Advances in Charge Displacement Analysis

Lessons from recent theoretical treatments of Al-M bonds (M = Fe, Cu, Ag, Au) that capture CO2

Complexes with Al-M bonds (M = transition metal) have emerged as platforms for discovering new reaction chemistry either through cooperative bond activation behaviour of the heterobinuclear unit or by modifying the properties of the M site through its interaction with the Al centre. Therefore, elucidating the nature of Al-M bonding is critical to advancing this research area and typically involves careful theoretical modelling. This Frontier article reviews selected recent case studies that included theoretical treatments of Al-M bonds, specifically highlighting complexes capable of cooperative CO2 activation and focusing on extracting lessons particular to the Al-M sub-field that will inform future studies with theoretical/computational components.

The Chemical Bond at the Bottom of the Periodic Table: The Case of the Heavy Astatine and the Super-Heavy Tennessine

In this work, we study the chemical bond in molecules containing heavy and super-heavy elements according to the current state-of-the-art bonding models. An Energy Decomposition Analysis in combination with Natural Orbital for Chemical Valence (EDA-NOCV) within the relativistic four-component Dirac-Kohn-Sham (DKS) framework is employed, which allows to successfully include the spin-orbit coupling (SOC) effects on the chemical bond description. Simple halogen-bonded adducts ClX⋯L (X=At, Ts; L=NH3, Br-, H2O, CO) of astatine and tennessine have been selected to assess a trend on descending along a group, while modulating the ClX⋯L bond features through the different electronic nature of the ligand L. Interesting effects caused by SOC have been revealed: i) a huge increase of the ClTs dipole moment (which is almost twice as that of ClAt), ii) a lowering of the ClX⋯L bonding energy arising from different contributions to the ClX…L interaction energy strongly depending on the nature of L, iii) a quenching of one of the π back-donation components to the bond. In the ClTs(CO) adduct, the back-donation from ClTs to CO becomes the most important component. The analysis of the electronic structure of the ClX dimers allows for a clear interpretation of the SOC effects in these systems.

Occupied-Virtual Orbitals for Chemical Valence with Applications to Charge Transfer in Energy Decomposition Analysis

In this article, we introduce the occupied-virtual orbitals for chemical valence (OVOCV). The OVOCVs can replace or complement the closely related idea of the natural orbitals for chemical valence (NOCV). The input is a difference density matrix connecting any initial single determinant to any final determinant, at a given molecular geometry, and a given one-particle basis. This arises in problems such as orbital rearrangement or charge transfer (CT) in energy decomposition analysis (EDA). The OVOCVs block-diagonalize the density difference operator into 2 × 2 blocks, which are spanned by one level that is filled in the initial state (the occupied OVOCV) and one that is empty (the virtual OVOCV). By contrast, the NOCVs fully diagonalize the density difference matrix and therefore are orbitals with mixed occupied-virtual character. Use of the OVOCVs makes it much easier to identify the donor and acceptor orbitals. We also introduce two different types of EDA methods with the OVOCVs and, most importantly, a charge decomposition analysis method that fixes the unreasonably large CT amount obtained directly from NOCV analysis. The square of the CT amount associated with each NOCV pair emerges as the appropriate value from the OVOCV analysis. When connecting the same initial and final states, this value is identical to the CT amount obtained from the independent absolutely localized molecular orbital (ALMO) complementary occupied-virtual orbital pair (COVP) analysis. The total, summed over all pairs, is also exactly the same as the independently suggested excitation number, as proved herein. Several examples are presented to compare NOCVs and OVOCVs: stretched H2+, a strong halogen bond between tetramethylthiourea and iodine, coordination of ethene in Zeise's salt, and binding in the Cp3La···C≡NCy complex.

Monomeric gold hydrides for carbon dioxide reduction: ligand effect on the reactivity

We analyzed the ligand electronic effect in the reaction between a [LAu(I)H]0/- hydride species and CO2, leading to a coordinated formate [LAu(HCOO)]0/-. We explored 20 different ligands, such as carbenes, phosphines and others, carefully selected to cover a wide range of electron-donor and -acceptor properties. We included in the study the only ligand, an NHC-coordinated diphosphene, that, thus far, experimentally demonstrated facile and reversible reaction between the monomeric gold(I) hydride and carbon dioxide. We elucidated the previously unknown reaction mechanism, which resulted to be concerted and common to all the ligands: the gold-hydrogen bond attacks the carbon atom of CO2 with one oxygen atom coordinating to the gold center. A correlation between the ligand σ donor ability, which affects the electron density at the reactive site, and the kinetic activation barriers of the reaction has been found. This systematic study offers useful guidelines for the rational design of new ligands for this reaction, while suggesting a few promising and experimentally accessible potential candidates for the stoichiometric or catalytic CO2 activation.

