo-Derivatives and Two Oxygen Acido Ligands

Based on the results of a quantum chemical calculation using the DFT method with the OPBE/TZVP and B3PW91/TZVP levels, the possibility of the existence of three cobalt heteroligand complexes containing in the inner coordination sphere porphyrazine, di[benzo]- and tetra[benzo]porphyrazine, and two oxygen (O^2-) ions with probable oxidation state VI of Co, which is unknown for this element at the present time, was shown. Data on the structural parameters are presented. It was shown that CoN₄ chelate nodes as well as all metal-chelate and non-chelate cycles in each of these complexes, were strictly planar. Besides, the bond angles formed by two donor nitrogen atoms and a Co atom were close or equal to 90°, while the bond angles formed by donor atoms N, Co, and O, in most cases, albeit insignificantly, differed from this value. Good agreement between the calculated data obtained using the above two versions of the DFT method was found. Standard thermodynamic parameters of formation (standard enthalpy ΔH⁰_{f, 298}, entropy S⁰_{f, 298} and Gibbs's energy ΔG⁰_{f, 298}) for the indicated complexes were presented too.

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

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