Understanding and Quantifying London Dispersion Effects in Organometallic Complexes

Dispersion-controlled C6-selective C-H borylation of indoles

Through DFT and NCI analysis, we designed a bulky tertiary phosphine directing group, enabling an iridium-catalyzed C6-selective borylation of indoles with a simple and commercially available ligand, 1,10-phenanthroline. The directing group has dual dispersive interactions with both phenanthroline and a Bpin group, which enhance selectivity and reactivity.

Unraveling cation-cation "attraction" in argentophilic interaction in 2,2'-bipydine coordinated silver complex

The nature of argentophilic interaction in the 2,2'-bipyridine-coordinated silver complex, which manifests counterintuitive cation-cation "attraction," is attributed to ligand stacking and solvation effects in the present article. While charged closed-shell transition metal complexes aggregating spontaneously to form oligomers has long been observed experimentally, the interpretation of the nature of so-called metallophilicity is still ongoing. For the dimer [(2,2'-bpy)2Ag]22+, qualitative electrostatic potential, non-covalent interaction, atoms-in-molecules analyses, and quantitative energy decomposition analysis calculations indicate that the electrostatic repulsion between two like formal charges at silver centers can be overcome by long-range dispersion attraction and short-range electronic correlation from ligands. In addition, delocalizing the net charges on silvers over the whole ligands can decrease electrostatic repulsion of metal centers to stabilize oligomers. The vital role of the screening effect of solvent has also been realized in the bound binding of the title system. Overall, this research highlights the importance of ligand stacking to argentophilicity, while d10-d10 attraction of silver centers presents quite little contribution.

Computational Modeling of the Enzymatic Achmatowicz Rearrangement by Heme-Dependent Chloroperoxidase: Reaction Mechanism, Enantiopreference, Regioselectivity, and Substrate Specificity

The chloroperoxidase from Caldariomyces fumago (CfCPO) catalyzes the oxidative ring expansion of α-heterofunctionalized furans via the Achmatowicz rearrangement, providing an elegant tool to convert furan rings into complex-prefunctionalized scaffolds. However, the mechanism of this transformation remains unclear. Herein, the CfCPO-catalyzed reaction of rac-1-(2-furyl)ethanol (1a) is studied by quantum chemical calculations and molecular dynamics simulations. The calculations reveal that the conversion follows the general mechanism of the Achmatowicz reaction. Notably, the binding of 1a to the enzyme's active site influences the Compound I (Cpd I) formation, and the (R)-1a enantiomer binding results in a lower barrier compared to (S)-1a, explaining the observed (R)-enantiopreference toward a racemic substrate. Additionally, due to the weaker steric hindrance between the porphyrin ring and substrate, the nucleophilic attack of Cpd I on the furan core of 1a is preferred at the less-substituted C4=C5 bond, providing a rationale for the experimentally observed regioselectivity. Finally, the bottleneck residues in the substrate delivery channel and also the active site surroundings are proposed to be responsible for the substrate specificity of CfCPO. This study lays a theoretical foundation for the rational design of new CPOs that catalyze the Achmatowicz rearrangement with a broader substrate spectrum or specific stereopreference.

Varying Projection Quality of Good Local Electric Field Gradients of Monochlorobenzaldehydes

Rotational spectroscopy is an excellent tool for structure determination, which can provide additional insights into local electronic structure by investigating the hyperfine pattern due to nuclear quadrupole coupling. Jet-cooled molecules are good experimental benchmark targets for electronic structure calculations, as they are free of environmental effects. We report the rotational spectra of 2-chlorobenzaldehyde, 3-chlorobenzaldehyde, and 4-chlorobenzaldehyde, including a complete experimental description of the nuclear quadrupole coupling constants, which were previously not experimentally determined. We identified two conformers for 3-chlorobenzaldehyde and one conformer each for 2-chlorobenzaldehyde and 4-chlorobenzaldehyde. Rigorous structure fitting of 4-chlorobenzaldehyde was performed to determine bond lengths for r0, rs, rese, and rm(1) structures. Comparing experimental nuclear quadrupole coupling constants to computational results showed agreement in the nuclear axis system, but the accuracy of the projection into the principal axis system decreases in near-oblate 2-chlorobenzaldehyde. The experimental angle Θaz = 19.16° between the principal a-axis and nuclear z-axis is larger than predicted by multiple computational methods by ≥4°. It is attributed to the high sensitivity of 2-chlorobenzaldehyde to low-energy vibrational contributions.

β-Diketonate Coordination: Vibrational Properties, Electronic Structure, Molecular Topology, and Intramolecular Interactions. Beryllium(II), Copper(II), and Lead(II) as Study Cases

Nine metal complexes formed by three symmetric β-diketonates (viz., acetylacetonate (acac), 1,1,1,3,3,3-hexafluoro-acetylacetonate (hfac), and 2,2,6,6-tetramethylheptane-3,5-dionate (tmhd)) and three metal ions (with three different coordination geometries, viz., BeII - tetrahedral, CuII - square planar, and PbII - "swing" square pyramidal) were investigated. The study combines structural analyses, vibrational spectroscopic techniques, and quantum chemical calculations with the aim of bridging crystal structure, electronic structure, molecular topology, and far-infrared (FIR) spectroscopic characteristics. The effect of intramolecular interactions on the structural, electronic, and spectroscopic features is the center of this study. The crystal structure of Be(tmhd)2 is also reported and discussed for the first time. A complete review of the experimental IR spectra is offered; discrepancies in the assignments of some peaks are revealed among the published works. Anharmonic effects were considered for acac complexes; however, they were negligible for the FIR modes. A systematic comparison between computed and experimentally measured data allowed us to design an inexpensive, yet efficient computational protocol to investigate large polynuclear complexes.

London dispersion forces and steric effects within nanocomposites tune interaction energies and chain conformation

The interplay between attractive London dispersion forces and steric effects due to repulsive forces resulting from the Pauli principle often determines the geometry and stability of nanostructures. Aromatic polyimides (PI) and carbon nanotubes (CNT) were chosen as building blocks as two components in the hetero delocalized electron nanostructures. Two PIs, having the same diamine part and different linkage substituents between two phenyl rings of dianhydride part, one linked with ether bond (C-O-C) (OPI), the other with C-(CF3)2 (FPI), were investigated. Surprisingly, two CNT/PI nanocomposites show distinct failure mode from CNT yielding to CNT pull-out failure. Calculation of the interaction energy and chain conformations of each PI upon CNT was performed by accurate density functional theory (DFT) calculations and molecular dynamic simulation (MDS). OPI chain adopt helically wrapping conformation around CNT with relatively strong interaction energy. FPI chain take the one-side wavelike conformation upon CNT with relatively weak interaction energy.

