New Benchmark Set of Transition-Metal Coordination Reactions for the Assessment of Density Functionals

Role of low-molecular-weight organic compounds on photochemical formation of Mn(III)-ligands in aqueous systems: Implications for BPA removal

Aqueous trivalent manganese [Mn(III)], an important reactive intermediate, is ubiquitous in natural surface water containing humic acid (HA). However, the effect of low-molecular-weight organic acids (LMWOAs) on the formation, stability and reactivity of Mn(III) intermediate is still unknown. In this study, six LMWOAs, including oxalic acid (Oxa), salicylic acid (Sal), catechol (Cat), caffeic acid (Caf), gallic acid (Gal) and ethylene diamine tetraacetic acid (EDTA), were selected to investigate the effects of LMWOAs on the degradation of BPA induced by in situ formed Mn(III)-L in the HA/Mn(II) system under light irradiation. The chromophoric constituents of HA could absorb light radiation and generate superoxide radical to promote the oxidation of Mn(II) to form Mn(III), which was further involved in transformation of BPA. Our results implied that different LMWOAs did significantly impact on Mn(III) production and its degradation of BPA due to their different functional group. EDTA, Oxa and Sal extensively increased the Mn(III) concentration from 50 to 100 μM compared to the system without LMWOAs, following the order of EDTA > Oxa > Sal, and also enhanced the degradation of BPA with the similar patterns. In contrast, Cat, Caf and Gal had an inhibitory effect on the formation of Mn(III), which is likely because they consumed the superoxide radicals generated from irradiated HA, resulting in the inhibition of Mn(II) oxidation and further BPA removal. The product identification and theoretical calculation indicated that a single electron transfer process occurred between Mn(III)-L and BPA, forming BPA radicals and subsequent self-coupling products. Our results demonstrated that the LMWOAs with different structures could alter the cycling process of Mn via complexation and redox reactions, which would provide new implications for the removal of organic pollutants in surface water.

Exploring Raloxifene-Based Metallodrugs: A Versatile Vector Combined with Platinum(II), Palladium(II) and Nickel(II) Dichlorides and Carborates against Triple-Negative Breast Cancer

Triple-negative breast cancer (TNBC) poses challenges in therapy due to the absence of target expression such as estrogen receptor (ER), progesterone receptor (PR), and human epidermal growth factor receptor 2 (HER2). Frequently, the treatment of TNBC involves the combination of several therapeutics. However, an enhanced therapeutic effect can be also achieved within a single molecule. The efficacy of raloxifene can be improved by designing a raloxifene-based hybrid drug bearing a 2,2'-bipyridine moiety (2). Integration of platinum(II), palladium(II), and nickel(II) complexes into this structure dramatically changed the cytotoxicity. The platinum(II) dichloride complex 3 did not demonstrate any activity, while palladium(II) and nickel(II) dichloride complexes 4 and 5 exhibited various cytotoxic behavior towards different types of hormone-receptor positive (HR+) cancer and TNBC cell lines. The replacement of the two chlorido ligands in 3-5 with a dicarbollide (carborate) ion [C2B9H11]2- resulted in reduced activity of compounds 6, 7, and 8. However, the palladacarborane complex 7 demonstrated higher selectivity towards TNBC. Furthermore, the mechanism of action was shifted from cytotoxic to explicitly cytostatic with detectable proliferation arrest and accelerated aging, characterized by senescence-associated phenotype of TNBC cells. This study provides valuable insights into the development of hybrid therapeutics against TNBC.

Photochemical H2 activation by an Zn-Fe heterometallic: a mechanistic investigation

Addition of H2 to a Zn-Fe complex was observed to occur under photochemical conditions (390 or 428 nm LED) and leads to the formation of a heterometallic dihydride complex. The reaction does not occur under thermal conditions and DFT calculations suggest this is an endergonic, light driven process. Through a combined experimental and computational approach, the plausible mechanisms for H2 activation were investigated. Inhibition experiments, double-label cross-over experiments, radical trapping experiments, EPR spectroscopy and DFT calculations were used to gain insight into this system. The combined data are consistent with two plausible mechanisms, the first involving ligand dissociation followed by oxidative addition of H2 at the Fe centre, the second involving homolytic fragmentation of the Zn-Fe heterometallic and formation of radical intermediates.

Early events in the mechanism of single-source chemical vapor deposition of zirconium and hafnium diboride: a computational investigation

Chemical vapor deposition (CVD) of group 4 metal-diboride ceramics from a single source is a versatile technique that finds many applications from hypersonic flight to microelectronics. Though the kinetics of CVD have been studied extensively-allowing significant process improvements-a mechanistic understanding of the process has yet to be attained. Computations suggest two plausible reaction pathways-one higher-energy and the second lower-that correlate well with experimental results reported in the literature, explaining phenomena such as high-temperature deposition resulting in films overstoichiometric in boron. These insights offer a new perspective that may be instrumental in the rational design of new precursors for single-source CVD.

