Theoretical study on conformational energies of transition metal complexes

An influence of electronic structure theory method, thermodynamic and implicit solvation corrections on the organic carbonates conformational and binding energies

An impact of an electronic structure or force field method, gas-phase thermodynamic correction, and continuum solvation model on organic carbonate clusters (S)n conformational and binding energies is explored. None of the tested force field (GFN-FF, GAFF, MMFF94) and standard semiempirical methods (PM3, AM1, RM1, PM6, PM6-D3, PM6-D3H4, PM7) can reproduce reference RI-SCS-MP2 conformational energies. Tight-binding GFNn-xTB methods provide more realistic conformational energies which are accurate enough to discard the least stable conformers. The effect of thermodynamic correction is moderate and can be ignored if the gas phase conformational stability ranking is a goal. The influence of continuum solvation is stronger, especially if reinforced with the Gibbs free energy thermodynamic correction, and results in the reduced spread of conformational energies. The cluster formation binding energies strongly depend on a particular approach to vibrational thermochemistry with the difference between traditional harmonic and modified scaled rigid - harmonic oscillator approximations reaching 10 kcal mol-1.

Phase-dependent polymerization isomerism in the coordination complexes of a flexible bis(β-diketonato) ligand

First prepared in the late 70s, the pro-ligand 1,3-bis(3,5-dioxo-1-hexyl)benzene (H2bdhb) contains two acetoacetyl terminations linked to a central 1,3-phenylene unit through dimethylene bridges. Since each termination can be either in diketonic or keto-enolic form, in organic solution it exists as a mixture of three spectroscopically resolvable tautomers. In the presence of pyridine, Co2+ and the bdhb2- anion form a crystalline dimeric compound with formula [Co2(bdhb)2(py)4] (2) and a Co⋯Co separation of more than 11 Å. Complex 2 contains two pseudo-octahedrally coordinated and non-interacting high-spin cobalt(II) ions (S = 3/2) displaying a large easy-plane anisotropy (D ∼ 70 cm-1), as consistently indicated by magnetic measurements, X-band EPR spectra, and complete active space self-consistent field/N-electron valence state perturbation theory (CASSCF/NEVPT2) calculations. At cryogenic temperatures (T < 7 K) and in an applied static magnetic field, the compound shows detectably slow magnetic relaxation, which occurs through direct and Raman mechanisms. Combined mass spectrometry, UV-Vis, and 1H/2H NMR data, including an isotopic labelling experiment and a determination of molecular weight by diffusion ordered spectroscopy (DOSY), show that 2 rearranges to monomeric high-spin [Co(bdhb)(py)x] species (x = 0, 1, or 2) in organic solution (CH2Cl2, THF) with concomitant partial dissociation of the py ligands. The X-band EPR spectra in a frozen CH2Cl2/toluene matrix concurrently suggest a significant alteration of the coordination environment upon dissolution. These observations are fairly well reproduced by density functional theory (DFT) and CASSCF/NEVPT2 calculations on the lowest Gibbs free energy conformers of each species, as provided by an extensive conformational search based on meta-dynamics simulations and semiempirical tight-binding methods. After the vanadyl analogue, compound 2 provides the second example of polymerization isomerism in the 1 : 1 adducts of bdhb2- with divalent metal ions.

Mechanism of Dinitrogen Photoactivation by P2PPhFe Complexes: Thermodynamic and Kinetic Computational Studies

The P2PPhFe(N2)(H)2 catalyst showed a significant ammonia yield under light irradiation. However, under thermal conditions, the hydrogen evolution reaction (HER) is favored over the nitrogen reduction reaction (N2RR), making P2PPhFe(N2)(H)2 an ideal system for studying the competition between both reactions. In this study, we used a series of computational tools to elucidate the photochemical reaction mechanism for the N2RR and thermal pathways leading to the HER with this catalyst. We calculated the energy profile for each transformation and estimated the rate constants for each step. Our results, which are consistent with experimental observations, indicate that photoinduced H2 elimination from P2PPhFe(N2)(H)2 promotes the formation of P2PPhFe(N2)2, which is on-path for N2RR. However, this elimination process is kinetically hindered due to high-energy barriers. Furthermore, our calculations reveal enhanced dinitrogen activation upon the conversion of P2PPhFe(N2)(H)2 to P2PPhFe(N2)2.

Binding modes of a flexible ruthenium polypyridyl complex to DNA

Ruthenium(II) polypyridyl complexes are attractive binders to DNA. Modifying the hydrophobicity, shape, or size of the ancillary ligands around the central ruthenium atom can induce changes in the binding mode to the DNA double helix. In this paper, we investigate the binding modes of [Ru(2,2'-bipyridine)2 (5-{4-[(pyren-1-yl)methyl]-1H-1,2,3-triazol-4-yl}-1,10-phenanthroline)]2+ (RuPy for short), a metal complex featuring a flexible pyrene moiety known for its intercalative properties. Classical molecular dynamics simulations are employed to gain insight into the non-covalent binding interactions of RuPy with two different 20 base pair DNA sequences, poly(dA)poly(dT) (AT) and poly(dC)poly(dG) (CG). In addition to examining the intercalation of the pyrene moiety from the major groove, the stability of RuPy-DNA adducts is investigated when the metal complex interacts externally with the DNA and with the major and minor groove pockets. The results indicate that external interaction and major groove binding are not stable, whereas intercalation consistently forms stable adducts. Minor groove binding showed less stability than intercalation and more variability, with some trajectories transitioning to intercalation, involving either the pyrene moiety or a bipyridine ligand. Pyrene intercalation, especially from the minor groove, was the most stable, while bipyridine intercalation was less favorable and associated with higher binding free energies.

Cryptate binding energies towards high throughput chelator design: metadynamics ensembles with cluster-continuum solvation

A tiered forcefield/semiempirical/meta-GGA pipeline together with a thermodynamic scheme designed with error cancellation in mind was developed to calculate binding energies of [2.2.2] cryptate complexes of mono- and divalent cations. Stable complexes of Na, K, Rb, Ca, Zn and Pb were generated, revealing consistent cation-N lengths but highly variable cation-O lengths and an amine stacking mechanism potentially augmenting the cation size selectivity. Metadynamics, used for searching the high-dimensional potential energy surface, together with a cluster-continuum model for affordable - yet accurate - solvation modeling, enabled the discovery of more stable geometries than those previously reported. Similar solvation energy curve shapes for lone vs. coordinated ions enabled rapid solvation convergence via the cancellation of errors stemming from finite cluster sizes. An R2 of 0.850 vs. experimental aqueous binding energies was obtained, validating this scheme as the backbone of a high-throughput workflow for chelator design.