Exploring the Dynamic Coordination Sphere of Lanthanide Aqua Ions: Insights from r2SCAN-3c Composite-DFT Born-Oppenheimer Molecular Dynamics Studies

Born-Oppenheimer molecular dynamics (BOMD) simulations were performed to investigate the structure and dynamics of the first hydration shells of five trivalent lanthanide ions (Ln3+) at room temperature. These ions are relevant in various environments, including the bulk aqueous solution. Despite numerous studies, accurately classifying the molecular geometry of the first hydration sphere remains a challenge. To addres this, a cluster microsolvation approach was employed to study the interaction of Ln3+ ions (La, Nd, Gd, Er, and Lu) with up to 27 explicit water molecules. Electronic structure calculations were performed with the composite r2SCAN-3c method. The results demonstrate that this method offers an optimal balance between precision and computational efficiency. Specifically, it accurately predicts average Ln-O distances (MAE = 0.02 Å) of the first hydration sphere and preferred coordination numbers (CN) for the different lanthanide cations as compared to reported data in bulk. Highly dynamic first hydration shells for the examined Ln3+ ions were found, with noticeable and rapid rearrangements in their coordination geometries, some of which can be recognized as the tricapped trigonal prism (TTP) and the capped square antiprism (CSAP) for CN = 9, and as the square antiprism (SAP), the bicapped trigonal prism (BTP), and the trigonal dodecahedron (DDH) for CN = 8. However, ca. 70% of the nonacoordinated configurations did not meet the criteria of TTP or CSAP structures. For CN = 8, the percentage of configurations that could not be assigned to SAP, BTP, or DDH was lower, around 30%. The theoretical EXAFS spectra obtained from the BOMD simulations are in good agreement with the experimental data and confirm that model microsolvated environments accurately represent the near-solvation structure of these trivalent rare-earth ions. Moreover, this demonstrates that the faster dynamics of the first hydration shell can be studied separately from the dynamics of water exchange in the bulk aqueous solution.

Accuracy of Discrete-Continuum Solvation Model for Cations: A Benchmark Study

Metal ions play important roles in chemistry, biochemistry, and material sciences. Accurately modeling ion solvation is crucial for simulating ion-containing systems. There are different models for ion solvation in computational chemistry, such as the explicit model, continuum model, and discrete-continuum model. Compared to the explicit model and continuum model, the discrete-continuum model of solvation is a hybrid solvation model in which the first solvation shell is described explicitly, and the remainder of the bulk liquid is characterized by a continuum model, which provides an excellent balance between accuracy and computational costs. This work serves as a systematic benchmark of the discrete-continuum model for the solvation of cations with +2, +3, and +4 charges. The calculated hydration free energies (HFEs) of ions were compared to those obtained by the SMD continuum model alone and the available experimental data. The discrete-continuum model showed improved performance over the continuum model alone via a smaller overall error and more consistent performance. Experimentally observed trends, such as the Irving-Williams series, are generally reproduced. In contrast, greater overall error was obtained for Ln3+ ions, and the HFE trend along the Ln3+ series was more difficult to reproduce, indicating these ions are challenging to model by the discrete-continuum model and continuum model. Overall, the discrete-continuum model is recommended to calculate the HFEs of cations when experimental data are not available.

Cuboctahedral Pd13 as a spherical aromatic noble metal core: insights from a ligand-protected [Pd13(Tr)6]2+ cluster

Low-valent palladium nanoparticles are efficient species promoting catalytic activity and selectivity in a number of chemical reactions. Recently, an atom-centered cuboctahedral Pd13 motif has been characterized as a ligand-protected [Pd13(Tr)6]2+ cluster featuring a 1s2 superatomic shell structure. In this report, we describe the ligand-cluster of and endohedral-cage interaction in [Pd13(Tr)6]2+, which accounts for a favorable situation in the overall cluster. In addition, the spherical aromatic properties of the cluster were evaluated to understand the behavior of the ligand-protected Pd13 cluster core. Our results indicate a sizable interaction towards carbon-based ligands in an overall spherical aromatic cluster featuring a long-range shielding cone. Thus, [Pd13(Tr)6]2+ is rationalized as the first ligand-protected palladium cluster to date exhibiting spherical aromatic properties, serving as a stable building block for molecule-based materials or as a dopant in porous carbon materials.

Computational Design of Ligands for the Ir-Catalyzed C5-Borylation of Indoles through Tuning Dispersion Interactions

The indole moiety is ubiquitous in natural products and pharmaceuticals. C-H borylation of the benzenoid moiety of indoles is a challenging task, especially at the C5 position. We have combined computational and experimental studies to introduce multiple noncovalent interactions, especially dispersion, between the substrate and catalytic ligand to realize C5-borylation of indoles with high reactivity and selectivity. The successful computational predictions of new ligands should be suitable for ligand design in other transition-metal catalyzed reactions.

Extension of the D3 and D4 London dispersion corrections to the full actinides series

Efficient dispersion corrections are an indispensable component of modern density functional theory, semi-empirical quantum mechanical, and even force field methods. In this work, we extend the well established D3 and D4 London dispersion corrections to the full actinides series, francium, and radium. To keep consistency with the existing versions, the original parameterization strategy of the D4 model was only slightly modified. This includes improved reference Hirshfeld atomic partial charges at the ωB97M-V/ma-def-TZVP level to fit the required electronegativity equilibration charge (EEQ) model. In this context, we developed a new actinide data set called AcQM, which covers the most common molecular actinide compound space. Furthermore, the efficient calculation of dynamic polarizabilities that are needed to construct CAB6 dispersion coefficients was implemented into the ORCA program package. The extended models are assessed for the computation of dissociation curves of actinide atoms and ions, geometry optimizations of crystal structure cutouts, gas-phase structures of small uranium compounds, and an example extracted from a small actinide complex protein assembly. We found that the novel parameterizations perform on par with the computationally more demanding density-dependent VV10 dispersion correction. With the presented extension, the excellent cost-accuracy ratio of the D3 and D4 models can now be utilized in various fields of computational actinide chemistry and, e.g., in efficient composite DFT methods such as r2SCAN-3c. They are implemented in our freely available standalone codes (dftd4, s-dftd3) and the D4 version will be also available in the upcoming ORCA 6.0 program package.

Preferred Electric Field Mechanism for Frustrated Lewis Pair Reactivity

This study employs computational methods to investigate the mechanism of H2 activation by frustrated Lewis pair (FLP) species, including both intermolecular and intramolecular nitrothane/borane FLP systems. Previous studies have proposed two qualitative reactivity mechanism models to explain the facile cleavage of H2 by FLPs. The findings of this study support the electric field mechanism as the favorable pathway for H2 cleavage. Utilizing frontier molecular orbital theory and energy decomposition analysis, the study explores the electronic structure and nature of the reactions under an external electric field (EEF). Analysis using the activation strain model highlights the significant influence of geometrical deformation energies of FLPs on the activation barriers of H2 activation reactions. Computational results suggest that H2 activation by FLP molecules follows the electric field mechanism, indicating the potential of the FLP/EEF combination as an effective activator for inert molecules.

Condensed Matter Systems Exposed to Radiation: Multiscale Theory, Simulations, and Experiment

This roadmap reviews the new, highly interdisciplinary research field studying the behavior of condensed matter systems exposed to radiation. The Review highlights several recent advances in the field and provides a roadmap for the development of the field over the next decade. Condensed matter systems exposed to radiation can be inorganic, organic, or biological, finite or infinite, composed of different molecular species or materials, exist in different phases, and operate under different thermodynamic conditions. Many of the key phenomena related to the behavior of irradiated systems are very similar and can be understood based on the same fundamental theoretical principles and computational approaches. The multiscale nature of such phenomena requires the quantitative description of the radiation-induced effects occurring at different spatial and temporal scales, ranging from the atomic to the macroscopic, and the interlinks between such descriptions. The multiscale nature of the effects and the similarity of their manifestation in systems of different origins necessarily bring together different disciplines, such as physics, chemistry, biology, materials science, nanoscience, and biomedical research, demonstrating the numerous interlinks and commonalities between them. This research field is highly relevant to many novel and emerging technologies and medical applications.