M11pz: A Nonlocal Meta Functional with Zero Hartree-Fock Exchange and with Broad Accuracy for Chemical Energies and Structures

The accuracy of Kohn-Sham density functional theory depends strongly on the approximation to the exchange-correlation functional. In this work, we present a new exchange-correlation functional called M11pz (M11 plus rung-3.5 terms with zero Hartree-Fock exchange) that is built on the M11plus functional with the goal of using its rung-3.5 terms without a Hartree-Fock exchange term, especially to improve the accuracy for strongly correlated systems. The M11pz functional is optimized with the same local and rung-3.5 ingredients that are used in M11plus but without any percentage of Hartree-Fock exchange. The performance of M11pz is compared with eight local functionals, and M11pz is found to be in top three when the errors or ranks are averaged over eight grouped and partially overlapping databases: AME418/22, atomic and molecular energies; MGBE172, main-group bond energies; TMBE40, transition-metal bond energies; SR309, single-reference systems; MR54, multireference systems; BH192, barrier heights; NC579, noncovalent interaction energies; and MS20, molecular structures. For calculations of band gaps of solids, M11pz is the second best of the nine tested functionals that have zero Hartree-Fock exchange.

Applying Large Graph Neural Networks to Predict Transition Metal Complex Energies Using the tmQM_wB97MV Data Set

Machine learning (ML) methods have shown promise for discovering novel catalysts but are often restricted to specific chemical domains. Generalizable ML models require large and diverse training data sets, which exist for heterogeneous catalysis but not for homogeneous catalysis. The tmQM data set, which contains properties of 86,665 transition metal complexes calculated at the TPSSh/def2-SVP level of density functional theory (DFT), provided a promising training data set for homogeneous catalyst systems. However, we find that ML models trained on tmQM consistently underpredict the energies of a chemically distinct subset of the data. To address this, we present the tmQM_wB97MV data set, which filters out several structures in tmQM found to be missing hydrogens and recomputes the energies of all other structures at the ωB97M-V/def2-SVPD level of DFT. ML models trained on tmQM_wB97MV show no pattern of consistently incorrect predictions and much lower errors than those trained on tmQM. The ML models tested on tmQM_wB97MV were, from best to worst, GemNet-T > PaiNN ≈ SpinConv > SchNet. Performance consistently improves when using only neutral structures instead of the entire data set. However, while models saturate with only neutral structures, more data continue to improve the models when including charged species, indicating the importance of accurately capturing a range of oxidation states in future data generation and model development. Furthermore, a fine-tuning approach in which weights were initialized from models trained on OC20 led to drastic improvements in model performance, indicating transferability between ML strategies of heterogeneous and homogeneous systems.

Exploring the potential of tamoxifen-based copper(ii) dichloride in breast cancer therapy

For decades, tamoxifen-based hormone therapy has effectively addressed oestrogen receptor positive (ER+) luminal A breast cancer. Nonetheless, the emergence of tamoxifen resistance required innovative approaches, leading to hybrid metallodrugs with several therapeutic effects besides the inhibition of oestrogen receptor α (ERα). Drawing inspiration from tamoxifen metabolite structures (4-hydroxytamoxifen and 4,4'-dihyroxytamoxifen), a phenyl ring was replaced by a bidentate 2,2'-bipyridine donor moiety to give 4-[1,1-bis(4-methoxyphenyl)but-1-en-2-yl]-2,2'-bipyridine (L), enabling coordination of bioactive transition metal compounds such as copper(ii) dichloride, yielding [CuCl(μ-Cl)(L-κ2N,N')]2 (1). Notably, copper(ii) complex 1 exhibited remarkable activity within the low micromolar concentration range against ER+ human glioblastoma U251, as well as breast carcinomas MDA-MB-361 and MCF-7, surpassing the efficacy of previously reported palladium(ii) and platinum(ii) dichloride analogs against these cell lines. The pronounced efficacy of complex 1 against triple-negative MDA-MB-231 cells highlights its potential multitherapeutic approach, evident through induction of apoptosis and antioxidant activity. This study evaluates the potential of copper-tamoxifen hybrid complex 1 as a potent therapeutic candidate, highlighting its diverse mechanism of action against challenging breast cancer subtypes.

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

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

Comparing Density Functional Theory Metal-Ligand Bond Dissociation Enthalpies with Experimental Solution-Phase Enthalpies of Activation for Bond Dissociation

The predictive ability of density functional theory is fundamental to its usefulness in chemical applications. Recent work has compared solution-phase enthalpies of activation for metal-ligand bond dissociation to enthalpies of reaction for bond dissociation, and the present work continues those comparisons for 43 density functional methods. The results for ligand dissociation enthalpies of 30 metal-ligand complexes tested in this work reveal significant inadequacies of some functionals as well as challenges from the dispersion corrections to some functionals. The analysis presented here demonstrates the excellent performance of a recent density functional, M11plus, which contains nonlocal rung-3.5 correlation. We also find a good agreement between theory and experiment for some functionals without empirical dispersion corrections such as M06, r2SCAN, M06-L, and revM11, as well as good performance for some functionals with added dispersion corrections such as ωB97X-D (which always has a correction) and BLYP, B3LYP, CAM-B3LYP, and PBE0 when the optional dispersion corrections are added.

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.

Automatic Generation of Auxiliary Basis Sets in Spherical Representation Using the Cholesky Decomposition

Density fitting techniques that use automatically generated auxiliary basis sets generally rely on the formation of basis function products. Recently, Lehtola [ J. Chem. Theory Comput. 2021, 17, 6886-6900] presented a procedure making use of a purely spherical representation by adding auxiliary basis functions coupled to the required angular momentum quantum numbers for the product of spherical harmonics and then removing linear dependencies by means of a Cholesky decomposition. In this work, we extend this idea by making use of the explicit equations for the product of two spherical harmonics in the angular part of the basis function product. Some of the resulting terms are not directly accessible when popular standard integral libraries are used, which could prevent the widespread use of the exact product form. For these terms, we introduce four approximations of increasing sophistication that require integrals involving only standard Gaussian-type orbitals and thus can be computed with standard libraries. We assess the accuracy of the different schemes in the context of the aCD for the reconstruction of the electron repulsion integral matrix and absolute and relative single point energies and in the framework of optimally tuned range-separated hybrid functionals.