Emerging Conformational-Analysis Protocols from the RTCONF55-16K Reaction Thermochemistry Conformational Benchmark Set

RTCONF55-16K is a new, reactive conformational data set based on cost-efficient methods to assess different conformational analysis protocols. Our reference calculations underpinned the accuracy of the CENSO (Grimme et al. J. Phys. Chem. A, 2021, 125, 4039) procedure and resulted in alternative recipes with different cost-accuracy compromises. Our general-purpose and economical protocols (CENSO-light and zero, respectively) were found to be 10-30 times faster than the original algorithm, adding only 0.4-0.7 kcal/mol absolute error to the relative free energy estimates.

Partial to Total Generation of 3D Transition-Metal Complexes

The design of transition-metal complexes (TMCs) has drawn much attention over the years because of their important applications as metallodrugs and functional materials. In this work, we present an extension of our recently reported approach, LigandDiff [Jin et al. J. Chem. Theory Comput. 20, 4377(2024)]. The new model, which we call multi-LigandDiff, is more flexible and greatly outperforms its predecessor. This scaffold-based diffusion model allows de novo ligand design with either existing ligands or without any ligand. Moreover, it allows users to predefine the denticity of the generated ligand. Our results indicate that multi-LigandDiff can generate well-defined ligands and is transferable to multiple transition metals and coordination geometries. In terms of its application, multi-LigandDiff successfully designed 338 Fe(II) spin-crossover (SCO) complexes from only 47 experimentally validated SCO complexes. And these generated complexes are configurationally diverse and structurally reasonable. Overall, the results show that multi-LigandDiff is an ideal tool to design novel TMCs from scratch.

Using atomic clustering based on structural and electronic descriptors that consider surrounding environment to evaluate local properties of DFT functionals

We developed a method for evaluating the accuracies of the local properties of DFT functionals in detail using a clustering method based on machine learning and structural/electronic descriptors. We generated 36 clusters consistent with human intuition using 30,436 carbon atoms from the QM9 dataset. The results were used to evaluate 13C NMR chemical shifts calculated using 84 DFT functionals. Carbon atoms were grouped based on their similar environments, reducing errors within these groups. This enables more accurate assessment of the accuracy using a specific DFT functional. Therefore, the present atomic clustering provides more detailed insight into accuracy verification.

Paving the road towards automated homogeneous catalyst design

In the past decade, computational tools have become integral to catalyst design. They continue to offer significant support to experimental organic synthesis and catalysis researchers aiming for optimal reaction outcomes. More recently, data-driven approaches utilizing machine learning have garnered considerable attention for their expansive capabilities. This Perspective provides an overview of diverse initiatives in the realm of computational catalyst design and introduces our automated tools tailored for high-throughput in silico exploration of the chemical space. While valuable insights are gained through methods for high-throughput in silico exploration and analysis of chemical space, their degree of automation and modularity are key. We argue that the integration of data-driven, automated and modular workflows is key to enhancing homogeneous catalyst design on an unprecedented scale, contributing to the advancement of catalysis research.

Modeling Zinc Complexes Using Neural Networks

Understanding the energetic landscapes of large molecules is necessary for the study of chemical and biological systems. Recently, deep learning has greatly accelerated the development of models based on quantum chemistry, making it possible to build potential energy surfaces and explore chemical space. However, most of this work has focused on organic molecules due to the simplicity of their electronic structures as well as the availability of data sets. In this work, we build a deep learning architecture to model the energetics of zinc organometallic complexes. To achieve this, we have compiled a configurationally and conformationally diverse data set of zinc complexes using metadynamics to overcome the limitations of traditional sampling methods. In terms of the neural network potentials, our results indicate that for zinc complexes, partial charges play an important role in modeling the long-range interactions with a neural network. Our developed model outperforms semiempirical methods in predicting the relative energy of zinc conformers, yielding a mean absolute error (MAE) of 1.32 kcal/mol with reference to the double-hybrid PWPB95 method.

CREST-A program for the exploration of low-energy molecular chemical space

Conformer-rotamer sampling tool (CREST) is an open-source program for the efficient and automated exploration of molecular chemical space. Originally developed in Pracht et al. [Phys. Chem. Chem. Phys. 22, 7169 (2020)] as an automated driver for calculations at the extended tight-binding level (xTB), it offers a variety of molecular- and metadynamics simulations, geometry optimization, and molecular structure analysis capabilities. Implemented algorithms include automated procedures for conformational sampling, explicit solvation studies, the calculation of absolute molecular entropy, and the identification of molecular protonation and deprotonation sites. Calculations are set up to run concurrently, providing efficient single-node parallelization. CREST is designed to require minimal user input and comes with an implementation of the GFNn-xTB Hamiltonians and the GFN-FF force-field. Furthermore, interfaces to any quantum chemistry and force-field software can easily be created. In this article, we present recent developments in the CREST code and show a selection of applications for the most important features of the program. An important novelty is the refactored calculation backend, which provides significant speed-up for sampling of small or medium-sized drug molecules and allows for more sophisticated setups, for example, quantum mechanics/molecular mechanics and minimum energy crossing point calculations.

Development of Novel Redox-Active Organic Materials Based on Benzimidazole, Benzoxazole, and Benzothiazole: A Combined Theoretical and Experimental Screening Approach

Sustainability is one of the hot topics of today's research, in particular when it comes to energy-storage systems such as batteries. Redox-active molecules implemented in organic batteries represent a promising alternative to lithium-ion batteries, which partially rely on non-sustainable heavy metal salts. As an alternative, we propose benzothiazole, -oxazole and -imidazole derivatives as redox-active moieties for polymers in organic (radical) batteries. The target molecules were identified by a combination of theoretical and experimental approaches for the investigation of new organic active materials. Herein, we present the synthesis, electrochemical characterization and theoretical investigation of the proposed molecules, which can later be introduced into a polymer backbone and used in organic polymer batteries.

Dinitrogen Activation Mediated by the (P2PPh)Fe Complex: Electronic Structure, Dimerization Mechanism, and Magnetic Coupling

Herein, we report the estimation of the extent of dinitrogen activation by different charged and structural forms of (P2PPh)Fe biomimetic catalysts, which, in the presence of light, exhibit significant yield in the N2-to-NH3 conversion. Complete active space self-consistent field (CASSCF) calculations have been used to determine the electronic structure of different reduced forms of the mononuclear complexes: the neutral (P2PPh)Fe(N2)2 adduct and the anionic [(P2PPh)Fe(N2)]- and [(P2PPh)Fe(N2)]2- complexes. These calculations also revealed that the extent of reduction of a dinitrogen molecule reaches up to one electron (N21-) due to the back-bonding from the Fe center, in agreement with the changes observed in the vibration frequency of the N-N bond in these complexes. In addition, the energy profile of the dimerization of the mononuclear (P2PPh)Fe(N2)2 complex to the dinuclear mono-N2-bridged [(P2PPh)Fe]2(μ-N2) complex has been determined by means of density functional theory (DFT) calculations. A three-step mechanism has been proposed for the dimerization, favored by both kinetics and thermodynamics criteria. Finally, the magnetic coupling constant in the diiron (μ-N2) complex is estimated from CASSCF/NEVPT2 calculations. Such a dinuclear complex presents a strong antiferromagnetic coupling resulting from the interaction between two S = 1 d6 Fe2+ ions, bridged by a highly activated dinitrogen molecule (N22-) with two electrons on the π* orbitals.