Leveraging Limited Experimental Data with Machine Learning: Differentiating a Methyl from an Ethyl Group in the Corey-Bakshi-Shibata Reduction

We present a case study on how to improve an existing metal-free catalyst for a particularly difficult reaction, namely, the Corey-Bakshi-Shibata (CBS) reduction of butanone, which constitutes the classic and prototypical challenge of being able to differentiate a methyl from an ethyl group. As there are no known strategies on how to address this challenge, we leveraged the power of machine learning by constructing a realistic (for a typical laboratory) small, albeit high-quality, data set of about 100 reactions (run in triplicate) that we used to train a model in combination with a key-intermediate graph (of substrate and catalyst) to predict the differences in Gibbs activation energies ΔΔG‡ of the enantiomeric reaction paths. With the help of this model, we were able to select and subsequently screen a small selection of catalysts and increase the selectivity for the CBS reduction of butanone to 80% enantiomeric excess (ee), the highest possible value achieved to date for this substrate with a metal-free catalyst, thereby also exceeding the best available enzymatic systems (64% ee) and the selectivity with Corey's original catalyst (60% ee). This translates into a >50% improvement in relative ΔG‡ from 0.9 to 1.4 kcal mol-1. We underscore the transformative potential of machine learning in accelerating catalyst design because we rely on a manageable small data set and a key-intermediate graph representing a combination of catalyst and substrate graphs in lieu of a transition-state model. Our results highlight the synergy of synthetic chemistry and data-centric approaches and provide a blueprint for future catalyst optimization.

Characterization of Deformational Isomerization Potential and Interconversion Dynamics with Ultrafast X-ray Solution Scattering

Dimeric complexes composed of d8 square planar metal centers and rigid bridging ligands provide model systems to understand the interplay between attractive dispersion forces and steric strain in order to assist the development of reliable methods to model metal dimer complexes more broadly. [Ir2 (dimen)4]2+ (dimen = para-diisocyanomenthane) presents a unique case study for such phenomena, as distortions of the optimal structure of a ligand with limited conformational flexibility counteract the attractive dispersive forces from the metal and ligand to yield a complex with two ground state deformational isomers. Here, we use ultrafast X-ray solution scattering (XSS) and optical transient absorption spectroscopy (OTAS) to reveal the nature of the equilibrium distribution and the exchange rate between the deformational isomers. The two ground state isomers have spectrally distinct electronic excitations that enable the selective excitation of one isomer or the other using a femtosecond duration pulse of visible light. We then track the dynamics of the nonequilibrium depletion of the electronic ground state population─often termed the ground state hole─with ultrafast XSS and OTAS, revealing a restoration of the ground state equilibrium in 2.3 ps. This combined experimental and theoretical study provides a critical test of various density functional approximations in the description of bridged d8-d8 metal complexes. The results show that density functional theory calculations can reproduce the primary experimental observations if dispersion interactions are added, and a hybrid functional, which includes exact exchange, is used.

Local Energy Decomposition Analysis of London Dispersion Effects: From Simple Model Dimers to Complex Biomolecular Assemblies

ConspectusLondon dispersion (LD) forces are ubiquitous in chemistry, playing a pivotal role in a wide range of chemical processes. For example, they influence the structure of molecular crystals, the selectivity of organocatalytic transformations, and the formation of biomolecular assemblies. Harnessing these forces for chemical applications requires consistent quantification of the LD energy across a broad and diverse spectrum of chemical scenarios. Despite the great progress made in recent years in the development of experimental strategies for LD quantification, quantum chemical methods remain one of the most useful tools in the hand of chemists for the study of these weak interactions. Unfortunately, the accurate quantification of LD effects in complex systems poses many challenges for electronic structure theories. One of the problems stems from the fact that LD forces originate from long-range electronic dynamic correlation, and hence, their rigorous description requires the use of complex, highly correlated wave function-based methods. These methods typically feature a steep scaling with the system size, limiting their applicability to small model systems. Another core challenge lies in disentangling short-range from long-range dynamic correlation, which from a rigorous quantum mechanical perspective is not possible.In this Account, we describe our research endeavors in the development of broadly applicable computational methods for LD quantification in molecular chemistry as well as challenging applications of these schemes in various domains of chemical research. Our strategy lies in the use of local correlation theories to reduce the computational cost associated with complex electronic structure methods while providing at the same time a simple means of decomposition of dynamic correlation into its long-range and short-range components. In particular, the local energy decomposition (LED) scheme at the domain-based local pair natural orbital coupled cluster (DLPNO-CCSD(T)) level has emerged as a powerful tool in our research, offering a clear-cut quantitative definition of the LD energy that remains valid across a plethora of different chemical scenarios. Typical applications of this scheme are examined, encompassing protein-ligand interactions and reactivity studies involving many fragments and complex electronic structures. In addition, our research also involves the development of novel cost-effective methodologies, which exploit the LED definition of the LD energy, for LD energy quantification that are, in principle, applicable to systems with thousands of atoms. The Hartree-Fock plus London Dispersion (HFLD) scheme, correcting the HF interaction energy using an approximate CCSD(T)-based LD energy, is a useful, parameter-free electronic structure method for the study of LD effects in systems with hundreds of molecular fragments. However, the usefulness of the LED scheme reaches beyond providing an interpretation of the calculated DLPNO-CCSD(T) or DLPNO-MP2 interaction energies. For example, the dispersion energies obtained from the LED can be fruitfully used in order to parametrize semiempirical dispersion models. We will demonstrate this in the context of an emerging semiempirical method, namely, the Natural Orbital Tied Constructed Hamiltonian (NOTCH) method. NOTCH incorporates LED-derived LD energies and shows promising accuracy at a minimum amount of empiricism. Thus, it holds substantial promise for large and complex systems.

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.

Advances and Prospects in Understanding London Dispersion Interactions in Molecular Chemistry

London dispersion (LD) interactions are the main contribution of the attractive part of the van der Waals potential. Even though LD effects are the driving force for molecular aggregation and recognition, the role of these omnipresent interactions in structure and reactivity had been largely underappreciated over decades. However, in the recent years considerable efforts have been made to thoroughly study LD interactions and their potential as a chemical design element for structures and catalysis. This was made possible through a fruitful interplay of theory and experiment. This review highlights recent results and advances in utilizing LD interactions as a structural motif to understand and utilize intra- and intermolecularly LD-stabilized systems. Additionally, we focus on the quantification of LD interactions and their fundamental role in chemical reactions.

Unraveling Atomic Contributions to the London Dispersion Energy: Insights into Molecular Recognition and Reactivity

We present a general framework that enables quantification with atomic resolution of the overall London dispersion energy, which can be readily integrated with currently available energy decomposition schemes. This approach can be used to determine the contribution of individual atoms and functional groups to molecular recognition, conformational preferences, molecular stability, and reactivity. Its efficacy across diverse realms of molecular chemistry and biology is demonstrated with application to molecular balances in solution, asymmetric organocatalytic transformations, and a subcomplex of the F1FO ATP synthase.