On the Prediction of Spectroscopic Fingerprints of Co2+ Complexes Relevant for the ZIF Nucleation Process

The nucleation process of zeolitic imidazolate frameworks (ZIFs) is to date not completely understood. Recently, it has been found that, during the formation of Co-ZIF-67, after mixing imidazole-type ligands with octahedral precursors containing oxygen-coordinated ligands, a metal-organic pool with a diversity of transition metal complexes (TMCs) is formed showing fingerprints of octahedral and tetrahedral Co2+ complexes with both types of ligands [Filez, M. Cell Rep. Phys. Sci. 2021, 2, 100680]. In order to further unravel this process, we aim to characterize the d-d transitions of the TMCs and focus on their number, intensity, and position, which change during the process and can thus serve as a fingerprint for the formed species. It was previously shown that the number of ligands and symmetry has a detrimental influence on the ground state properties of Co2+ TMCs. Herein, we investigate how far excited state properties of TMCs relevant during nanoporous formation processes can be predicted by time-dependent density functional theory (TDDFT) and ligand field density functional theory (LFDFT). As TMCs are known to be challenging systems with possibly degenerate ground states and double excitations, we first investigate the performance of both techniques on first-row octahedral aqua-complexes. With this knowledge, we then focus on tetrahedral Co2+ complexes with aqua and imidazole-type ligands in order to investigate in how far we can propose a spectroscopic fingerprint that allows us to follow the Co2+ complexes during the formation of Co-ZIF-67. The results of TDDFT and LFDFT are qualitatively in agreement and provide complementary information. We found that various features can be used to distinguish between the species. However, as LFDFT is not suited for TMCs possessing the extended imidazole-type ligands and double and spin-flip states are not included in TDDFT, both techniques need to be complemented with more advanced methods to obtain complete insight into the d-d excitations of TMCs with imidazole ligands. Therefore, we particularly explored ab initio ligand field theory, which is capable of describing double excitations and is, in contrast to LFDFT, suitable for TMCs with extended ligands.

Modular Synthesis of Phosphino Hydrazones and Their Use as Ligands in a Palladium-Catalysed Cu-Free Sonogashira Cross-Coupling Reaction

Phosphino hydrazones represent a versatile class of nitrogen-containing phosphine ligands. Herein, we report a modular synthesis of phosphino hydrazone ligands by hydrazone condensation reaction of three different aryl hydrazines with 3-(diphenylphosphino)propanal (PCHO). Complexation reactions of these phosphino hydrazone ligands with palladium(II) and platinum(II) were investigated and the catalytic activity of the palladium(II) complexes was explored in a Cu-free Sonogashira cross-coupling reaction achieving yields up to 96 %. Additionally it was shown that the catalytically active species is homogeneous.

Density Functional Theory-Based Protocol to Calculate the Redox Potentials of First-row Transition Metal Complexes for Aqueous Redox Targeting Flow Batteries

Transition metal complexes are a promising class of redox mediators for targeting redox flow batteries due to the tunability of their electrochemical potentials. However, reliable time-efficient tools for the prediction of their reduction potentials are needed. In this work, we establish a suitable density functional theory protocol for their prediction using an initial experimental data set of aqueous iron complexes with bidentate ligands. The approach is then cross-validated using different complexes found in the redox-flow literature. We find that the solvation model affects the prediction accuracy more than the functional or basis set. The smallest errors are obtained using the COSMO-RS solvation model (mean average error (MAE)=0.24 V). With implicit solvation models, a general deviation from experimental results is observed. For a set of similar ligands, they can be corrected using simple linear regression (MAE=0.051 V for the initial set of iron complexes).

Insights into the coordination chemistry of antineoplastic doxorubicin with 3d-transition metal ions Zn2+, Cu2+, and VO2+: a study using well-calibrated thermodynamic cycles and chemical interaction quantum chemistry models

We present a computational strategy based on thermodynamic cycles to predict and describe the chemical equilibrium between the 3d-transition metal ions Zn²⁺, Cu²⁺, and VO²⁺ and the widely used antineoplastic drug doxorubicin. Our method involves benchmarking a theoretical protocol to compute gas-phase quantities using DLPNO Coupled-Cluster calculations as reference, followed by estimating solvation contributions to the reaction Gibbs free energies using both explicit partial (micro)solvation steps for charged solutes and neutral coordination complexes, as well as a continuum solvation procedure for all solutes involved in the complexation process. We rationalized the stability of these doxorubicin-metal complexes by inspecting quantities obtained from the topology of their electron densities, particularly the bond critical points and non-covalent interaction index. Our approach allowed us to identify representative species in solution phase, infer the most likely complexation process for each case, and identify key intramolecular interactions involved in the stability of these compounds. To the best of our knowledge, this is the first study reporting thermodynamic constants for the complexation of doxorubicin with transition metal ions. Unlike other methods, our procedure is computationally affordable for medium-sized systems and provides valuable insights even with limited experimental data. Furthermore, it can be extended to describe the complexation process between 3d-transition metal ions and other bioactive ligands.