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.

Deposition products predicted from conceptual DFT: The hydrolysis reactions of MoF6, WF6, and UF6

Metal hexafluorides hydrolyze at ambient temperature to deposit compounds having fluorine-to-oxygen ratios that depend upon the identity of the metal. Uranium-hexafluoride hydrolysis, for example, deposits uranyl fluoride (UO2F2), whereas molybdenum hexafluoride (MoF6) and tungsten hexafluoride deposit trioxides. Here, we pursue general strategies enabling the prediction of depositing compounds resulting from multi-step gas-phase reactions. To compare among the three metal-hexafluoride hydrolyses, we first investigate the mechanism of MoF6 hydrolysis using hybrid density functional theory (DFT). Intermediates are then validated by performing anharmonic vibrational simulations and comparing with infrared spectra [McNamara et al., Phys. Chem. Chem. Phys. 25, 2990 (2023)]. Conceptual DFT, which is leveraged here to quantitatively evaluate site-specific electrophilicity and nucleophilicity metrics, is found to reliably predict qualitative deposition propensities for each intermediate. In addition to the nucleophilic potential of the oxygen ligands, several other contributing characteristics are discussed, including amphoterism, polyvalency, fluxionality, steric hindrance, dipolar strength, and solubility. To investigate the structure and composition of pre-nucleation clusters, an automated workflow is presented for the simulation of particle growth. The workflow entails a conformer search at the density functional tight-binding level, structural refinement at the hybrid DFT level, and computation of a composite free-energy profile. Such profiles can be used to estimate particle nucleation kinetics. Droplet formation is also considered, which helps to rationalize the different UO2F2 particle morphologies observed under varying levels of humidity. Development of predictive methods for simulating physical and chemical deposition processes is important for the advancement of material manufacturing involving coatings and thin films.

Assessment of DLPNO-MP2 Approximations in Double-Hybrid DFT

The unfavorable scaling (N5) of the conventional second-order Møller-Plesset theory (MP2) typically prevents the application of double-hybrid (DH) density functionals to large systems with more than 100 atoms. A prominent approach to reduce the computational demand of electron correlation methods is the domain-based local pair natural orbital (DLPNO) approximation that is successfully used in the framework of DLPNO-CCSD(T). Its extension to MP2 [Pinski P.; Riplinger, C.; Valeev, E. F.; Neese, F. J. Chem. Phys. 2015, 143, 034108.] paved the way for DLPNO-based DH (DLPNO-DH) methods. In this work, we assess the accuracy of the DLPNO-DH approximation compared to conventional DHs on a large number of 7925 data points for thermochemistry and 239 data points for structural features, including main-group and transition-metal systems. It is shown that DLPNO-DH-DFT can be applied successfully to perform energy calculations and geometry optimizations for large molecules at a drastically reduced computational cost. Furthermore, PNO space extrapolation is shown to be applicable, similar to its DLPNO-CCSD(T) counterpart, to reduce the remaining error.

High-throughput screening of spin states for transition metal complexes with spin-polarized extended tight-binding methods

The semiempirical GFNn-xTB ( n = 1 , 2 ) tight-binding methods are extended with a spin-dependent energy term (spin-polarization), enabling the fast and efficient screening of different spin states for transition metal complexes. While GFNn-xTB methods inherently can not differentiate properly between high-spin (HS) and low-spin (LS) states, this shortcoming is corrected with the presented methods termed spGFNn-xTB. The performance of spGFNn-xTB methods for spin state energy splittings is evaluated on a newly compiled benchmark set of 90 complexes (27 HS and 63 LS complexes) containing 3d, 4d, and 5d transition metals (termed TM90S) employing DFT references at the TPSSh-D4/def2-QZVPP level of theory. The challenging TM90S set contains complexes with charges between - 4 and +3, spin multiplicities between 1 and 6, and spin-splitting energies that range from - 47.8 to 146.6 kcal/mol with a mean average of 32.2 kcal/mol. On this set the (sp)GFNn-xTB methods, the PM6-D3H4 method, and the PM7 method are evaluated with spGFN1-xTB yielding the lowest MAD of 19.6 kcal/mol followed by spGFN2-xTB with 24.8 kcal/mol. While for the 4d and 5d subsets small or no improvements are observed with spin-polarization, large improvements are obtained for the 3d subset with spGFN1-xTB yielding the smallest MAD of 14.2 kcal/mol followed by spGFN2-xTB with 17.9 kcal/mol and PM6-D3H4 with 28.4 kcal/mol. The correct sign of the spin state splittings is obtained with spGFN2-xTB in 89% of all cases closely followed by spGFN1-xTB with 88%. On the full set, a pure semiempirical vertical spGFN2-xTB//GFN2-xTB-based workflow for screening purposes yields a slightly better MAD of 22.2 kcal/mol due to error compensation, while being qualitative correct for one additional case. In combination with their low computational cost (scanning spin states in seconds), the spGFNn-xTB methods represent robust tools for pre-screening steps of spin state calculations and high-throughput workflows.

PyConSolv: A Python Package for Conformer Generation of (Metal-Containing) Systems in Explicit Solvent

We introduce PyConSolv, a freely available Python package that automates the generation of conformers of metal- and nonmetal-containing complexes in explicit solvent, through classical molecular dynamics simulations. Using a streamlined workflow and interfacing with widely used computational chemistry software, PyConSolv is an all-in-one tool for the generation of conformers in any solvent. Input requirements are minimal; only the geometry of the structure and the desired solvent in xyz (XMOL) format are needed. The package can also account for charged systems, by including arbitrary counterions in the simulation. A bonded model parametrization is performed automatically, utilizing AmberTools, ORCA, and Multiwfn software packages. PyConSolv provides a selection of preparametrized solvents and counterions for use in classical molecular dynamics simulations. We show the applicability of our package on a number of (transition-metal-containing) systems. The software is provided open source and free of charge.

Can Catenated Nitrogen Compounds with Amine-like Structures Become Candidates for High-Energy-Density Compounds?