Interception of Transient Allyl Radicals with Low-Valent Allylpalladium Chemistry: Tandem Pd(0/II/I)-Pd(0/II/I/II) Cycles in Photoredox/Pd Dual-Catalytic Enantioselective C(sp3)-C(sp3) Homocoupling

We present comprehensive computational and experimental studies on the mechanism of an asymmetric photoredox/Pd dual-catalytic reductive C(sp3)-C(sp3) homocoupling of allylic electrophiles. In stark contrast to the canonical assumption that photoredox promotes bond formation via facile reductive elimination from high-valent metal-organic species, our computational analysis revealed an intriguing low-valent allylpalladium pathway that features tandem operation of Pd(0/II/I)-Pd(0/II/I/II) cycles. Specifically, we propose that (i) the photoredox/Pd system enables the in situ generation of allyl radicals from low-valent Pd(I)-allyl species, and (ii) effective interception of the fleeting allyl radical by the chiral Pd(I)-allyl species results in the formation of an enantioenriched product. Notably, the cooperation of the two pathways highlights the bifunctional role of Pd(I)-allyl species in the generation and interception of transient allyl radicals. Moreover, the mechanism implies divergent substrate-activation modes in this homocoupling reaction, suggesting a theoretical possibility for cross-coupling. Combined, the current study offers a novel mechanistic hypothesis for photoredox/Pd dual catalysis and highlights the use of low-valent allylpalladium as a means to efficiently intercept radicals for selective asymmetric bond constructions.

Contributions of London Dispersion Forces to Solution-Phase Association Processes

ConspectusDespite their ubiquity and early discovery, London dispersion forces are often overlooked. This is due, in part, to the difficulty in assessing their contributions to molecular and polymeric structure, stability, properties, and reactivities. However, recent advances in modeling have revealed that dispersion interactions play an important role in many important chemical and biological processes. Experimental confirmation of their impact in solution has been challenging, leading to controversies about their relative importance.In the course of studying noncovalent interactions using molecular devices, our understanding and appreciation for the importance of dispersion interactions have evolved. This Account follows this intellectual journey by using examples from the literature. The goals are twofold: to describe recent advances in understanding the interaction and to provide guidance to researchers studying weak noncovalent interactions. However, first, the experimental methods for measuring the effects of dispersion interactions and the strategies for isolating their influence are described. These include the design of molecular devices to measure these weak noncovalent interactions and the strategies to disentangle the solvation, solvophobic, and dispersion components of the resulting equilibria.The literature examples are organized around five fundamental questions. (1) Do dispersion interactions have a measurable effect on solution equilibria? (2) To what extent do solvents attenuate or compensate for dispersion interactions? (3) To what extent do the solvation and solvophobic terms influence the dispersion equilibria? (4) Can we predict whether a system will form attractive dispersion or repulsive steric interactions? (5) Can the dispersion term be isolated and interrogated? We were often surprised by the answers to these questions. In each case, we describe how the systems were designed to address these questions and discuss possible interpretations of the results.While dispersion interactions in solution were weak (usually <1 kcal/mol), their influence on complexation and conformational equilibria can be observed and measured. This underscores the significance of these interactions in molecular recognition, coordination chemistry, reaction design, and catalysis. The solvent components of the dispersion equilibria can also be significant. Therefore, the isolation of the dispersion contributions from the solvation and solvophobic effects represents an ongoing challenge. The experimental studies also provide important benchmarks and offer valuable insights to help refine the next generation of computational solvent models.

Combined Spectroscopic, Thermodynamic, and Theoretical Approach for Detecting and Quantifying Hydrogen Bonding and Dispersion Interaction in Ionic Liquids

ConspectusIonic liquids (ILs) are attracting increasing interest in science and engineering due to their unique properties that can be tailored for specific applications. Clearly, a better understanding of their behavior on the microscopic scale will help to elucidate macroscopic fluid phenomena and thereby promote potential applications. The advantageous properties of these innovative fluids arise from the delicate balance of Coulomb interactions, hydrogen bonding, and dispersion forces. The development of these properties requires a fundamental understanding of the strength, location, and direction of the different types of interactions and their contribution to the overall phase behavior. Contrary to expectations, hydrogen bonding and dispersion interactions have a significant influence on the structure, dynamics, and phase behavior of ILs.The synergy between experimental and theoretical methods has now advanced to a stage where hydrogen bonds and dispersion effects as well as the competition between the two can be studied in detail. In this account, we demonstrate that a suitable combination of spectroscopic, thermodynamic, and theoretical methods enables the detection, dissection, and quantification of noncovalent interactions, even in complex systems such as ionic liquids. This approach encompasses far-infrared vibrational spectroscopy (FIR), various thermodynamic methods for determining enthalpies of vaporization, and quantum chemical techniques that allow us to switch dispersion contributions on or off when calculating the energies and spectroscopic properties of clusters.We briefly discuss these experimental and theoretical methods, before providing various examples illustrating how the mélange of Coulomb interaction, hydrogen bonds, and dispersion forces can be analyzed, and their individual contributions quantified. First, we demonstrated that both hydrogen bonding and dispersion interactions are manifested in the FIR spectra and can be quantified by observed shifts of characteristic spectral signatures. Through the selection of suitable protic ionic liquids (PILs) featuring anions with varying interaction strengths and alkyl chain lengths, we were able to demonstrate that dispersion interactions can compete with hydrogen bonding. The resultant transition enthalpy serves as a measure of the dispersion interaction. Contrary to expectations, PILs possess lower enthalpies of vaporization compared with aprotic ILs (AILs). The reason for this is simple: In protic ILs, ion pairs carry both the hydrogen bond and attractive dispersion between the cation and anion into the gas phase. By utilizing a well-curated set of protic ILs and molecular analogues, we successfully disentangled Coulomb interaction, hydrogen bonding, and dispersion interaction through purely thermodynamic methods.

The Decay of Dispersion Interaction and Its Remarkable Effects on the Kinetics of Activation Reactions Involving Alkyl Chains

The importance of dispersion interactions in many chemical processes is well recognized. It is known that the dispersion strength would decay with the increasing separation between the interacting groups; however, its effects on chemical reactivity have not been well understood. Here we reveal the decay law of dispersion interactions along the n-alkyl chain, its effective interaction ranges for common functional groups, and their remarkable effects on the kinetics of activation reactions involving alkyl chains. This is achieved by DLPNO-CCSD(T) calculations and the local energy decomposition analysis and is supported by experimental findings. In particular, our calculations indicate that the lifetime of alkyl-substituted cis-azobenzenes increases with the alkyl chain length but reaches a steady value when alkyl chains are longer than butyl groups, which is in satisfactory accordance with experimental measurements. We also propose a concise expression to describe the dispersion decay, which shows excellent agreement with our computed results.

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.

Accelerating σ-Bond Metathesis at Sn(II) Centers

Molecular main-group hydride catalysts are attractive as cheap and Earth-abundant alternatives to transition-metal analogues. In the case of the latter, specific steric and electronic tuning of the metal center through ligand choice has enabled the iterative and rational development of superior catalysts. Analogously, a deeper understanding of electronic structure-activity relationships for molecular main-group hydrides should facilitate the development of superior main-group hydride catalysts. Herein, we report a modular Sn-Ni bimetallic system in which we systematically vary the ancillary ligand on Ni, which, in turn, tunes the Sn center. This tuning is probed using Sn L1 XAS as a measure of electron density at the Sn center. We demonstrate that increased electron density at Sn centers accelerates the rate of σ-bond metathesis, and we employ this understanding to develop a highly active Sn-based catalyst for the hydroboration of CO2 using pinacolborane. Additionally, we demonstrate that engineering London dispersion interactions within the secondary coordination sphere of Sn allows for further rate acceleration. These results show that the electronics of main-group catalysts can be controlled without the competing effects of geometry perturbations and that this manifests in substantial reactivity differences.

