Free energy of spin-crossover complexes calculated with density functional methods

Accurate state energetics in spin-crossover systems using pure density functional theory

The energy difference between different spin states of systems with transition metals is an outstanding challenge for electronic structure calculation methods. The small energy difference between high- and low-spin states in spin-crossover systems makes most post-Hartree-Fock or density functional theory-based methods provide inaccurate values. A test case of twenty systems showing spin transitions has been used to evaluate the accuracy of a new family of training meta-GGA (Generalized Gradient Approximation) functionals. One of the functionals of this new family provides comparable or even better values than the best functional reported so far for this type of system, the TPSSh hybrid meta-GGA functional, but without having to use the exact exchange term. It also improves the results obtained with the r2SCAN meta-GGA functional, which was the best alternative to the TPSSh hybrid functional. This makes it possible to calculate the spin energetics of any kind of compound, especially large systems or periodic structures where the exact exchange requires large computational resources.

Modeling Fe(II) Complexes Using Neural Networks

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

Machine Learning Prediction of the Experimental Transition Temperature of Fe(II) Spin-Crossover Complexes

Spin-crossover (SCO) complexes are materials that exhibit changes in the spin state in response to external stimuli, with potential applications in molecular electronics. It is challenging to know a priori how to design ligands to achieve the delicate balance of entropic and enthalpic contributions needed to tailor a transition temperature close to room temperature. We leverage the SCO complexes from the previously curated SCO-95 data set [Vennelakanti et al. J. Chem. Phys. 159, 024120 (2023)] to train three machine learning (ML) models for transition temperature (T1/2) prediction using graph-based revised autocorrelations as features. We perform feature selection using random forest-ranked recursive feature addition (RF-RFA) to identify the features essential to model transferability. Of the ML models considered, the full feature set RF and recursive feature addition RF models perform best, achieving moderate correlation to experimental T1/2 values. We then compare ML T1/2 predictions to those from three previously identified best-performing density functional approximations (DFAs) which accurately predict SCO behavior across SCO-95, finding that the ML models predict T1/2 more accurately than the best-performing DFAs. In addition, we study ML model predictions for a set of 18 SCO complexes for which only estimated T1/2 values are available. Upon excluding outliers from this set, the RF-RFA RF model shows a strong correlation to estimated T1/2 values with a Pearson's r of 0.82. In contrast, DFA-predicted T1/2 values have large errors and show no correlation to estimated T1/2 values over the same set of complexes. Overall, our study demonstrates slightly superior performance of ML models in comparison with some of the best-performing DFAs, and we expect ML models to improve further as larger data sets of SCO complexes are curated and become available for model training.

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

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

Benchmarks for transition metal spin-state energetics: why and how to employ experimental reference data?

Accurate prediction of energy differences between alternative spin states of transition metal complexes is essential in computational (bio)inorganic chemistry-for example, in characterization of spin crossover materials and in the theoretical modeling of open-shell reaction mechanisms-but it remains one of the most compelling problems for quantum chemistry methods. A part of this challenge is to obtain reliable reference data for benchmark studies, as even the highest-level applicable methods are known to give divergent results. This Perspective discusses two possible approaches to method benchmarking for spin-state energetics: using either theoretically computed or experiment-derived reference data. With the focus on the latter approach, an extensive general review is provided for the available experimental data of spin-state energetics and their interpretations in the context of benchmark studies, targeting the possibility of back-correcting the vibrational effects and the influence of solvents or crystalline environments. With a growing amount of experience, these effects can be now not only qualitatively understood, but also quantitatively modeled, providing the way to derive nearly chemically accurate estimates of the electronic spin-state gaps to be used as benchmarks and advancing our understanding of the phenomena related to spin states in condensed phases.

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.

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.

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.

Insights into the nonlinear optical (NLO) response of pure Aum (2 ≥ m ≤ 7) and copper-doped Au m -xCu x clusters

A series of small pure Au m (2 ≥ m ≤ 7) and copper-doped Au m-x Cu x clusters was evaluated by density functional theory (DFT) at the CAM-B3LYP/LANL2DZ level for their geometric, electronic, and nonlinear optical (NLO) properties. The charge transfer for the Au cluster significantly improved by reducing the HOMO-LUMO energy gap from 3.67 eV to 0.91 eV after doping with Cu atoms. The doping of Cu also showed noteworthy impacts on other optical and NLO properties, including a decrease in the excitation energy and increase in the dipole moment and oscillator strength. Furthermore, changes in the linear isotropic and anisotropic polarizabilities (α iso and α aniso) and first and second NLO hyperpolarizabilities (β static, γ static) were also observed in the pure and Cu-doped clusters, which enhanced the NLO response. The nonlinear optical properties of the clusters were evaluated by calculating the static and frequency dependent second- and third-order NLO polarizabilities at 1064 nm wavelength. Among all the doped structures, the Au3Cu1 cluster showed the largest static first hyperpolarizability of β (total) = 4.73 × 103 au, while the Au1Cu6 cluster showed frequency dependent first hyperpolarizability of β (-2w;w,w) = 1.26 × 106 au. Besides this, large static and frequency-dependent second hyperpolarizability values of 6.30 × 105 au and 1.05 × 10 au were exhibited by Cu7 and Au1Cu6, respectively. This study offers an effective approach to design high-performance NLO materials utilizing mixed metal clusters which might have broad applications in the fields of optoelectronics and electronics.