The worthwhile idea of whether amine-like catenated nitrogen compounds are stable enough to be used as high-energy materials was proposed and answered. Abstracting the NH3 structure into NR3 (R is the substituent) yields a new class of amine-like catenated nitrogen compounds. Most of the azole ring structures have a high nitrogen content and stability. Inspired by this idea, a series of new amine-like catenated nitrogen compounds (A1 to H5) were designed, and their basic energetic properties were calculated. The results showed that (1) amine-like molecular structures are often characterized by low density; however, the density of these compounds increases as the number of nitrogens in the azole ring increases; (2) these catenated nitrogen compounds generally have extremely high enthalpies of formation (882.91-2652.03 kJ/mol), and the detonation velocity of some compounds exceeds 9254.00 m/s; (3) the detonation performance of amine-like catenated nitrogen compounds designed based on imidazole and pyrazole rings is poor due to their low nitrogen content; and (4) the bond dissociation enthalpy of trigger bonds of most compounds is higher than 84 kJ/mol, indicating that these compounds have a certain thermodynamic stability. In summary, amine-like catenated nitrogen compounds have the potential to become energetic compounds with excellent detonation properties and should be considered to be synthesized by experimental chemists.

Challenges for Kinetics Predictions via Neural Network Potentials: A Wilkinson's Catalyst Case

Ab initio kinetic studies are important to understand and design novel chemical reactions. While the Artificial Force Induced Reaction (AFIR) method provides a convenient and efficient framework for kinetic studies, accurate explorations of reaction path networks incur high computational costs. In this article, we are investigating the applicability of Neural Network Potentials (NNP) to accelerate such studies. For this purpose, we are reporting a novel theoretical study of ethylene hydrogenation with a transition metal complex inspired by Wilkinson's catalyst, using the AFIR method. The resulting reaction path network was analyzed by the Generative Topographic Mapping method. The network's geometries were then used to train a state-of-the-art NNP model, to replace expensive ab initio calculations with fast NNP predictions during the search. This procedure was applied to run the first NNP-powered reaction path network exploration using the AFIR method. We discovered that such explorations are particularly challenging for general purpose NNP models, and we identified the underlying limitations. In addition, we are proposing to overcome these challenges by complementing NNP models with fast semiempirical predictions. The proposed solution offers a generally applicable framework, laying the foundations to further accelerate ab initio kinetic studies with Machine Learning Force Fields, and ultimately explore larger systems that are currently inaccessible.

Architector for high-throughput cross-periodic table 3D complex building

Rare-earth and actinide complexes are critical for a wealth of clean-energy applications. Three-dimensional (3D) structural generation and prediction for these organometallic systems remains a challenge, limiting opportunities for computational chemical discovery. Here, we introduce Architector, a high-throughput in-silico synthesis code for s-, p-, d-, and f-block mononuclear organometallic complexes capable of capturing nearly the full diversity of the known experimental chemical space. Beyond known chemical space, Architector performs in-silico design of new complexes including any chemically accessible metal-ligand combinations. Architector leverages metal-center symmetry, interatomic force fields, and tight binding methods to build many possible 3D conformers from minimal 2D inputs including metal oxidation and spin state. Over a set of more than 6,000 x-ray diffraction (XRD)-determined complexes spanning the periodic table, we demonstrate quantitative agreement between Architector-predicted and experimentally observed structures. Further, we demonstrate out-of-the box conformer generation and energetic rankings of non-minimum energy conformers produced from Architector, which are critical for exploring potential energy surfaces and training force fields. Overall, Architector represents a transformative step towards cross-periodic table computational design of metal complex chemistry.

Insights into the deviation from piecewise linearity in transition metal complexes from supervised machine learning models

Virtual high-throughput screening (VHTS) and machine learning (ML) with density functional theory (DFT) suffer from inaccuracies from the underlying density functional approximation (DFA). Many of these inaccuracies can be traced to the lack of derivative discontinuity that leads to a curvature in the energy with electron addition or removal. Over a dataset of nearly one thousand transition metal complexes typical of VHTS applications, we computed and analyzed the average curvature (i.e., deviation from piecewise linearity) for 23 density functional approximations spanning multiple rungs of "Jacob's ladder". While we observe the expected dependence of the curvatures on Hartree-Fock exchange, we note limited correlation of curvature values between different rungs of "Jacob's ladder". We train ML models (i.e., artificial neural networks or ANNs) to predict the curvature and the associated frontier orbital energies for each of these 23 functionals and then interpret differences in curvature among the different DFAs through analysis of the ML models. Notably, we observe spin to play a much more important role in determining the curvature of range-separated and double hybrids in comparison to semi-local functionals, explaining why curvature values are weakly correlated between these and other families of functionals. Over a space of 187.2k hypothetical compounds, we use our ANNs to pinpoint DFAs for which representative transition metal complexes have near-zero curvature with low uncertainty, demonstrating an approach to accelerate screening of complexes with targeted optical gaps.

Synthesis and characterization of potential polycyclic energetic materials using bicyclic triazole and azetidine structures as building blocks

Exploring the design strategy of new energetic materials is crucial to promote the development of energetic materials. In this study, a method for designing polycyclic energetic materials is proposed by combining the azetidine structure with azobis-1,2,4-triazole or bi-1,2,4-triazole. A series of typical triazolyl polycyclic compounds were designed and synthesized by simple nucleophilic reaction, which included 5,5'-dichloro-3,3'-bis(3,3'-difluoroazetidine)-4,4'-azobis-1,2,4-triazole (1), 5,5'-dichloro-3,3'-bis(3,3'-difluoroazetidine)-4,4'-bi-1,2,4-triazole (2), 5,5'-dichloro-3-(N,N-dimethyl)-3'-(3,3'-difluoroazetidine)-4,4'-bi-1,2,4-triazole (3) 5,5'-dichloro-3,3'-bis(3,3'-dinitroazetidine)-4,4'-bi-1,2,4-triazole (4), 5,5'-dichloro-3-(N,N-dimethyl)-3'-(3,3'-dinitroazetidine)-4,4'-bi-1,2,4-triazole (5), and 5,5'-diazido-3,3'-bis(3,3'-difluoroazetidine)-4,4'-azo-1,2,4-triazole (6). These designed and synthesized polycyclic compounds (1, 2, 3) have high decomposition temperatures (>200 °C). The molecular van der Waals surface electrostatic potentials suggested the reactivity of compounds 1, 2, and 3 when attacked by nucleophiles. The natural bond orbital and Hirshfeld surface analysis proved the essential reason for the stability of these compounds in theory. The formula design example suggests that some triazolyl polycyclic compounds (4, 5, and 6) are potentially explosives, suggesting that this strategy is feasible for constructing the triazolyl polycyclic energetic compounds.