An NMR Spectroscopy View on London Dispersion in Catalysis: Detection, Quantification, and Application in Ion Pair and Transition Metal Catalysis

ConspectusThe energetic contribution of London dispersion (LD) can cover a broad range from very few to hundreds of kJ mol-1 for extended interaction interfaces due to its pairwise additivity. However, for a designed and successful application of LD in chemical catalysis, there are still many obstacles and questions that remain. In principle, LD can be regarded as the attractive part of the van der Waals potential. Thus, considering the whole van der Waals potential, including the repulsive part (steric repulsion), the ideal solution to the problem in catalysis would be to design compatible interaction interfaces at exactly the correct distance. In the case of a self-assembled, flexible structure arrangement, entropic contributions and solvent interactions might be detrimental. In the case of a rigid catalyst pocket, steric hindrance might not allow for large substituents that are usually applied as dispersion energy donors (DEDs). For a working catalytic system, the following question arises: how is it possible to dissect the complex interaction interfaces in terms of energetic contributions? Usually, the energetic contribution of LD to catalysis is addressed by using calculations. However, adequately computing the correct energetic contributions can be extremely challenging for a vast conformational space with all kinds of intermolecular interactions. Thus, experimental data are essential for comparison or benchmarking.Therefore, in this Account, we describe our quest for detailed experimental data obtained via NMR spectroscopy to experimentally dissect and quantify LD in catalytic systems. In addition, we address the question of whether bulky substituents used as DEDs can be used in confined catalytic pockets. With the example of Pd phosphoramidite complexes, we show how it is possible to experimentally dissect and quantify the contribution of individual interaction areas in complicated transition metal complexes. Furthermore, a correlation between conformational rigidity and heterodimer preference clearly reveals that LD can only unfold its full potential in cases where entropic contributions are minimized. This finding can also explain the small contribution of LD in flexible and solvent-exposed molecular balances. In the field of Brønsted acid catalysis, we demonstrated that LD has a strong influence on the structures, stability, and populations of confined catalytic intermediates. LD is key for populating higher aggregates such as dimers. In addition, offsets between the experimental and computational results were observed and attributed to solvent-solute dispersion interactions. We studied the delicate interplay of attractive and repulsive interactions by adding bulky DED substituents onto a substrate, which can function as a molecular balance system. Intriguingly, the effect of LD on the free substrate was straightforwardly transferred onto the highly confined intermediates. Furthermore, this effect could even be read out in the enantioselectivities of the underlying reaction. This conceptualized a general approach regarding how LD can be used beneficially in catalysis to convert from moderate/good to excellent stereoselectivities. It showcased that bulky groups such as tert-butyl must not only be regarded as occupied volumes.

London Dispersion Effects on the Stability of Heavy Tetrel Molecules

London dispersion (LD) interactions, which stem from long-range electron correlations arising from instantaneously induced dipoles can occur between neighboring atoms or molecules, for example, between H atoms within ligand C-H groups. These interactions are currently of interest as a new method of stabilizing long bonds and species with unusual oxidation states. They can also limit reactivity by installing LD enhanced groups into organic frameworks or ligand substituents. Here, we address the most recent advances in the design of LD enhanced ligands, the sterically counterintuitive structures that can be generated and the consequences that these interactions can have on the structures and reactivity of sterically crowded heavy group 14 species.

Assessment of Density Functional Theory Methods for the Structural Prediction of Transition and Post-Transition Metal-Nucleic Acid Complexes

Understanding the structure of metal-nucleic acid systems is important for many applications such as the design of new pharmaceuticals, metal detection platforms, and nanomaterials. Herein, we explore the ability of 20 density functional theory (DFT) functionals to reproduce the crystal structure geometry of transition and post-transition metal-nucleic acid complexes identified in the Protein Data Bank and Cambridge Structural Database. The environmental extremes of the gas phase and implicit water were considered, and analysis focused on the global and inner coordination geometry, including the coordination distances. Although gas-phase calculations were unable to describe the structure of 12 out of the 53 complexes in our test set regardless of the DFT functional considered, accounting for the broader environment through implicit solvation or constraining the model truncation points to crystallographic coordinates generally afforded agreement with the experimental structure, suggesting that functional performance for these systems is likely due to the models rather than the methods. For the remaining 41 complexes, our results show that the reliability of functionals depends on the metal identity, with the magnitude of error varying across the periodic table. Furthermore, minimal changes in the geometries of these metal-nucleic acid complexes occur upon use of the Stuttgart-Dresden effective core potential and/or inclusion of an implicit water environment. The overall top three performing functionals are ωB97X-V, ωB97X-D3(BJ), and MN15, which reliably describe the structure of a broad range of metal-nucleic acid systems. Other suitable functionals include MN15-L, which is a cheaper alternative to MN15, and PBEh-3c, which is commonly used in QM/MM calculations of biomolecules. In fact, these five methods were the only functionals tested to reproduce the coordination sphere of Cu²⁺-containing complexes. For metal-nucleic acid systems that do not contain Cu²⁺, ωB97X and ωB97X-D are also suitable choices. These top-performing methods can be utilized in future investigations of diverse metal-nucleic acid complexes of relevance to biology and material science.

Binding of Nitriles and Isonitriles to V(III) and Mo(III) Complexes: Ligand vs Metal Controlled Mechanism

The synthesis and structures of nitrile complexes of V(N[^tBu]Ar)₃, 2 (Ar = 3,5-Me₂C₆H₃), are described. Thermochemical and kinetic data for their formation were determined by variable temperature Fourier transform infrared (FTIR), calorimetry, and stopped-flow techniques. The extent of back-bonding from metal to coordinated nitrile indicates that electron donation from the metal to the nitrile plays a less prominent role for 2 than for the related complex Mo(N[^tBu]Ar)₃, 1. Kinetic studies reveal similar rate constants for nitrile binding to 2, but the activation parameters depend critically on the nature of R in RCN. Activation enthalpies range from 2.9 to 7.2 kcal·mol^-1, and activation entropies from -9 to -28 cal·mol^-1·K^-1 in an opposing manner. Density functional theory (DFT) calculations provide a plausible explanation supporting the formation of a π-stacking interaction between a pendant arene of the metal anilide of 2 and the arene substituent on the incoming nitrile in favorable cases. Data for ligand binding to 1 do not exhibit this range of activation parameters and are clustered in a small area centered at ΔH^‡ = 5.0 kcal·mol^-1 and ΔS^‡ = -26 cal·mol^-1·K^-1. Computational studies are in agreement with the experimental data and indicate a stronger dependence on electronic factors associated with the change in spin state upon ligand binding to 1.

Uncovering the Mechanism of Azepino-Indole Skeleton Formation via Pictet-Spengler Reaction by Strictosidine Synthase: A Quantum Chemical Investigation

Strictosidine synthase (STR) catalyzes the Pictet-Spengler (PS) reaction of tryptamine and secologanin to produce strictosidine. Recent studies demonstrated that the enzyme can also catalyze the reaction of non-natural substrates to form new alkaloid skeletons. For example, the PS condensation of 1H-indole-4-ethanamine with secologanin could be promoted by the STR from Rauvolfia serpentina (RsSTR) to generate a rare class of skeletons with a seven-membered ring, namely azepino-[3,4,5-cd]-indoles, which are precursors for the synthesis of new compounds displaying antimalarial activity. In the present study, the detailed reaction mechanism of RsSTR-catalyzed formation of the rare seven-membered azepino-indole skeleton through the PS reaction was revealed at the atomic level by quantum chemical calculations. The structures of the transition states and intermediates involved in the reaction pathway were optimized, and the energetics of the complete reaction were analyzed. Based on our calculation results, the most likely pathway of the enzyme-catalyzed reaction was determined, and the rate-determining step of the reaction was clarified. The mechanistic details obtained in the present study are important in understanding the promiscuous activity of RsSTR in the formation of the rare azepino-indole skeleton molecule and are also helpful in designing STR enzymes for the synthesis of other new alkaloid skeleton molecules.