Cooperative small molecule activation by apolar and weakly polar bonds through the lens of a suitable computational protocol

Small molecule activation processes are central in chemical research and cooperativity is a valuable tool for the fine-tuning of the efficiency of these reactions. In this contribution, we discuss recent and remarkable examples in which activation processes are mediated by bimetallic compounds featuring apolar or weakly polar metal-metal bonds. Relevant experimental breakthroughs are thoroughly analyzed from a computational perspective. We highlight how the rational and non-trivial application of selected computational approaches not only allows rationalization of the observed reactivities but also inferring of general principles applicable to activation processes, such as the breakdown of the structure-reactivity relationship in carbon dioxide activation in a cooperative framework. We finally provide a simple yet unbiased computational protocol to study these reactions, which can support experimental advances aimed at expanding the range of applications of apolar and weakly polar bonds as catalysts for small molecule activation.

Yet another perspective on hole interactions, part II: lp-hole vs. lp-hole interactions

Most of the experimental and theoretical work in hole interactions (HIs) is mainly focused on exploiting the nature and characteristics of σ and π-holes. In this perspective, we focus our attention on understanding the origin and properties of lone-pair holes. These holes are present on an atom opposite to its lone-pair region. Utilizing some new and old examples, such as X₃N/P⋯F^- (X = F/Cl/Br/I), F-Cl/Br/I⋯H₃P⋯NCH and H₃B-NBr₃ along with other molecular systems, we explored to what extent these lp-holes participate in lp-hole interactions, if they participate at all.

Gold-Aluminyl and Gold-Diarylboryl Complexes: Bonding and Reactivity with Carbon Dioxide

The unconventional carbon dioxide insertion reaction of a gold-aluminyl [^tBu₃PAuAl(NON)] complex has been recently shown to be related to the electron-sharing character of the Au–Al bond that acts as a nucleophile and stabilizes the insertion product through a radical-like behavior. Since a gold-diarylboryl [IPrAuB(o-tol)₂] complex with similar reactivity features has been recently reported, in this work we computationally investigate the reaction of carbon dioxide with [LAuX] (L = phosphine, N-heterocyclic carbene (NHC); X = Al(NON), B(o-tol)₂) complexes to get insights into the Al/B anionic and gold ancillary ligand effects on the Au–Al/B bond nature, electronic structure, and reactivity of these compounds. We demonstrate that the Au–Al and Au–B bonds possess a similar electron-sharing nature, with diarylboryl complexes displaying a slightly more polarized bond as Au(δ⁺)–B(δ^–). This feature reduces the radical-like reactivity toward CO₂, and the Al/B anionic ligand effect is found to favor aluminyls over boryls, despite the greater oxophilicity of B. Remarkably, the ancillary ligand of gold has a negligible electronic trans effect on the Au–X bond and only a minor impact on the formation of the insertion product, which is slightly more stable with carbene ligands. Surprisingly, we find that the modification of the steric hindrance at the carbene site may exert a sizable control over the reaction, with more sterically hindered ligands thermodynamically disfavoring the formation of the CO₂ insertion product.

The Au−Al and Au−B bonds have both an electron-sharing nature, with the diarylboryl gold complexes displaying a more polarized Au^δ+−B^δ− bond. The gold ligand (phosphine or N-heterocyclic carbene) has a negligible electronic effect on the Au−X bond, consistently with a radical-like reactivity of the complexes with carbon dioxide, which favors the gold-aluminyl over the gold-diarylboryl complexes.

What Singles out Aluminyl Anions? A Comparative Computational Study of the Carbon Dioxide Insertion Reaction in Gold-Aluminyl, -Gallyl, and -Indyl Complexes