ωB97X-3c: A composite range-separated hybrid DFT method with a molecule-optimized polarized valence double-ζ basis set

A new composite density functional theory (DFT) method is presented. It is based on ωB97X-V as one of the best-performing density functionals for the GMTKN55 thermochemistry database and completes the family of "3c" methods toward range-separated hybrid DFT. This method is consistently available for all elements up to Rn (Z = 1-86). Its further key ingredients are a polarized valence double-ζ (vDZP) Gaussian basis set, which was fully optimized in molecular DFT calculations, in combination with large-core effective core potentials and a specially adapted D4 dispersion correction. Unlike most existing double-ζ atomic orbital sets, vDZP shows only small basis set superposition errors (BSSEs) and can compete with standard sets of triple-ζ quality. Small residual BSSE effects are efficiently absorbed by the D4 damping scheme, which overall eliminates the need for an explicit treatment or empirical corrections for BSSE. Thorough tests on a variety of thermochemistry benchmark sets show that the new composite method, dubbed ωB97X-3c, is on par with or even outperforms standard hybrid DFT methods in a quadruple-zeta basis set at a small fraction of the computational cost. Particular strengths of this method are the description of non-covalent interactions and barrier heights, for which it is among the best-performing density functionals overall.

Best-Practice DFT Protocols for Basic Molecular Computational Chemistry

Nowadays, many chemical investigations are supported by routine calculations of molecular structures, reaction energies, barrier heights, and spectroscopic properties. The lion's share of these quantum-chemical calculations applies density functional theory (DFT) evaluated in atomic-orbital basis sets. This work provides best-practice guidance on the numerous methodological and technical aspects of DFT calculations in three parts: Firstly, we set the stage and introduce a step-by-step decision tree to choose a computational protocol that models the experiment as closely as possible. Secondly, we present a recommendation matrix to guide the choice of functional and basis set depending on the task at hand. A particular focus is on achieving an optimal balance between accuracy, robustness, and efficiency through multi-level approaches. Finally, we discuss selected representative examples to illustrate the recommended protocols and the effect of methodological choices.

Theoretical calculations of formation and reactivity of o-quinomethide derivatives of resorcin[4]arene with reference to empirical data

This paper describes theoretical reaction pathways of alkoxybenzyl derivatives of resorcin[4]arene leading to the formation of o-quinomethide derivatives of resorcin[4]arene (o-QMR[4]A). For each case, the activation energies for the formation of one o-QMR[4]A unit and the activation energies for the backward reaction were calculated. Based on the calculated reaction pathways, the reaction mechanism of o-QMR[4]A formation was proposed. Using the example of o-QMR[4]A generated from a methoxy derivative of resorcin[4]arene, the activation energies with selected nucleophiles were calculated and the reaction mechanisms discussed. Reaction path calculations were performed using the nudged elastic band method and semiempirical extended tight-binding method (GFN2-xTB). Using hydroxybenzyl derivatives of resorcin[4]arene as an example, a comparison of calculated activation energies by selected density-functional theory methods with GFN2-xTB and B97-3c geometries was performed. B97-3c and wB97XD methods were used to calculate the energies of the reactants (R), transition states (TS) and products (P) of the analysed reactions. Theoretical reaction mechanisms were discussed with respect to the orbital-weighted Fukui dual descriptor (Δfw ) and experimental data.

Solution-Phase Conformational/Vibrational Anharmonicity in Comonomer Incorporation Polyolefin Catalysis

The prediction of comonomer incorporation statistics in polyolefin catalysis necessitates an accurate calculation of free energies corresponding to monomer binding and insertion, often requiring sub-kcal/mol resolution to resolve experimental free energies. Batch reactor experiments are used to probe incorporation statistics of ethene and larger α-olefins for three constrained geometry complexes which are employed as model systems. Herein, over 6 ns of quantum mechanics/molecular mechanics (QM/MM) molecular dynamics is performed in combination with the zero-temperature string method to characterize the solution-phase insertion barrier and to analyze the contributions from conformational and vibrational anharmonicity arising both in vacuum and in solution. Conformational sampling in the solution-phase results in 0-2 kcal/mol corrections to the insertion barrier which are on the same scale necessary to resolve experimental free energies. Anharmonic contributions from conformational sampling in the solution phase are crucial energy contributions missing from static density functional theory calculations and implicit solvation models, and the accurate calculation of these contributions is a key step toward the quantitative prediction of comonomer incorporation statistics.

Conformational energies of microsolvated Na+ clusters with protic and aprotic solvents from GFNn-xTB methods

Performance of contemporary tight-binding semiempirical GFNn-xTB methods for the conformational energies of singly charged sodium clusters Na⁺ (S)_n (n = 4-8) with 3 protic and 8 aprotic solvents is examined against the reference RI-MP2/CBS method. The median Pearson correlation coefficients of ρ = 0.84 (GFN2-xTB) and ρ = 0.82 (GFN1-xTB) do not give the clear preference to any tested approach. GFN1-xTB method demonstrates more stable performance than its GFN2-xTB successor with the average mean absolute errors (MAEs)/mean signed errors (MSEs) of 1.2/0.2 and 2.3/1.6 kcal mol^-1 , respectively. Conformational energies produced by the computationally efficient DFT functional PBE and double-ζ basis set complemented with -D3(BJ) dispersion correction are suitable for the preliminary sampling (median ρ = 0.93), but should be used with a caution for the calculations of the average ensemble properties (MAE/MSE = 1.7/1.1 kcal mol^-1 ). Higher-ranking PBE0-D3(BJ) and ωB97M-V with triple-ζ basis sets yield significantly lower MAEs/MSEs of 0.55/0.20 and 0.51/0.23 kcal mol^-1 , respectively.

A litmus test for the balanced description of dispersion interactions and coordination chemistry of lanthanoids

The influence of long-range interactions on the structure of complexes of Eu(III) with four 9-hydroxy-phenalen-1-one ligands (HPLN) and one alkaline earth metal dication [Eu(PLN)₄AE]⁺ (AE: Mg, Ca, Sr, and Ba) is analyzed. Through the [Eu(PLN)₄Ca]⁺ complex, which is a charged complex with two metals-one of them a lanthanoid-and with four relatively fluxional π-ligands, the difficulties of describing such systems are identified. The inclusion of the D3(BJ) or D4 corrections to different density functionals introduces significant changes in the structure, which are shown to stem from the interaction between pairs of PLN ligands. This interaction is studied further with a variety of density functionals, wave-function based methods, and by means of the random phase approximation. By comparing the computed results with those from experimental evidence of gas-phase photoluminescence and ion mobility measurements it is concluded that the inclusion of dispersion corrections does not always yield structures that are in agreement with the experimental findings.