A Computational Study on the Reaction Mechanism of Stereocontrolled Synthesis of β-Lactam within [2]Rotaxane

The macrocycle effect of [2]rotaxane on the highly trans-stereoselective cyclization reaction of N-benzylfumaramide was extensively investigated by various computational methods, including DFT and high-level DLPNO-CCSD(T) methods. Our computational results suggest that the most favorable mechanism of the CsOH-promoted cyclization of the fumaramide into trans-β-lactam within [2]rotaxane initiates with deprotonation of a N-benzyl group of the interlocked fumaramide substrate by CsOH, followed by the trans-selective C-C bond formation and protonation by one amide functional group of the macrocycle. Our distortion/interaction analysis further shows that the uncommon trans-stereoselective cyclization forming β-lactam within the rotaxane may be attributed to a higher distortion energy (mainly from the distortion of the twisted cis-fumaramide conformation enforced by the rotaxane). Our systematic study should give deeper mechanistic insight into the reaction mechanism influenced by a supramolecular host.

On the potentially transformative role of auxiliary-field quantum Monte Carlo in quantum chemistry: A highly accurate method for transition metals and beyond

Approximate solutions to the ab initio electronic structure problem have been a focus of theoretical and computational chemistry research for much of the past century, with the goal of predicting relevant energy differences to within "chemical accuracy" (1 kcal/mol). For small organic molecules, or in general, for weakly correlated main group chemistry, a hierarchy of single-reference wave function methods has been rigorously established, spanning perturbation theory and the coupled cluster (CC) formalism. For these systems, CC with singles, doubles, and perturbative triples is known to achieve chemical accuracy, albeit at O(N7) computational cost. In addition, a hierarchy of density functional approximations of increasing formal sophistication, known as Jacob's ladder, has been shown to systematically reduce average errors over large datasets representing weakly correlated chemistry. However, the accuracy of such computational models is less clear in the increasingly important frontiers of chemical space including transition metals and f-block compounds, in which strong correlation can play an important role in reactivity. A stochastic method, phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC), has been shown to be capable of producing chemically accurate predictions even for challenging molecular systems beyond the main group, with relatively low O(N3 - N4) cost and near-perfect parallel efficiency. Herein, we present our perspectives on the past, present, and future of the ph-AFQMC method. We focus on its potential in transition metal quantum chemistry to be a highly accurate, systematically improvable method that can reliably probe strongly correlated systems in biology and chemical catalysis and provide reference thermochemical values (for future development of density functionals or interatomic potentials) when experiments are either noisy or absent. Finally, we discuss the present limitations of the method and where we expect near-term development to be most fruitful.

Benchmarking the quadrupolar coupling tensor for chlorine to probe weak-bonding interactions

Rotational spectroscopy relies on quantum chemical calculations to interpret observed spectra. Among the most challenging molecules to assign are those with additional angular momenta coupling to the rotation, contributing to the complexity of the spectrum. This benchmark study of computational methods commonly used by rotational spectroscopists targets the nuclear quadrupole coupling constants of chlorine containing molecules and the geometry of its complexes and clusters. For each method, the quality of both structural and electronic parameter predictions is compared with the experimental values. Ab initio methods are found to perform best overall in predicting both the geometry of the complexes and the coupling constants of chlorine with moderate computational cost. This cost can be reduced by combining these methods with density functional theory structure optimization, which still yields adequate predictions. This work constitutes a first step in expanding Bailey's quadrupole coupling data set to encompass molecular clusters. [W. C. Bailey, Calculation of Nuclear Quadrupole Coupling Constants in Gaseous State Molecule, 2019, https://nqcc.wcbailey.net/].

DFT calculations in solution systems: solvation energy, dispersion energy and entropy

DFT calculations of reaction mechanisms in solution have always been a hot topic, especially for transition-metal-catalyzed reactions. The calculation of solvation energy is performed using either the polarizable continuum model (PCM) or the universal solvation model SMD. The PCM calculation is very sensitive to the choice of atomic radii to form a cavity, where the self-consistent isodensity PCM (SCI-PCM) has been recognized as the best choice and our IDSCRF radii can provide a similar cavity. Moving from a gas-phase case to a solution case, dispersion energy and entropy should be carefully treated. The solvent-solute dispersion is also important in solution systems, and it should be calculated together with the solute dispersion. Only half of the solvent-solute dispersion energy from the PCM calculation belongs to the solute molecules to maintain a thermal equilibrium between a solute molecule and its cavity, similar to the treatment of electrostatic energy. Relative solute dispersion energy should also be shared equally with the newly formed cavity. The entropy change from a gas phase to a liquid phase is quite large, but the modern quantum chemistry programs can only calculate the gas-phase translational entropy based on the idea-gas equation. In this review, we will provide an operable method to calculate the solution translational entropy, which has been coded in our THERMO program.

A Combined Computational–Experimental Study on the Substrate Binding and Reaction Mechanism of Salicylic Acid Decarboxylase

Salicylic acid decarboxylase (SDC) from the amidohydrolase superfamily (AHS) catalyzes the reversible decarboxylation of salicylic acid to form phenol. In this study, the substrate binding mode and reaction mechanism of SDC were investigated using computational and crystallographic methods. Quantum chemical calculations show that the enzyme follows the general mechanism of AHS decarboxylases. Namely, the reaction begins with proton transfer from a metal-coordinated aspartic acid residue (Asp298 in SDC) to the C1 of salicylic acid, which is followed by the C–C bond cleavage, to generate the phenol product and release CO2. Interestingly, the calculations show that SDC is a Mg-dependent enzyme rather than the previously proposed Zn-dependent, and the substrate is shown to be bidentately coordinated to the metal center in the catalysis, which is also different from the previous proposal. These predictions are corroborated by the crystal structure of SDC solved in complex with the substrate analogue 2-nitrophenol. The mechanistic insights into SDC in the present study provide important information for the rational design of the enzyme.

Efficient Computation of the Interaction Energies of Very Large Non-covalently Bound Complexes

We present a new benchmark set consisting of 16 large non-covalently bound systems (LNCI16) ranging from 380 up to 1988 atoms and featuring diverse interaction motives. Gas-phase interaction energies are calculated with various composite DFT, semi-empirical quantum mechanical (SQM), and force field (FF) methods and are evaluated using accurate DFT reference values. Of the employed QM methods, PBEh-3c proves to be the most robust for large systems with a relative mean absolute deviation (relMAD) of 8.5% with respect to the reference interaction energies. r2SCAN-3c yields an even smaller relMAD, at least for the subset of complexes for which the calculation could be converged, but is less robust for systems with smaller HOMO–LUMO gaps. The inclusion of Fock-exchange is therefore important for the description of very large non-covalent interaction (NCI) complexes in the gas phase. GFN2-xTB was found to be the best performer of the SQM methods with an excellent result of only 11.1% deviation. From the assessed force fields, GFN-FF and GAFF achieve the best accuracy. Considering their low computational costs, both can be recommended for routine calculations of very large NCI complexes, with GFN-FF being clearly superior in terms of general applicability. Hence, GFN-FF may be routinely applied in supramolecular synthesis planning.