Metallodrugs against Breast Cancer: Combining the Tamoxifen Vector with Platinum(II) and Palladium(II) Complexes

The luminal A-subtype of breast cancer, where the oestrogen receptor α (ERα) is overexpressed, is the most frequent one. The prodrug tamoxifen (1) is the clinically used agent, inhibiting the ERα activity via the formation of several active metabolites, such as 4-hydroxytamoxifen (2) or 4,4'-dihydroxytamoxifen (3). In this study, we present the tamoxifen derivative 4-[1,1-bis(4-methoxyphenyl)but-1-en-2-yl]-2,2'-bipyridine (4), which was combined with platinum or palladium dichloride, the former a well-known scaffold in anticancer treatment, to give [PtCl₂(4-κ²N,N')] (5) or [PdCl₂(4-κ²N,N'] (6). To prevent fast exchange of weakly coordinating chlorido ligands in aqueous solution, a bulky, highly stable and hydrophobic nido-carborate(-2) ([C₂B₉H₁₁]^2-) was incorporated. The resulting complexes [3-(4-κ²N,N')-3,1,2-PtC₂B₉H₁₁] (7) and [3-(4-κ²N,N')-3,1,2-PdC₂B₉H₁₁] (8) exhibit a dramatic change in electronic and biological properties compared to 5 and 6. Thus, 8 is highly selective for triple-negative MDA-MB-231 cells (IC₅₀ = 3.7 μM, MTT test), while 7 is completely inactive against this cell line. The observed cytotoxicity of compounds 4-6 and 8 against this triple-negative cell line suggests off-target mechanisms rather than only ERα inhibition, for which these compounds were originally designed. Spectroscopic properties and electronic structures of the metal complexes were investigated for possible explanations of the biological activities.

On the accuracy of orbital based multi-level approaches for closed-shell transition metal chemistry

In this work, we investigate the accuracy of the local molecular orbital molecular orbital (LMOMO) scheme and projection-based wave function-in-density functional theory (WF-in-DFT) embedding for the prediction of reaction energies and barriers of typical reactions involving transition metals. To analyze the dependence of the accuracy on the system partitioning, we apply a manual orbital selection for LMOMO as well as the so-called direct orbital selection (DOS) for both approaches. We benchmark these methods on 30 closed shell reactions involving 16 different transition metals. This allows us to devise guidelines for the manual selection as well as settings for the DOS that provide accurate results within an error of 2 kcal mol^-1 compared to local coupled cluster. To reach this accuracy, on average 55% of the occupied orbitals have to be correlated with coupled cluster for the current test set. Furthermore, we find that LMOMO gives more reliable relative energies for small embedded regions than WF-in-DFT embedding.

PtOx Cly (OH)z (H2 O)n Complexes under Oxidative and Reductive Conditions: Impact of the Level of Theory on Thermodynamic Stabilities

Platinum-based catalysts with Cl^- , OH^- , O^2- and H₂ O ligands, are involved in many industrial processes. Their final chemical properties are impacted by calcination and reduction applied during the preparation and activation steps. We investigate their stability under these reactive conditions with density functional theory (DFT). We benchmark various functionals (PBE-dDsC, optPBE, B3LYP, HSE06, PBE0, TPSS, RTPSS and SCAN) against ACFDT-RPA. PBE-dDsC is well adapted, although hybrid functionals are more accurate for redox reactions. Thermodynamic phase diagrams are determined by computing the chemical potential of the species as a function of temperature and partial pressures of H₂ O, HCl, O₂ and H₂ . The stability and nature of the Pt species are highly sensitive to the activation conditions. Under O₂ , high temperatures favour PtO₂ while under H₂ , platinum is easily reduced to Pt(0). Chlorine modifies the coordination sphere of platinum during calcination by stabilizing PtCl₄ and shifts the reduction of platinum to higher temperatures under H₂ .

Redox-active ligands as a challenge for electronic structure methods

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

Excellent removal performance of 4,4'-biphenyldicarboxaldehyde m-phenylenediamine Schiff base magnetic polymer towards phenanthrene and 9-phenanthrol: Experimental, modeling and DFT calculations studies

Phenanthrene (PTH) and 9-phenanthrol (9-PTH) exhibited severe health threats and ecological hazards, for this reason, exploring a high-efficient removing strategy for PTH and 9-PTH could be considered of great urgency. Herein the 4,4'-biphenyldicarboxaldehyde m-phenylenediamine Schiff base magnetic polymer (magnetic BIPH-PHEN) was successfully fabricated via Schiff base polycondensation reaction and the subsequently one-pot embedded method. The mutual aromatic nucleus of BIPH-PHEN polymer and PTH/9-PTH could form π-π interaction, thus improving the capture ability, the embedded Fe₃O₄ nanoparticles provided the possibility for rapid separation. The physical and chemical properties of the magnetic BIPH-PHEN were systematically characterized. The removal rate of magnetic BIPH-PHEN towards PTH and 9-PTH was 85.65 % and 98.52 %, respectively (PTH or 9-PTH: 8 mg/L; Adsorbent: 0.2 g/L). The DFT calculations including energy calculations and electrostatic potential distribution analyzed the different bonding modes and proposed the most possible bonding modes in the adsorbent/adsorbate system. Moreover, the LUMO and HOMO orbits combined with energy gaps analysis proved the existence and specific types of the π-π interaction. The monolayer adsorption occurred on the homogeneous magnetic BIPH-PHEN surface, simultaneously the chemisorption was dominant. This work not only proposed new sights on assembling magnetic Schiff base polymer for removing polycyclic aromatic hydrocarbons, but also provided a deeper understanding of intramolecular interactions.