Optimization of the r2SCAN-3c Composite Electronic-Structure Method for Use with Slater-Type Orbital Basis Sets

The "Swiss army knife" composite density functional electronic-structure method r²SCAN-3c (J. Chem. Phys. 2021, 154, 064103) is extended and optimized for the use with Slater-type orbital basis sets. The meta generalized-gradient approximation (meta-GGA) functional r²SCAN by Furness et al. is combined with a tailor-made polarized triple-ζ Slater-type atomic orbital (STO) basis set (mTZ2P), the semiclassical London dispersion correction (D4), and a geometrical counterpoise (gCP) correction. Relativistic effects are treated explicitly with the scalar-relativistic zeroth-order regular approximation (SR-ZORA). The performance of the new implementation is assessed on eight geometry and 74 energy benchmark sets, including the extensive GMTKN55 database as well as recent sets such as ROST61 and IONPI19. In geometry optimizations, the STO-based r²SCAN-3c is either on par with or more accurate than the hybrid density functional approximation M06-2X-D3(0)/TZP. In energy calculations, the overall accuracy is similar to the original implementation of r²SCAN-3c with Gaussian-type atomic orbitals (GTO), but basic properties, intermolecular noncovalent interactions, and barrier heights are better described with the STO approach, resulting in a lower weighted mean absolute deviation (WTMAD-2(STO) = 7.15 vs 7.50 kcal mol^-1 with the original method) for the GMTKN55 database. The STO-optimized r²SCAN-3c outperforms many conventional hybrid/QZ approaches in most common applications at a fraction of their cost. The reliable, robust, and accurate r²SCAN-3c implementation with STOs is a promising alternative to the original implementation with GTOs and can be generally used for a broad field of quantum chemical problems.

[3 + 2] Cycloadditions and Retrocycloadditions of Niobium Imido Complexes: An Experimental and Computational Mechanistic Study

We demonstrate reactivity between a β-diketiminate-supported niobium(III) imido complex and alkyl azides to form niobatetrazene complexes (BDI)Nb(N^tBu)(RNNNNR) (BDI = N,N-bis(2,6-diisopropylphenyl)-3,5-dimethyl-β-diketiminate; R = cyclohexyl (1), benzyl (2)). Intriguingly, niobatetrazene complexes 1 and 2 can be interconverted via addition of an appropriate alkyl azide, likely through a series of concerted [3 + 2] cycloaddition and retrocycloaddition reactions in which π-loaded bis(imido) intermediates are formed. The bis(imido) intermediates were trapped upon addition of alkyl isocyanides to yield five-coordinate bis(imido) complexes (BDI)Nb(N^tBu)(NCy)(CNR) (R = tert-butyl (4a), cyclohexyl (4b)). Two computational methods─density functional theory and density functional tight binding (DFTB)─were employed to calculate the lowest energy pathway across the potential energy surface for this multistep transformation. Reaction path calculations for individual cycloaddition or retrocycloaddition processes along the multistep reaction pathway showed that these transformations occur via a concerted, yet highly asynchronous mechanism, in which the two bond-breaking or -making events do not occur simultaneously. The use of the DFTB method in this work highlights its advantages and utility for studying transition metal systems.

A Biophysical Study of Ru(II) Polypyridyl Complex, Properties and its Interaction with DNA

Mononuclear Ru(II)Polypyridyl complexes of type [Ru(A)₂BPIIP] (ClO₄)₂.2H₂O, where BPIIP = 2-(3-(4-bromophenyl)isoxazole-5-yl)-1 H-imidazo [4,5-f] [1, 10] phenanthroline and A = bpy = bipyridyl (1), phen = 1,10 Phenanthroline (2), dmb = 4, 4' -dimethyl 2, 2'- bipyridine (3) & dmp = 4,4'-dimethyl-1,10 -Ortho Phenanthroline (4), were synthesized and their antibacterial activity were examined. The synthesized complexes were characterized and their interaction with DNA was studied using Computational and Biophysical methods (Absorption, emission methods, and viscosity). Molecular modelling studies were carried out for molecular geometry and electronic properties (Frontier molecular orbital HOMO-LUMO). The electrostatic potential surface contours for the complexes were analysed to give their nucleophilic level of sensitivity. The study reveals that the Ru(II) Polypyridyl complexes bind to DNA preponderantly by intercalation. The results recommend that the phen and dmp complex have more effective binding ability than the bpy and dmb, indicating the role of the ancillary ligand in determining their specificity for DNA binding. Further molecular docking studies suggested an octahedral geometry and bind to DNA by preferential binding to Guanine. The docking study additionally sustains the binding constant data acquired with the absorption and emission techniques.The results reveal that the nature of the ancillary Ligand plays a considerable role for the intercalation of the Ru(II) polypyridyl complex to DNA, which subsequently influences the antibacterial activity. Biological studies conducted on Gram-Negative (E.coli and K.pneumonia) and Gram-Positive (S. aureus and E. faecalis) bacteria establish that complex 1 and 2 were considerably active against S. aureus and E. coli.

Unlocking the computational design of metal-organic cages

Metal-organic cages are macrocyclic structures that can possess an intrinsic void that can hold molecules for encapsulation, adsorption, sensing, and catalysis applications. As metal-organic cages may be comprised from nearly any combination of organic and metal-containing components, cages can form with diverse shapes and sizes, allowing for tuning toward targeted properties. Therefore, their near-infinite design space is almost impossible to explore through experimentation alone and computational design can play a crucial role in exploring new systems. Although high-throughput computational design and screening workflows have long been known as powerful tools in drug and materials discovery, their application in exploring metal-organic cages is more recent. We show examples of structure prediction and host-guest/catalytic property evaluation of metal-organic cages. These examples are facilitated by advances in methods that handle metal-containing systems with improved accuracy and are the beginning of the development of automated cage design workflows. We finally outline a scope for how high-throughput computational methods can assist and drive experimental decisions as the field pushes toward functional and complex metal-organic cages. In particular, we highlight the importance of considering realistic, flexible systems.

ChemSpaX: exploration of chemical space by automated functionalization of molecular scaffold

Exploration of the local chemical space of molecular scaffolds by post-functionalization (PF) is a promising route to discover novel molecules with desired structure and function. PF with rationally chosen substituents based on known electronic and steric properties is a commonly used experimental and computational strategy in screening, design and optimization of catalytic scaffolds. Automated generation of reasonably accurate geometric representations of post-functionalized molecular scaffolds is highly desirable for data-driven applications. However, automated PF of transition metal (TM) complexes remains challenging. In this work a Python-based workflow, ChemSpaX, that is aimed at automating the PF of a given molecular scaffold with special emphasis on TM complexes, is introduced. In three representative applications of ChemSpaX by comparing with DFT and DFT-B calculations, we show that the generated structures have a reasonable quality for use in computational screening applications. Furthermore, we show that ChemSpaX generated geometries can be used in machine learning applications to accurately predict DFT computed HOMO-LUMO gaps for transition metal complexes. ChemSpaX is open-source and aims to bolster and democratize the efforts of the scientific community towards data-driven chemical discovery.