1 Introduction

2 The LNCI16 Benchmark Set

3 Computational Details

4 Generation of Reference Values

5 Results and Discussion

6 Conclusions

Structure-property relationships of photofunctional diiridium(II) complexes with tetracationic charge and an unsupported Ir-Ir bond

In contrast to the extensively studied dirhodium(II) complexes and iridium(III) complexes, neutral or dicationic dinuclear iridium(II) complexes with an unsupported ligand are underdeveloped. Here, a series of tetracationic dinuclear iridium(II) complexes, featuring the unsupported Ir(II)-Ir(II) single bond with long bond distances (2.8942(4)-2.9731(4) Å), are synthesized and structurally characterized. Interestingly, compared to the previous unsupported neutral or dicationic diiridium(II) complexes, our DFT and high-level DLPNO-CCSD(T) results found the largest binding energy in these tetracationic complexes even with the long Ir(II)-Ir(II) bond. Our study further reveals that London dispersion interactions enhance the stability cooperatively and significantly to overcome the strong electrostatic repulsion between two half dicationic metal fragments. This class of complexes also exhibit photoluminescence in solution and solid states, which, to our knowledge, represents the first example of this unsupported dinuclear iridium(II) system. In addition, their photoreactivity involving the generation of iridium(II) radical monomer from homolytic cleavage was also explored. The experimental results of photophysical and photochemical behaviours were also correlated with computational studies.

Photochemical Dearomative Cycloadditions of Quinolines and Alkenes: Scope and Mechanism Studies

Photochemical dearomative cycloaddition has emerged as a useful strategy to rapidly generate molecular complexity. Within this context, stereo- and regiocontrolled intermolecular para-cycloadditions are rare. Herein, a method to achieve photochemical cycloaddition of quinolines and alkenes is shown. Emphasis is placed on generating sterically congested products and reaction of highly substituted alkenes and allenes. In addition, the mechanistic details of the process are studied, which revealed a reversible radical addition and a selectivity-determining radical recombination. The regio- and stereochemical outcome of the reaction is also rationalized.

Simulating the solvation structure of low- and high-spin [Fe(bpy)3]2+: long-range dispersion and many-body effects

When characterizing transition metal complexes and their functionalities, the importance of including the solvent as an active participant is becoming more and more apparent. Whereas many studies have evaluated long-range dispersion effects inside organic molecules and organometallics, less is known about their role in solvation. Here, we have analysed the components within solute-solvent and solvent-solvent interactions of one of the most studied iron-based photoswitch model systems, in two spin states. We find that long-range dispersion effects modulate the coordination significantly, and that this is accurately captured by density functional theory models including dispersion corrections. We furthermore correlate gas-phase relaxed complex-water clusters to thermally averaged molecular densities. This shows how the gas-phase interactions translate to solution structure, quantified through 3D molecular densities, angular distributions, and radial distribution functions. We show that finite-size simulation cells can cause the radial distribution functions to have artificially enlarged amplitudes. Finally, we quantify the effects of many-body interactions within the solvent shells, and find that almost a fifth of the total interaction energy of the solute-shell system in the high-spin state comes from many-body contributions, which cannot be captured by by pair-wise additive force field methods.

Revisiting the Bonding Model for Gold(I) Species: The Importance of Pauli Repulsion Revealed in a Gold(I)-Cyclobutadiene Complex

Understanding the bonding of gold(I) species has been central to the development of gold(I) catalysis. Herein, we present the synthesis and characterization of the first gold(I)-cyclobutadiene complex, accompanied with bonding analysis by state-of-the-art energy decomposition analysis methods. Analysis of possible coordination modes for the new species not only confirms established characteristics of gold(I) bonding, but also suggests that Pauli repulsion is a key yet hitherto overlooked element. Additionally, we obtain a new perspective on gold(I)-bonding by comparison of the gold(I)-cyclobutadiene to congeners stabilized by p-, d-, and f-block metals. Consequently, we refine the gold(I) bonding model, with a delicate interplay of Pauli repulsion and charge transfer as the key driving force for various coordination motifs. Pauli repulsion is similarly determined as a significant interaction in AuI -alkyne species, corroborating this revised understanding of AuI bonding.

Beyond Steric Crowding: Dispersion Energy Donor Effects in Large Hydrocarbon Ligands

Interactions between sterically crowded hydrocarbon-substituted ligands are widely considered to be repulsive because of the intrusion of the electron clouds of the ligand atoms into each other's space, which results in Pauli repulsion. Nonetheless, there is another interaction between the ligands which is less widely publicized but is always present. This is the London dispersion (LD) interaction which can occur between atoms or molecules in which dipoles can be induced instantaneously, for example, between the H atoms from the ligand C-H groups.These LD interactions are always attractive, but their effects are not as widely recognized as those of the Pauli repulsion despite their central role in the formation of condensed matter. Their relatively poor recognition is probably due to the relative weakness (ca. 1 kcal mol^-1) of individual H···H interactions owing to their especially strong distance dependence. In contrast, where there are numerous H···H interactions, a collective LD energy equaling several tens of kcal mol^-1 may ensue. As a result, in some molecules the latent importance of the LD attraction energies emerges and assumes a prominence that can overshadow the Pauli effects (e.g., in the stabilization of high-oxidation-state transition-metal alkyls, inducing disproportionation reactions, or in the stabilization of otherwise unstable bonds).Despite being known for over a century, the accurate quantification of individual H···H LD effects in molecular species is a relatively recent phenomenon and at present is based mainly on modified DFT calculations. A few leading reviews summarized these earlier studies of the C-H···H-C LD interactions in organic molecules, and their effects on the structures and stabilities were described. LD effects in sterically crowded inorganic and organometallic molecules have been recognized.The author's interest in these LD effects arose fortuitously over a decade ago during research on sterically crowded heavier main-group element carbene analogues and two-coordinate, open-shell (d¹-d⁹) transition-metal complexes where counterintuitive steric effects were observed. More detailed explanations of these effects were provided by dispersion-corrected DFT calculations in collaboration with the groups of Tuononen and Nagase (see below).This Account describes our development of these initial results for other inorganic molecular classes. More recently, the work has led us to move to the planned inclusion of dispersion effects in ligands to stabilize new molecular types with theoretical input from the groups of Vasko and Grimme (see below). Our approach sought to use what Grimme has described as dispersion effect donor (DED) groups (i.e., spatially close-lying, densely packed substituents either as ligands (e.g., -C₆H₂-2,4,6-Cy₃, Cy = cyclohexyl) or as parts of ligands (e.g., a Cy substituent) that produce relatively large dispersion energies to stabilize these new compounds.We predict that the future design of sterically crowding hydrocarbon ligands will include the consideration and incorporation of LD effects as a standard methodology for directed use in the attainment of new synthetic targets.