Mechanistic views and computational studies on transition-metal-catalyzed reductive coupling reactions

Transition-metal-catalyzed reductive coupling reactions have been considered as a powerful tool to convert two electrophiles into value-added products. Numerous related reports have shown the fascinating potential. Mechanistic studies, especially theoretical studies, can provide important implications for the design of novel reductive coupling reactions. In this review, we summarize the representative advancements in theoretical studies on transition-metal-catalyzed reductive coupling reactions and systematically elaborate the mechanisms for the key steps of reductive coupling reactions. The activation modes of electrophiles and the deep insights of selectivity generation are mechanistically discussed. In addition, the mechanism of the reduction of high-oxidation-state catalysts and further construction of new chemical bonds are also described in detail.

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

Encapsulation Enhances the Catalytic Activity of C-N Coupling: Reaction Mechanism of a Cu(I)/Calix[8]arene Supramolecular Catalyst

Development of C-N coupling methodologies based on Earth-abundant metals is a promising strategy in homogeneous catalysis for sustainable processes. However, such systems suffer from deactivation and low catalytic activity. We here report that encapsulation of Cu(I) within the phenanthroyl-containing calix[8]arene derivative 1,5-(2,9-dimethyl-1,10-phenanthroyl)-2,3,4,6,7,8-hexamethyl-p-tert-butylcalix[8]arene (C8PhenMe6 ) significantly enhances C-N coupling activity up to 92 % yield in the reaction of aryl halides and aryl amines, with low catalyst loadings (2.5 % mol). A tailored multiscale computational protocol based on Molecular Dynamics simulations and DFT investigations revealed an oxidative addition/reductive elimination process of the supramolecular catalyst [Cu(C8PhenMe6)I]. The computational investigations uncovered the origins of the enhanced catalytic activity over its molecular analogues: Catalyst deactivation through dimerization is prevented, and product release facilitated. Capturing the dynamic profile of the macrocycle and the impact of non-covalent interactions on reactivity allows for the rationalization of the behavior of the flexible supramolecular catalysts employed.

Three-Electron Nickel(I)/Nickel(0) Half-Bond

An (N-heterocyclic carbene)nickel(I) cation precursor reacts with the corresponding nickel(0) complex to form a dinickel(I,0) monocation. The Ni···Ni distance in this cation is 0.93 Å shorter than in the analogous dinickel(0) complex. Although the solid-state structure shows equivalent Ni centers, density functional theory calculations indicate significant electronic localization. Reactions with CO and NO form mononuclear carbonyl and nitrosyl complexes. Oxidative addition of an aryl bromide results in C-arylation of the carbene ligands.

Metal-organic frameworks as O2-selective adsorbents for air separations

Oxygen is a critical gas in numerous industries and is produced globally on a gigatonne scale, primarily through energy-intensive cryogenic distillation of air. The realization of large-scale adsorption-based air separations could enable a significant reduction in associated worldwide energy consumption and would constitute an important component of broader efforts to combat climate change. Certain small-scale air separations are carried out using N2-selective adsorbents, although the low capacities, poor selectivities, and high regeneration energies associated with these materials limit the extent of their usage. In contrast, the realization of O2-selective adsorbents may facilitate more widespread adoption of adsorptive air separations, which could enable the decentralization of O2 production and utilization and advance new uses for O2. Here, we present a detailed evaluation of the potential of metal-organic frameworks (MOFs) to serve as O2-selective adsorbents for air separations. Drawing insights from biological and molecular systems that selectively bind O2, we survey the field of O2-selective MOFs, highlighting progress and identifying promising areas for future exploration. As a guide for further research, the importance of moving beyond the traditional evaluation of O2 adsorption enthalpy, ΔH, is emphasized, and the free energy of O2 adsorption, ΔG, is discussed as the key metric for understanding and predicting MOF performance under practical conditions. Based on a proof-of-concept assessment of O2 binding carried out for eight different MOFs using experimentally derived capacities and thermodynamic parameters, we identify two existing materials and one proposed framework with nearly optimal ΔG values for operation under user-defined conditions. While enhancements are still needed in other material properties, the insights from the assessments herein serve as a guide for future materials design and evaluation. Computational approaches based on density functional theory with periodic boundary conditions are also discussed as complementary to experimental efforts, and new predictions enable identification of additional promising MOF systems for investigation.

Orbital Pair Selection for Relative Energies in the Domain-Based Local Pair Natural Orbital Coupled-Cluster Method

For the accurate computation of relative energies, domain-based local pair natural orbital coupled-cluster [DLPNO-CCSD(T0)] has become increasingly popular. Even though DLPNO-CCSD(T0) shows a formally linear scaling of the computational effort with the system size, accurate predictions of relative energies remain costly. Therefore, multi-level approaches are attractive that focus the available computational resources on a minor part of the molecular system, e.g., a reaction center, where changes in the correlation energy are expected to be the largest. We present a pair-selected multi-level DLPNO-CCSD(T0) ansatz that automatically partitions the orbital pairs according to their contribution to the overall correlation energy change in a chemical reaction. To this end, the localized orbitals are mapped between structures in the reaction; all pair energies are approximated through computationally efficient semi-canonical second-order Møller--Plesser perturbation theory, and the orbital pairs for which the pair energies change significantly are identified. This multi-level approach is significantly more robust than our previously suggested, orbital selection-based multi-level DLPNO-CCSD(T0) ansatz [ J. Chem. Phys. 2021, 155, 224102] for reactions showing only small changes in the occupied orbitals. At the same time, it is even more efficient without added input complexity or accuracy loss compared to the full DLPNO-CCSD(T0) calculation. We demonstrate the accuracy of the multi-level approach for a total of 128 chemical reactions and potential energy curves of weakly interacting complexes from the S66x8 benchmark set.