DFT Study of the Molecular and Electronic Structure of Metal-Free Tetrabenzoporphyrin and Its Metal Complexes with Zn, Cd, Al, Ga, In

The electronic and molecular structures of metal-free tetrabenzoporphyrin (H₂TBP) and its complexes with zinc, cadmium, aluminum, gallium and indium were investigated by density functional theory (DFT) calculations with a def2-TZVP basis set. A geometrical structure of ZnTBP and CdTBP was found to possess D_4h symmetry; AlClTBP, GaClTBP and InClTBP were non-planar complexes with C_4v symmetry. The molecular structure of H₂TBP belonged to the point symmetry group of D_2h. According to the results of the natural bond orbital (NBO) analysis, the M-N bonds had a substantial ionic character in the cases of the Zn(II) and Cd(II) complexes, with a noticeably increased covalent contribution for Al(III), Ga(III) and In(III) complexes with an axial –Cl ligand. The lowest excited states were computed with the use of time-dependent density functional theory (TDDFT) calculations. The model electronic absorption spectra indicated a weak influence of the nature of the metal on the Q-band position.

16OSTM10: A new open-shell transition metal conformational energies database to challenge contemporary semiempirical and force field methods

transition metal (OSTM) complexes has been developed. Contemporary composite density functional theory (DFT) (PBEh-3c, B97-3c), semiempirical (PM6, PM7) and the methods of GFNn-xTB/FF family were examined against conventional DFT (PBE-D3(BJ),...

Ligand Protonation at Carbon, not Nitrogen, during H2 Production with Amine-Rich Iron Electrocatalysts

We present monometallic H₂ production electrocatalysts containing electron-rich triamine-cyclopentadienyl (Cp) ligands coordinated to iron. After selective CO extrusion from the iron tricarbonyl precursors, electrocatalysis is observed via cyclic voltammetry in the presence of an exogenous acid. Contrary to the fact that amines in the secondary coordination sphere are often protonated during electrocatalysis, comprehensive quantum-chemical calculations indicate that the amines likely do not function as proton relays; instead, endo-Cp ring protonation is most favorable after 1e^- reduction. This unusual mechanistic pathway emphasizes the need to consider a broad domain of H⁺/e^- addition products by synergistically combining experimental and theoretical resources.

Automated Quantum Chemistry-Based Calculation of Optical Rotation for Large Flexible Molecules

The calculation of optical rotation (OR, [α]_D) for nonrigid molecules was limited to small systems due to the challenging problem of generating reliable conformer ensembles, calculating accurate Boltzmann populations and the extreme sensitivity of the OR to the molecules' three-dimensional structure. Herein, we describe and release the crenso workflow for the automated computation of conformer ensembles in solution and corresponding [α]_D values for flexible molecules. A comprehensive set of 28 organic drug molecules (28-144 atoms) with experimentally determined values is used in our assessment. In all cases, the correct OR sign is obtained with an overall mean relative deviation of 72% (mean absolute deviation of 82 °[dm(g/cm³)]^-1 for experimental values in the range -160 to 287 °[dm(g/cm³)]^-1). We show that routine [α]_D computations for very flexible, biologically active molecules are both feasible and reproducible in about a day of computation time on a standard workstation computer. Furthermore, we observed that the effect of energetically higher-lying structures in the ensemble on the OR is often averaged out and that in 23 out of 28 cases, the correct OR sign is obtained by just considering only the lowest free energy conformer. In four example cases, we show that the approach can also describe the OR of pairs of flexible diastereomers properly. In summary, even very sensitive, multifactorial physicochemical properties appear reliably predictable with minimal user input from efficiently automated quantum chemical methods.

Closer Look at Inverse Electron Demand Diels–Alder and Nucleophilic Addition Reactions on s-Tetrazines Using Enhanced Sampling Methods

Inverse electron demand [4+2] Diels–Alder (iEDDA) reactions as well as unprecedented nucleophilic (azaphilic) additions of R-substituted silyl-enol ethers (where R is Phenyl, Methyl, and Hydrogen) to 1,2,4,5-tetrazine (s-tetrazine) catalyzed by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {BF}_{3}$$\end{document}BF3 have recently been discovered (Simon et al. in Org Lett 23(7):2426–2430, 2021), where static calculations were employed for calculation of activation energies. In order to have a more realistic dynamic description of these reactions in explicit solution at ambient conditions, in this work we use a semiempirical tight-binding method combined with enhanced sampling techniques to calculate free energy surfaces (FESs) of the iEDDA and azaphilic addition reactions. Relevant products of not only s-tetrazine but also its derivatives such as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {BF}_{3}$$\end{document}BF3-mediated s-tetrazine adducts are investigated. We reconstruct the FESs of the iEDDA and azaphilic addition reactions using metadynamics and blue moon ensemble, and compare the ability of different collective variables (CVs) including bond distances, Social PeRmutation INvarianT (SPRINT) coordinates, and path-CV to describe the reaction pathway. We find that when a bulky Phenyl is used as a substituent at the dienophile the azaphilic addition is preferred over the iEDDA reaction. In addition, we also investigate the effect of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {BF}_{3}$$\end{document}BF3 in the diene and steric hindrance in the dienophile on the competition between the iEDDA and azaphilic addition reactions, providing chemical insight for reaction design.

Machine learning to tame divergent density functional approximations: a new path to consensus materials design principles

Virtual high-throughput screening (VHTS) with density functional theory (DFT) and machine-learning (ML)-acceleration is essential in rapid materials discovery. By necessity, efficient DFT-based workflows are carried out with a single density functional approximation (DFA). Nevertheless, properties evaluated with different DFAs can be expected to disagree for cases with challenging electronic structure (e.g., open-shell transition-metal complexes, TMCs) for which rapid screening is most needed and accurate benchmarks are often unavailable. To quantify the effect of DFA bias, we introduce an approach to rapidly obtain property predictions from 23 representative DFAs spanning multiple families, “rungs” (e.g., semi-local to double hybrid) and basis sets on over 2000 TMCs. Although computed property values (e.g., spin state splitting and frontier orbital gap) differ by DFA, high linear correlations persist across all DFAs. We train independent ML models for each DFA and observe convergent trends in feature importance, providing DFA-invariant, universal design rules. We devise a strategy to train artificial neural network (ANN) models informed by all 23 DFAs and use them to predict properties (e.g., spin-splitting energy) of over 187k TMCs. By requiring consensus of the ANN-predicted DFA properties, we improve correspondence of computational lead compounds with literature-mined, experimental compounds over the typically employed single-DFA approach.

Machine learning (ML)-based feature analysis reveals universal design rules regardless of density functional choices. Using the consensus among multiple functionals, we identify robust lead complexes in ML-accelerated chemical discovery.