New Insights and Predictions into Complex Homogeneous Reactions Enabled by Computational Chemistry in Synergy with Experiments: Isotopes and Mechanisms

Homogeneous catalysis and biocatalysis have been widely applied in synthetic, medicinal, and energy chemistry as well as synthetic biology. Driven by developments of new computational chemistry methods and better computer hardware, computational chemistry has become an essentially indispensable mechanistic "instrument" to help understand structures and decipher reaction mechanisms in catalysis. In addition, synergy between computational and experimental chemistry deepens our mechanistic understanding, which further promotes the rational design of new catalysts. In this Account, we summarize new or deeper mechanistic insights (including isotope, dispersion, and dynamical effects) into several complex homogeneous reactions from our systematic computational studies along with subsequent experimental studies by different groups. Apart from uncovering new mechanisms in some reactions, a few computational predictions (such as excited-state heavy-atom tunneling, steric-controlled enantioswitching, and a new geminal addition mechanism) based on our mechanistic insights were further verified by ensuing experiments.The Zimmerman group developed a photoinduced triplet di-π-methane rearrangement to form cyclopropane derivatives. Recently, our computational study predicted the first excited-state heavy-atom (carbon) quantum tunneling in one triplet di-π-methane rearrangement, in which the reaction rates and ¹²C/¹³C kinetic isotope effects (KIEs) can be enhanced by quantum tunneling at low temperatures. This unprecedented excited-state heavy-atom tunneling in a photoinduced reaction has recently been verified by an experimental ¹²C/¹³C KIE study by the Singleton group. Such combined computational and experimental studies should open up opportunities to discover more rare excited-state heavy-atom tunneling in other photoinduced reactions. In addition, we found unexpectedly large secondary KIE values in the five-coordinate Fe(III)-catalyzed hetero-Diels-Alder pathway, even with substantial C-C bond formation, due to the non-negligible equilibrium isotope effect (EIE) derived from altered metal coordination. Therefore, these KIE values cannot reliably reflect transition-state structures for the five-coordinate metal pathway. Furthermore, our density functional theory (DFT) quasi-classical molecular dynamics (MD) simulations demonstrated that the coordination mode and/or spin state of the iron metal as well as an electric field can affect the dynamics of this reaction (e.g., the dynamically stepwise process, the entrance/exit reaction channels).Moreover, we unveiled a new reaction mechanism to account for the uncommon Ru(II)-catalyzed geminal-addition semihydrogenation and hydroboration of silyl alkynes. Our proposed key gem-Ru(II)-carbene intermediates derived from double migrations on the same alkyne carbon were verified by crossover experiments. Additionally, our DFT MD simulations suggested that the first hydrogen migration transition-state structures may directly and quickly form the key gem-Ru-carbene structures, thereby "bypassing" the second migration step. Furthermore, our extensive study revealed the origin of the enantioselectivity of the Cu(I)-catalyzed 1,3-dipolar cycloaddition of azomethine ylides with β-substituted alkenyl bicyclic heteroarenes enabled by dual coordination of both substrates. Such mechanistic insights promoted our computational predictions of the enantioselectivity reversal for the corresponding monocyclic heteroarene substrates and the regiospecific addition to the less reactive internal C═C bond of one diene substrate. These predictions were proven by our experimental collaborators. Finally, our mechanistic insights into a few other reactions are also presented. Overall, we hope that these interactive computational and experimental studies enrich our mechanistic understanding and aid in reaction development.

Dispersion corrected r2SCAN based global hybrid functionals: r2SCANh, r2SCAN0, and r2SCAN50

The regularized and restored semilocal meta-generalized gradient approximation (meta-GGA) exchange-correlation functional r²SCAN [Furness et al., J. Phys. Chem. Lett. 11, 8208-8215 (2020)] is used to create three global hybrid functionals with varying admixtures of Hartree-Fock "exact" exchange (HFX). The resulting functionals r²SCANh (10% HFX), r²SCAN0 (25% HFX), and r²SCAN50 (50% HFX) are combined with the semi-classical D4 London dispersion correction. The new functionals are assessed for the calculation of molecular geometries, main-group, and metalorganic thermochemistry at 26 comprehensive benchmark sets. These include the extensive GMTKN55 database, ROST61, and IONPI19 sets. It is shown that a moderate admixture of HFX leads to relative improvements of the mean absolute deviations for thermochemistry of 11% (r²SCANh-D4), 16% (r²SCAN0-D4), and 1% (r²SCAN50-D4) compared to the parental semi-local meta-GGA. For organometallic reaction energies and barriers, r²SCAN0-D4 yields an even larger mean improvement of 35%. The computation of structural parameters (geometry optimization) does not systematically profit from the HFX admixture. Overall, the best variant r²SCAN0-D4 performs well for both main-group and organometallic thermochemistry and is better or on par with well-established global hybrid functionals, such as PW6B95-D4 or PBE0-D4. Regarding systems prone to self-interaction errors (SIE4x4), r²SCAN0-D4 shows reasonable performance, reaching the quality of the range-separated ωB97X-V functional. Accordingly, r²SCAN0-D4 in combination with a sufficiently converged basis set [def2-QZVP(P)] represents a robust and reliable choice for general use in the calculation of thermochemical properties of both main-group and organometallic chemistry.

Benchmark Study on the Calculation of 119Sn NMR Chemical Shifts

A new benchmark set termed SnS51 for assessing quantum chemical methods for the computation of ¹¹⁹Sn NMR chemical shifts is presented. It covers 51 unique ¹¹⁹Sn NMR chemical shifts for a selection of 50 tin compounds with diverse bonding motifs and ligands. The experimental reference data are in the spectral range of ±2500 ppm measured in seven different solvents. Fifteen common density functional approximations, two scalar- and one spin-orbit relativistic approach are assessed based on conformer ensembles generated using the CREST/CENSO scheme and state-of-the-art semiempirical (GFN2-xTB), force field (GFN-FF), and composite DFT methods (r²SCAN-3c). Based on the results of this study, the spin-orbit relativistic method combinations of SO-ZORA with PBE0 or revPBE functionals are generally recommended. Both yield mean absolute deviations from experimental data below 100 ppm and excellent linear regression determination coefficients of ≤0.99. If spin-orbit calculations are not affordable, the use of SR-ZORA with B3LYP or X2C with ωB97X or M06 may be considered to obtain qualitative predictions if no severe spin-orbit effects, for example, due to heavy nuclei containing ligands, are expected. An empirical linear scaling correction is demonstrated to be applicable for further improvement, and respective empirical parameters are given. Conformational effects on chemical shifts are studied in detail but are mostly found to be small. However, in specific cases when the ligand sphere differs substantially between conformers, chemical shifts can change by up to several hundred ppm.

Unveiling a key catalytic pocket for the ruthenium NHC-catalysed asymmetric heteroarene hydrogenation

The chiral ruthenium(ii)bis-SINpEt complex is a versatile and powerful catalyst for the hydrogenation of a broad range of heteroarenes. This study aims to provide understanding of the active form of this privileged catalyst as well as the reaction mechanism, and to identify the factors which control enantioselectivity. To this end we used computational methods and in situ NMR spectroscopy to study the hydrogenation of 2-methylbenzofuran promoted by this system. The high flexibility and conformational freedom of the carbene ligands in this complex lead to the formation of a chiral pocket interacting with the substrate in a "lock-and-key" fashion. The non-covalent stabilization of the substrate in this particular pocket is an exclusive feature of the major enantiomeric pathway and is preserved throughout the mechanism. Substrate coordination leading to the minor enantiomer inside this pocket is inhibited by steric repulsion. Rather, the catalyst exhibits a "flat" interaction surface with the substrate in the minor enantiomer pathway. We probe this concept by computing transition states of the rate determining step of this reaction for a series of different substrates. Our findings open up a new approach for the rational design of chiral catalysts.