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.

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.

CASPT2 molecular geometries of Fe(II) spin-crossover complexes

Using fully internally contracted (FIC)-CASPT2 analytical gradients, geometry optimizations of spin-crossover complexes are reported. This approach is tested on a series of Fe(II) complexes with different sizes, ranging from 13 to 61 atoms. A combination of active space and basis set choices are employed to investigate their role in determining reliable molecular geometries. The reported strategy demonstrates that a wave function-based level of theory can be used to optimize the geometries of metal complexes in reasonable times and enables one to treat the molecular geometry and electronic structure of the complexes using the same level of theory. For a series of smaller Fe(II) SCO complexes, strong field ligands in the LS state result in geometries with the largest differences between DFT and CASPT2; however, good agreement overall is observed between DFT and CASPT2. For the larger complexes, moderate sized basis sets yield geometries that compare well with DFT and available experimental data. We recommend using the (10e,12o) active space since convergence to a minimum structure was more efficient than with truncated active spaces despite having similar Fe-ligand bond distances.

Role of Magnetization on Catalytic Pathways of Non-Oxidative Methane Activation on Neutral Iron Carbide Clusters

Methane has emerged as a promising fuel due to its abundance and clean combustion properties. It is also a raw material for various value added chemicals. However, the conversion of...

Co(ii), Ni(ii), Cu(ii) and Cd(ii)-thiocarbonohydrazone complexes: spectroscopic, DFT, thermal, and electrical conductivity studies

New and stable coordinated compounds have been isolated in a good yield. The chelates have been prepared by mixing Co(ii), Ni(ii), Cu(ii), and Cd(ii) metal ions with (1E)-1-((6-methyl-4-oxo-4H-chromen-3-yl)methylene)thiocarbonohydrazide (MCMT) in 2 : 1 stoichiometry (MCMT : M²⁺). Various techniques, including elemental microanalyses, molar conductance, thermal studies, FT-IR, ¹H-NMR, UV-Vis, and XRD spectral analyses, magnetic moment measurements, and electrical conductivity, were applied for the structural and spectroscopic elucidation of the coordinating compounds. Further, computational studies using the DFT-B3LYP method were reported for MCMT and its metal complexes. MCMT behaves as a neutral NS bidentate moiety that forms octahedral complexes with general formula [M(MCMT)₂Cl(OH₂)]Cl·XH₂O (M = Cu²⁺; (X = ½), Ni²⁺, Co²⁺; (X = 1)); [Cd(MCMT)₂Cl₂]·½H₂O. There is good confirmation between experimental infrared spectral data and theoretical DFT-B3LYP computational outcomes where MCMT acts as a five-membered chelate bonded to the metal ion through azomethine nitrogen and thiocarbonyl sulphur donors. The thermal analysis is studied to confirm the elucidated structure of the complexes. Also, the kinetic and thermodynamic parameters of the thermal decomposition steps were evaluated. The measured optical band gap values of the prepared compounds exhibited semiconducting nature. AC conductivity and dielectric properties of the ligand and its complexes were examined, which showed that Cu(ii) complex has the highest dielectric constant referring to its high polarization and storage ability.

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.

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.

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.

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

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

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.

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

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

Copper (IV) Stabilization in Macrocyclic Complexes with 3,7,11,15-Tetraazaporphine, Its Di[benzo]- or Tetra[benzo] Derivatives and Oxide Anion: Quantum-Chemical Research

Using the data of a quantum chemical modeling of molecular structures obtained by the density functional theory (DFT), the possibility of the existence of a copper macrocyclic complexes with 3,7,11,15-tetraazaaporphine, trans-di[benzo] 3,7,11,15-tetraazaaporphine or tetra[benzo] 3,7,11,15-tetraazaaporphine and oxide anion where oxidation state of copper is IV, was shown. The values of the parameters of molecular structures and NBO analysis for such complexes were presented, too.

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.