The transferability limits of static benchmarks

Every practical method to solve the Schrödinger equation for interacting many-particle systems introduces approximations. Such methods are therefore plagued by systematic errors. For computational chemistry, it is decisive to quantify the specific error for some system under consideration. Traditionally, the primary way for such an error assessment has been benchmarking data, usually taken from the literature. However, their transferability to a specific molecular system, and hence, the reliability of the traditional approach always remains uncertain to some degree. In this communication, we elaborate on the shortcomings of this traditional way of static benchmarking by exploiting statistical analyses using one of the largest quantum chemical benchmark sets available. We demonstrate the uncertainty of error estimates in the light of the choice of reference data selected for a benchmark study. To alleviate the issues with static benchmarks, we advocate to rely instead on a rolling and system-focused approach for rigorously quantifying the uncertainty of a quantum chemical result.

Since the errors of quantum chemical methods can strongly vary across chemical space, the transferability of traditional benchmarks is limited. This can be overcome by quantifying the uncertainty of quantum chemical results in a system-focused way.

Low-energy electron interaction and focused electron beam-induced deposition of molybdenum hexacarbonyl (Mo(CO)6)

Motivated by the potential role of molybdenum in semiconductor materials, we present a combined theoretical and experimental gas-phase study on dissociative electron attachment (DEA) and dissociative ionization (DI) of Mo(CO)₆ in comparison to focused electron beam-induced deposition (FEBID) of this precursor. The DEA and DI experiments are compared to previous work, differences are addressed, and the nature of the underlying resonances leading to the observed DEA processes are discussed in relation to an earlier electron transmission study. Relative contributions of individual ionic species obtained through DEA and DI of Mo(CO)₆ and the average CO loss per incident are calculated and compared to the composition of the FEBID deposits produced. These are also compared to gas phase, surface science and deposition studies on W(CO)₆ and we hypothesize that reductive ligand loss through electron attachment may promote metal-metal bond formation in the deposition process, leading to further ligand loss and the high metal content observed in FEBID for both these compounds.

New perspectives on the laser initiation for metal tetrazine complexes: a theoretical study

In order to understand the relationship between laser initiation and charge transfer of metal tetrazine complexes (MTCs), several sets of MTCs with different metals and ligands were designed and their charge transfer (CT) characters were examined using a time-dependent density functional theory method (TD-DFT) in combination with UV-vis spectra, hole-electron distribution, interfragment charge transition, and transition density matrix analyses. Results show that Fe(II), Mn(II), and Cu(II) are suitable divalent transition metal cores in constructing the optical initiation tetrazine complexes. By replacing the divalent metal cores with a monovalent center, new sets of complexes are proved to possess metal-to-ligand charge transfer (MLCT) character and stronger absorption intensity in the near-infrared (NIR) region, which implies that monovalent MTCs are more in favor of low-energy laser initiation than divalent MTCs. Reasonable tuning of the structure of pyrazole substituent can expect to enhance the explosive performance while preserving the optical characteristics, which is an important design principle. This work thoroughly depicts the photoactive states for MTCs and gives a train of thought to explore new desirable laser initiation explosives.

Direct orbital selection within the domain-based local pair natural orbital coupled-cluster method

Domain-based local pair natural orbital coupled cluster (DLPNO-CC) has become increasingly popular to calculate relative energies (e.g., reaction energies and reaction barriers). It can be applied within a multi-level DLPNO-CC-in-DLPNO-CC ansatz to reduce the computational cost and focus the available computational resources on a specific subset of the occupied orbitals. We demonstrate how this multi-level DLPNO-CC ansatz can be combined with our direct orbital selection (DOS) approach [M. Bensberg and J. Neugebauer, J. Chem. Phys. 150, 214106 (2019)] to automatically select orbital sets for any multi-level calculation. We find that the parameters for the DOS procedure can be chosen conservatively such that they are transferable between reactions. The resulting automatic multi-level DLPNO-CC method requires no user input and is extremely robust and accurate. The computational cost is easily reduced by a factor of 3 without sacrificing accuracy. We demonstrate the accuracy of the method for a total of 61 reactions containing up to 174 atoms and use it to predict the relative stability of conformers of a Ru-based catalyst.