Anionic aluminum(I) anions ("aluminyls") are the most recent discovery along Group 13 anions, and the understanding of the unconventional reactivity they are able to induce at a coordinated metal site is at an early stage. A striking example is the efficient insertion of carbon dioxide into the Au-Al bond of a gold-aluminyl complex. The reaction occurs via a cooperative mechanism, with the gold-aluminum bond being the actual nucleophile and the Al site also behaving as an electrophile. In the complex, the Au-Al bond has been shown to be mainly of an electron-sharing nature, with the two metal fragments displaying a diradical-like reactivity with CO2. In this work, the analogous reactivity with isostructural Au-X complexes (X = Al, Ga, and In) is computationally explored. We demonstrate that a kinetically and thermodynamically favorable reactivity with CO2 may only be expected for the gold-aluminyl complex. The Au-Al bond nature, which features the most (nonpolar) electron-sharing character among the Group 13 anions analyzed here, is responsible for its highest efficiency. The radical-like reactivity appears to be a key ingredient to stabilize the CO2 insertion product. This investigation elucidates the special role of Al in these hetero-binuclear compounds, providing new insights into the peculiar electronic structure of aluminyls, which may help for the rational control of their unprecedented reactivity toward carbon dioxide.

Variational Energy Decomposition Analysis of Charge-Transfer Interactions between Metals and Ligands in Carbonyl Complexes

Variational energy decomposition analyses have been presented to quantify the σ-dative, ligand-to-metal forward charge transfer (CT) and the π-conjugative, metal-to-ligand backward charge delocalization on a series of isolelectronic transition-metal carbonyl complexes M(CO)₆, including M = Ti^2-, V^-, Cr, Mn⁺, and Fe²⁺. Although the qualitative features of these energy terms are understood, well-defined quantitative studies have been scarce. Consistent with early findings, electrostatic and Pauli exchange effects play a key role in σ-donation, resulting in blue shifts in ligand vibrational frequency in the complex geometries. Excluding chemical bonding interactions between the CO ligand and the metal fragments in the energy decomposition analysis, we found that loosely bound electrostatic complexes can be formed at a longer metal-to-ligand distance due to the exponential decay of Pauli exchange. In all complexes, the overall binding stabilization can be attributed to CT effects, with opposing trends between σ-donation and π-back bonding that follows an order of Ti^2- (4.4) > V^1- (2.6) > Cr (1.5) > Mn¹⁺ (1.1) > Fe²⁺ (0.5) in π-to-σ CT ratio. These electronic and energetic features are mirrored in the vibrational frequency shifts induced by different factors. The present investigation may help stimulate the use of energy decomposition techniques to understand the structure and activity of metallocatalysts using density functional theory.

Reactivity of a Gold-Aluminyl Complex with Carbon Dioxide: A Nucleophilic Gold?

A gold-aluminyl complex has been recently reported to feature an unconventional gold nucleophilic center, which was revealed through reactivity with carbon dioxide leading to the Au-CO₂ coordination mode. In this work, we computationally investigate the reaction mechanism, which is found to be cooperative, with the gold-aluminum bond being the actual nucleophile and Al also behaving as electrophile. The Au-Al bond is shown to be mainly of an electron-sharing nature, with the two metal fragments displaying a diradical-like reactivity with CO₂.

Comparison of Chemical and Interpretative Methods: the Carbon-Boron π-Bond as a Test Case*

Quantum chemical calculations and NBO, ETS-NOCV, QTAIM and ELF interpretative approaches have been carried out on C-donor ligand-stabilized dihydrido borenium cations. Numerous descriptors of the C-B π-bond strength obtained from orbital localization, energy partitioning or topological methods as well as from structural and chemical parameters have been calculated for 39 C-donor ligands including N-heterocyclic carbenes and carbones. Comparison of the results allows the identification of relative and absolute descriptors of the π interaction. For both families of descriptors excellent correlations are obtained. This enables the establishment of a π-donation capability scale and shows that the interpretative methods, despite their conceptual differences, describe the same chemical properties. These results also reveal noticeable shortcomings in these popular methods, and some precautions that need to be taken to interpret their results adequately.

Analysis and visualization of energy densities. II. Insights from linear-response time-dependent density functional theory calculations

Inspired by the analysis of Kohn-Sham energy densities by Nakai and coworkers, we extended the energy density analysis to linear-response time-dependent density functional theory (LR-TDDFT) calculations. Using ethylene-tetrafluoroethylene and oxyluciferin-water complexes as examples, distinctive distribution patterns were demonstrated for the excitation energy densities of local excitations (within a molecular fragment) and charge-transfer excitations (between molecular fragments). It also provided a simple way to compute the effective energy of both hot carriers (particle and hole) from charge-transfer excitations via an integration of the excitation energy density over the donor and acceptor grid points.