Quantum-Chemical Design of Molecular Structures of Tetra-, Penta- and Hexanuclear Metal Clusters Containing Aluminum and 3d-Element Atoms

Various data on the structural and thermodynamic characteristics of polynuclear metal clusters containing atoms of aluminum and various d-elements with the general formula Al_nM_m where (n + m) is 4, 5, or 6, and which can be precursors for the formation of nanoparticles of elemental metals or intermetallic compounds, have been systematized and discussed. It has been noted that each of these metal clusters in principle is able to exist in very diverse structural isomers, differing significantly among themselves in terms of the total energy and spin multiplicity of the ground state, the number of which is determined by both the specific values of n and m, and the nature of d-elements in their compositions. The presence of very complex dynamics with respect to the changes of the individual thermodynamic characteristics of the metal clusters under consideration as well as the thermodynamic parameters of the reactions of their formation, depending on the nature of the d-element, were also ascertained. In the main, the given review is devoted to the authors’ works published over the last 10 years. Bibliography – 96 references.

M(VI) Oxidation State Stabilization in Iron, Cobalt and Nickel Heteroligand Metal Chelates Containing 3,7,11,15-Tetraazaporphine and Two Axial Oxo Ligands: Quantum-Chemical Simulation

The quantum-chemical calculation of iron, cobalt and nickel heteroligand complexes with the double deprotonated form of (NNNN)-donor atomic ligand—3,7,11,15-tetraazaporphine—and two oxo ligands has been carried out. Data on the structural and standard thermodynamic parameters, NBO analysis and multiplicity of the ground states of these complexes have been presented. The given calculation has been made by using the density functional theory (DFT) method with the OPBE/TZVP basis set. Based on the results of this calculation, the possibility of the existence of oxidation state VI for the chemical elements indicated above—unusual for iron and cobalt, and for nickel, unknown at all—has been shown.

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

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

Structural and Electronic Rearrangements in Fe2S2, Fe3S4, and Fe4S4 Atomic Clusters under the Attack of NO, CO, and O2

We report results, based on density functional theory-generalized gradient approximation calculations, that shed light on how NO, CO, and O₂ interact with Fe₂S₂, Fe₃S₄, and Fe₄S₄ clusters and how they modify their structural and electronic properties. The interest in these small iron sulfide clusters comes from the fact that they are at the protein cores and that elucidating fundamental aspects of their interaction with those light molecules which are known to modify their functionality may help in understanding complex behaviors in biological systems. CO and NO are found to bind molecularly, leading to moderate relaxations in the clusters, but nevertheless to changes in the spin-polarized electronic structure and related properties. In contrast, dissociative chemisorption of O₂ is much more stable than molecular adsorption, giving rise to significant structural distortions, particularly in Fe₄S₄ that splits into two Fe₂S₂ subclusters. As a consequence, oxygen tends to strongly reduce the spin polarization in Fe and to weaken the Fe-Fe interaction inducing antiparallel couplings that, in the case of Fe₄S₄, clearly arise from indirect Fe-Fe exchange coupling mediated by O. The three molecules (particularly CO) enhance the stability of the iron-sulfur clusters. This increase is noticeably more pronounced for Fe₂S₂ than for the other iron-sulfur clusters of different compositions, a result that correlates with the fact that in recent experiments of CO reaction with Fe_mS_m (m = 1-4), the Fe₂S₂CO product results as a prominent one.

Light-Induced Spin Crossover in an Intermediate-Spin Penta-Coordinated Iron(III) Complex

(PMe₃)₂FeCl₃ is an Fe(III) complex that exists in the intermediate-spin ground state in a distorted trigonal bipyramidal geometry. An electronic state with high-spin configuration lies in close vicinity to the ground state, making it a potential spin crossover candidate. A mechanistic account of the spin crossover from the lowest quartet state (Q₀) to the lowest sextet state (S₁) of this complex is provided by exploring both thermal and light-induced pathways. The presence of a large barrier between the two spin states suggests a possible thermal spin crossover at a rather high temperature. The light-induced spin crossover is investigated by employing complete active space self-consistent field calculations together with dynamic correlation and spin-orbit coupling for the lowest seven quartet and lowest five sextet states. The system in the Q₀ state upon light absorption is excited to the optically bright Q₄ LMCT state. By following minimum energy pathways along the electronic states, two light-induced pathways for spin crossover are identified. From the Q₄ state, the system can photo-regenerate the ground intermediate-spin state (Q₀) through an internal conversion of Q₄/Q₃ followed by Q₃/S₁ and S₁/Q₀ intersystem crossings. In an alternate route, through Q₄/S₂ intersystem crossing followed by S₂/S₁ internal conversion, the system can complete the spin crossover from the Q₀ to S₁ state.