Assessing Density Functional Theory for Chemically Relevant Open-Shell Transition Metal Reactions

Due to the principle lack of systematic improvement possibilities of density functional theory, careful assessment of the performance of density functional approximations (DFAs) on well-designed benchmark sets, for example, for reaction energies and barrier heights, is crucial. While main-group chemistry is well covered by several available sets, benchmark data for transition metal chemistry is sparse. This is especially the case for larger, chemically relevant molecules. Addressing this issue, we recently introduced the MOR41 benchmark which covers chemically relevant reactions of closed-shell complexes. In this work, we extend these efforts to single-reference open-shell systems and introduce the "reactions of open-shell single-reference transition metal complexes" (ROST61) benchmark set. ROST61 includes accurate coupled-cluster reference values for 61 reaction energies with a mean reaction energy of -42.8 kcal mol^-1. Complexes with 13-93 atoms covering 20 d-block elements are included, but due to the restriction to single-reference open-shell systems, important elements such as iron or platinum could not be taken into account, or only to a small extent. We assess the performance of 31 DFAs in combination with three London dispersion (LD) correction schemes. Further, DFT-based composite methods, MP2, and a few semiempirical quantum chemical methods are evaluated. Consistent with the results for the MOR41 closed-shell benchmark, we find that the ordering of DFAs according to Jacob's ladder is preserved and that adding an LD correction is crucial, clearly improving almost all tested methods. The recently introduced r²SCAN-3c composite method stands out with a remarkable mean absolute deviation (MAD) of only 2.9 kcal mol^-1, which is surpassed only by hybrid DFAs with low amounts of Fock exchange (e.g., 2.3 kcal mol^-1 for TPSS0-D4/def2-QZVPP) and double-hybrid (DH) DFAs but at a significantly higher computational cost. The lowest MAD of only 1.6 kcal mol^-1 is obtained with the DH DFA PWPB95-D4 in the def2-QZVPP basis set approaching the estimated accuracy of the reference method. Overall, the ROST61 set adds important reference data to a sparsely sampled but practically relevant area of chemistry. At this point, it provides valuable orientation for the application and development of new DFAs and electronic structure methods in general.

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.

Palladium Goes First: A Neutral Asymmetric Heteroditopic N,P Ligand Forming Pd-3d Heterobimetallic Complexes

A facile two-step synthesis of bis(1-methylhydrazinyl)pyrimidine from pyridine-2-carbaldehyde and 2-diphenylphosphanylbenzaldehyde gave access to the new asymmetric ligand 1. The phosphane selectively guides Pd^II into the softer tridentate N,N,P pocket, yielding monometallic complex 2. A second reaction with a 3d transition metal complex precursor (groups 7 to 12) fills the vacant N,N,N pocket and thus provides a variety of heterobimetallic complexes of the type Pd^II/M^II (M = Mn (3), Fe (4), Co (5), Ni (6), Cu (7), Zn (8)). Single-crystal X-ray diffraction studies were performed for all complexes. The assembly of μ₂-chlorido-bridged dimers was observed for complexes 5-7 in the solid state, while DOSY NMR experiments have shown that 5-7 are unbridged monomers in solution. As an exception, Fe^II prefers to form the homoleptic meridional complex [Fe{PdCl(1)}₂](OTf)₄ (4). The electrochemical behavior and the effective magnetic moment in solution were investigated for all complexes by cyclic voltammetry and Evans method, respectively. Experimental UV/vis results were interpreted by performing TD-DFT calculations on 1, 2, and 3.

Multiwavelets applied to metal-ligand interactions: Energies free from basis set errors

Transition metal-catalyzed reactions invariably include steps where ligands associate or dissociate. In order to obtain reliable energies for such reactions, sufficiently large basis sets need to be employed. In this paper, we have used high-precision multiwavelet calculations to compute the metal-ligand association energies for 27 transition metal complexes with common ligands, such as H₂, CO, olefins, and solvent molecules. By comparing our multiwavelet results to a variety of frequently used Gaussian-type basis sets, we show that counterpoise corrections, which are widely employed to correct for basis set superposition errors, often lead to underbinding. Additionally, counterpoise corrections are difficult to employ when the association step also involves a chemical transformation. Multiwavelets, which can be conveniently applied to all types of reactions, provide a promising alternative for computing electronic interaction energies free from any basis set errors.

Stereoselective Synthesis of Cyclohepta[b]indoles by Visible-Light-Induced [2+2]-Cycloaddition/retro-Mannich-type Reactions

A novel method for the concise synthesis of cyclohepta[b]indoles in high yields was developed. The method involves a visible-light-induced, photocatalyzed [2+2]-cycloaddition/ retro-Mannich-type reaction of enaminones. Experimental and computational studies suggested that the reaction is a photoredox process initiated by single-electron oxidation of an enaminone moiety, which undergoes subsequent cyclobutane formation and rapidly fragmentation in a radical-cation state to form cyclohepta[b]indoles.

Modeling Gas-Phase Unimolecular Dissociation for Bond Dissociation Energies: Comparison of Statistical Rate Models within RRKM Theory

The Rice-Ramsperger-Kassel-Marcus (RRKM) theory provides a simple yet powerful rate theory for calculating microcanonical rate constants. In particular, it has found widespread use in combination with gas-phase kinetic experiments of unimolecular dissociations to extract experimental bond dissociation energies (BDEs). We have previously found several discrepancies between the computed BDE values and the respective experimental ones, obtained with our empirical rate model, named L-CID. To investigate the reliability of our rate model, we conducted a theoretical analysis and comparison of the performance of conventional rate models and L-CID within the RRKM framework. Using the previously published microcanonical rate data as well as reaction cross-section data, we show that the BDE values obtained with the L-CID model agree with the ones from the other rate models within the expected uncertainty bounds. Based on this agreement, we discuss the possible rationalization of the good performance of the L-CID model.