On the Origin of E-Selectivity in the Ring-Opening Metathesis Polymerization with Molybdenum Imido Alkylidene N-Heterocyclic Carbene Complexes

The understanding and control of stereoselectivity is a central aspect in ring-opening metathesis polymerization (ROMP). Herein, we report detailed quantum chemical studies on the reaction mechanism of E-selective ROMP of norborn-2-ene (NBE) with Mo(N-2,6-Me2-C6H3)(CHCMe3)(IMes)(OTf)2 (1, IMes = 1,3-dimesitylimidazol-2-ylidene) as a first step to stereoselective polymerization. Four different reaction pathways based on an ene syn or ene anti approach of NBE to either the syn- or anti-isomer of the neutral precatalyst have been studied. In contrast to the recently established associative mechanism with a terminal alkene, where a neutral olefin adduct is formed, NBE reacts directly with the catalyst via [2 + 2] cycloaddition to form molybdacyclobutane with a reaction barrier about 30 kJ mol-1 lower in free energy than via the formation of a catalyst-monomer adduct. However, the direct cycloaddition of NBE was only found for one out of four stereoisomers. Our findings strongly suggest that this stereoselective approach is responsible for E-selectivity and point toward a substrate-specific reaction mechanism in olefin metathesis with neutral Mo imido alkylidene N-heterocyclic carbene bistriflate complexes.

Reaction Monitoring and Structural Characterisation of Coordination Driven Self-Assembled Systems by Ion Mobility-Mass Spectrometry

Nature creates exquisite molecular assemblies, required for the molecular-level functions of life, via self-assembly. Understanding and harnessing these complex processes presents an immense opportunity for the design and fabrication of advanced functional materials. However, the significant industrial potential of self-assembly to fabricate highly functional materials is hampered by a lack of knowledge of critical reaction intermediates, mechanisms, and kinetics. As we move beyond the covalent synthetic regime, into the domain of non-covalent interactions occupied by self-assembly, harnessing and embracing complexity is a must, and non-targeted analyses of dynamic systems are becoming increasingly important. Coordination driven self-assembly is an important subtype of self-assembly that presents several wicked analytical challenges. These challenges are "wicked" due the very complexity desired confounding the analysis of products, intermediates, and pathways, therefore limiting reaction optimisation, tuning, and ultimately, utility. Ion Mobility-Mass Spectrometry solves many of the most challenging analytical problems in separating and analysing the structure of both simple and complex species formed via coordination driven self-assembly. Thus, due to the emerging importance of ion mobility mass spectrometry as an analytical technique tackling complex systems, this review highlights exciting recent applications. These include equilibrium monitoring, structural and dynamic analysis of previously analytically inaccessible complex interlinked structures and the process of self-sorting. The vast and largely untapped potential of ion mobility mass spectrometry to coordination driven self-assembly is yet to be fully realised. Therefore, we also propose where current analytical approaches can be built upon to allow for greater insight into the complexity and structural dynamics involved in self-assembly.

Efficient Computation of Geometries for Gold Complexes

Computationally obtaining structural parameters along a reaction coordinate is commonly performed with Kohn‐Sham density functional theory which generally provides a good balance between speed and accuracy. However, CPU times still range from inconvenient to prohibitive, depending on the size of the system under study. Herein, the tight binding GFN2‐xTB method [C. Bannwarth, S. Ehlert, S. Grimme, J. Chem. Theory Comput. 2019, 15, 1652] is investigated as an alternative to produce reasonable geometries along a reaction path, that is, reactant, product and transition state structures for a series of transformations involving gold complexes. A small mean error (1 kcal/mol) was found, with respect to an efficient composite hybrid‐GGA exchange‐correlation functional (PBEh‐3c) paired with a double‐ζ basis set, which is 2–3 orders of magnitude slower. The outlined protocol may serve as a rapid tool to probe the viability of proposed mechanistic pathways in the field of gold catalysis.

Deep neural network analysis of nanoparticle ordering to identify defects in layered carbon materials

Smoothness/defectiveness of the carbon material surface is a key issue for many applications, spanning from electronics to reinforced materials, adsorbents and catalysis. Several surface defects cannot be observed with conventional analytic techniques, thus requiring the development of a new imaging approach. Here, we evaluate a convenient method for mapping such "hidden" defects on the surface of carbon materials using 1-5 nm metal nanoparticles as markers. A direct relationship between the presence of defects and the ordering of nanoparticles was studied experimentally and modeled using quantum chemistry calculations and Monte Carlo simulations. An automated pipeline for analyzing microscopic images is described: the degree of smoothness of experimental images was determined by a classification neural network, and then the images were searched for specific types of defects using a segmentation neural network. An informative set of features was generated from both networks: high-dimensional embeddings of image patches and statics of defect distribution.

Efficient Quantum Chemical Calculation of Structure Ensembles and Free Energies for Nonrigid Molecules

The application of quantum chemical, automatic multilevel modeling workflows for the determination of thermodynamic (e.g., conformation equilibria, partition coefficients, pK_a values) and spectroscopic properties of relatively large, nonrigid molecules in solution is described. Key points are the computation of rather complete structure (conformer) ensembles with extremely fast but still reasonable GFN2-xTB or GFN-FF semiempirical methods in the CREST searching approach and subsequent refinement at a recently developed, accurate r²SCAN-3c DFT composite level. Solvation effects are included in all steps by accurate continuum solvation models (ALPB, (D)COSMO-RS). Consistent inclusion of thermostatistical contributions in the framework of the modified rigid-rotor-harmonic-oscillator approximation (mRRHO) based on xTB/FF computed PES is also recommended.

r2SCAN-3c: A "Swiss army knife" composite electronic-structure method

The recently proposed r²SCAN meta-generalized-gradient approximation (mGGA) of Furness and co-workers is used to construct an efficient composite electronic-structure method termed r²SCAN-3c. To this end, the unaltered r²SCAN functional is combined with a tailor-made triple-ζ Gaussian atomic orbital basis set as well as with refitted D4 and geometrical counter-poise corrections for London-dispersion and basis set superposition error. The performance of the new method is evaluated for the GMTKN55 database covering large parts of chemical space with about 1500 data points, as well as additional benchmarks for non-covalent interactions, organometallic reactions, and lattice energies of organic molecules and ices, as well as for the adsorption on polar salt and non-polar coinage-metal surfaces. These comprehensive tests reveal a spectacular performance and robustness of r²SCAN-3c: It by far surpasses its predecessor B97-3c at only twice the cost and provides one of the best results of all semi-local density-functional theory (DFT)/QZ methods ever tested for the GMTKN55 database at one-tenth of the cost. Specifically, for reaction and conformational energies as well as non-covalent interactions, it outperforms prominent hybrid-DFT/QZ approaches at two to three orders of magnitude lower cost. Perhaps, the most relevant remaining issue of r²SCAN-3c is self-interaction error (SIE), owing to its mGGA nature. However, SIE is slightly reduced compared to other (m)GGAs, as is demonstrated in two examples. After all, this remarkably efficient and robust method is chosen as our new group default, replacing previous composite DFT and partially even expensive high-level methods in most standard applications for systems with up to several hundreds of atoms.