A 2,2'-diphosphinotolane as a versatile precursor for the synthesis of P-ylidic mesoionic carbenes via reversible C-P bond formation

A metal-templated synthetic route to cyclic (aryl)(ylidic) mesoionic carbenes (CArY-MICs) featuring an endocyclic P-ylide is presented. This approach, which requires metal templates with two cis-positioned open coordination sites, is based on the controlled cyclisation of a P,P'-diisopropyl-substituted 2,2'-diphosphinotolane (1) and leads to chelate complexes coordinated by a phosphine donor and the CArY-MIC carbon atom. The C-P bond formation involved in the former partial cyclisation of 1 proceeds under mild conditions and was shown to be applicable all over the d-block. In the presence of a third fac-positioned open coordination site, the P-C bond formation was found to be reversible, as shown for a series of molybdenum complexes. DFT modelling studies are in line with an interpretation of the target compounds as CArY-MICs.

Mechanistic investigations via DFT support the cooperative heterobimetallic C-H and O-H bond activation across Ta[double bond, length as m-dash]Ir multiple bonds

A rare heterobimetallic oxidative addition of X-H (X = C, O) bonds is reported. DFT suggests that steric constraints around the bimetallic core play a critical role to synergistically activate C-H bonds across the two metals and thus explains the exceptional H/D exchange catalytic activity of unhindered surface organometallic Ta/Ir species observed experimentally.

Theoretical study on conformational energies of transition metal complexes

Conformational energies are an important chemical property for which a performance assessment of theoretical methods is mandatory. Existing benchmark sets are often limited to biochemical or main group element containing molecules, while organometallic systems are generally less studied. A key problem herein is to routinely generate conformers for these molecules due to their complexity and manifold of possible coordination patterns. In this study we used our recently published CREST protocol [Pracht et al., Phys. Chem. Chem. Phys., 2020, 22, 7169-7192] to generate conformer ensembles for a variety of 40 challenging transition metal containing molecules, which were then used to form a comprehensive conformational energy benchmark set termed TMCONF40. Several low-cost semiempirical, density functional theory (DFT) and force-field methods were compared to high level DLPNO-CCSD(T1) and double-hybrid DFT reference values. Close attention was paid to the energetic ordering of the conformers in the statistical evaluation. With respect to the double-hybrid references, both tested low-cost composite DFT methods produce high Pearson correlation coefficients of rp,mean,B97-3c//B97-3c = 0.922 and rp,mean,PBEh-3c//B97-3c = 0.890, with mean absolute deviations close to or below 1 kcal mol-1. This good performance also holds for a comparison to DLPNO-CCSD(T1) reference energies for a smaller subset termed TMCONF5. Based on DFT geometries, the GFNn-xTB methods yield reasonable Pearson correlation coefficients of rp,mean,GFN1-xTB//B97-3c = 0.617 (MADmean = 2.15 kcal mol-1) and rp,mean,GFN2-xTB//B97-3c = 0.567 (MADmean = 2.68 kcal mol-1), outperforming the widely used PMx methods on the TMCONF40 test set. Employing the low-cost composite DFT method B97-3c on GFN2-xTB geometries yields an slightly improved correlation of rp,mean,B97-3c//GFN2-xTB = 0.632. Furthermore, for 68% of the investigated complexes at least one low-energy conformer was found that is more stable than the respective crystal structure conformation, which signals the importance of conformational studies. General recommendations for the application of the CREST protocol and DFT methods for transition metal conformational energies are given.

First-Principles Calculations on Ni,Fe-Containing Carbon Monoxide Dehydrogenases Reveal Key Stereoelectronic Features for Binding and Release of CO2 to/from the C-Cluster

In view of the depletion of fossil fuel reserves and climatic effects of greenhouse gas emissions, Ni,Fe-containing carbon monoxide dehydrogenase (Ni-CODH) enzymes have attracted increasing interest in recent years for their capability to selectively catalyze the reversible reduction of CO₂ to CO (CO₂ + 2H⁺ + 2e^– CO + H₂O). The possibility of converting the greenhouse gas CO₂ into useful materials that can be used as synthetic building blocks or, remarkably, as carbon fuels makes Ni-CODH a very promising target for reverse-engineering studies. In this context, in order to provide insights into the chemical principles underlying the biological catalysis of CO₂ activation and reduction, quantum mechanics calculations have been carried out in the framework of density functional theory (DFT) on different-sized models of the Ni-CODH active site. With the aim of uncovering which stereoelectronic properties of the active site (known as the C-cluster) are crucial for the efficient binding and release of CO₂, different coordination modes of CO₂ to different forms and redox states of the C-cluster have been investigated. The results obtained from this study highlight the key role of the protein environment in tuning the reactivity and the geometry of the C-cluster. In particular, the protonation state of His93 is found to be crucial for promoting the binding or the dissociation of CO₂. The oxidation state of the C-cluster is also shown to be critical. CO₂ binds to C_red2 according to a dissociative mechanism (i.e., CO₂ binds to the C-cluster after the release of possible ligands from Fe_u) when His93 is doubly protonated. CO₂ can also bind noncatalytically to C_red1 according to an associative mechanism (i.e., CO₂ binding is preceded by the binding of H₂O to Fe_u). Conversely, CO₂ dissociates when His93 is singly protonated and the C-cluster is oxidized at least to the C_int redox state.

Density functional theory was used to investigate Ni,Fe-containing carbon monoxide dehydrogenase enzymes. Different coordination modes of the substrate CO₂ to several forms and redox states of the C-cluster—the enzyme active site—were considered. The obtained results highlight the key role of the protein environment in tuning the reactivity and the geometry of the C-cluster. This helps to uncover which stereoelectronic properties of the active site are crucial for the efficient binding and release of CO₂.