The role of the halogen bond in iodothyronine deiodinase: Dependence on chalcogen substitution in naphthyl-based mimetics

The effects on the activity of thyroxine (T4) due to the chalcogen replacement in a series of peri-substituted naphthalenes mimicking the catalytic function of deiodinase enzymes are computationally examined using density functional theory. In particular, T4 inner-ring deiodination pathways assisted by naphthyl-based models bearing two tellurols and a tellurol-thiol pair in peri-position are explored and compared with the analogous energy profiles for the naphthalene mimic having two selenols. The presence of a halogen bond (XB) in the intermediate formed in the first step and involved in the rate-determining step of the reaction is assumed to facilitate the process increasing the rate of the reaction. The rate-determining step calculated energy barrier heights allow rationalizing the experimentally observed superior catalytic activity of tellurium containing mimics. Charge displacement analysis is used to ascertain the presence and the role of the electron density charge transfer occurring in the rate-determining step of the reaction, suggesting the incipient formation or presence of a XB interaction. © 2019 Wiley Periodicals, Inc.

Influence of halogen bonding on gold(i)-ligand bond components and DFT characterization of a gold-iodine halogen bond

A gold(i) complex bearing nitrogen acyclic carbene (NAC) and selenourea (SeU) has been used to verify whether the second-sphere SeI halogen bond (XB) is able to modify the Dewar-Chatt-Duncanson components of the Au-C and Au-Se bonds. The chosen system was found to be thermically unstable but it allowed an in-depth theoretical study by means of Energy Decomposition Analysis, Natural Bond Orbital and Natural Orbitals for Chemical Valence methods, coupled with Charge Displacement analysis. Indeed, in the presence of iodoperfluoroalkanes as XB donors, iodine interacts with the lone pair of the coordinated selenium, enhancing the Au ← C σ donation and depressing the Au → C π back-donation, as demonstrated also by the increase of the rotational barrier of the C-N bond of the NAC (see G. Ciancaleoni and others, Chem. - Eur. J., 2015, 21, 2467). On the other hand, in the presence of N-iodosuccinimide (NIS), the gold directly establishes a XB with the iodine by using its d lone pairs. This AuI XB is favored by the low steric hindrance of the ligands coordinated to the gold and the presence of the amino protons of SeU, which establish additional hydrogen bonds with the NIS. Also in this case, the effect is to increase the σ acidity and decrease the π basicity of the metal.

Computational Ligand Descriptors for Catalyst Design

Ligands, especially phosphines and carbenes, can play a key role in modifying and controlling homogeneous organometallic catalysts, and they often provide a convenient approach to fine-tuning the performance of known catalysts. The measurable outcomes of such catalyst modifications (yields, rates, selectivity) can be set into context by establishing their relationship to steric and electronic descriptors of ligand properties, and such models can guide the discovery, optimization, and design of catalysts. In this review we present a survey of calculated ligand descriptors, with a particular focus on homogeneous organometallic catalysis. A range of different approaches to calculating steric and electronic parameters are set out and compared, and we have collected descriptors for a range of representative ligand sets, including 30 monodentate phosphorus(III) donor ligands, 23 bidentate P,P-donor ligands, and 30 carbenes, with a view to providing a useful resource for analysis to practitioners. In addition, several case studies of applications of such descriptors, covering both maps and models, have been reviewed, illustrating how descriptor-led studies of catalysis can inform experiments and highlighting good practice for model comparison and evaluation.

Interplay between Gold(I)-Ligand Bond Components and Hydrogen Bonding: A Combined Experimental/Computational Study

The influence of weak interactions on the donation/back-donation bond components in the complex [(NHC)Au(SeU)]⁺ (NHC = N-heterocyclic carbene; SeU = selenourea) has been studied by coupling experimental and theoretical techniques. In particular, NMR ¹H and pulsed-field gradient spin-echo titrations allowed us to characterize the hydrogen bond (HB) between the -NH₂ moieties of SeU and the anions PF₆ ^- and ClO₄ ^-, whereas ⁷⁷Se NMR spectroscopy allowed us to characterize the Au-Se bond. Theoretically, the Au-Se and Au-C orbital interactions have been decomposed using the natural orbital for the chemical valence framework and the bond components quantified through the charge displacement analysis. This methodology provides the quantification of the Dewar-Chatt-Duncanson (DCD) components for the Au-C and Au-Se bonds in the absence and presence of the second-sphere HB. The results presented here show that the anion has a dual mode action: it modifies the conformation of the cation by ion pairing (and this already influences the DCD components) and it induces new polarization effects that depend on the relative anion/cation relative orientation. The perchlorate polarizes SeU, enhancing the Se → Au σ donation and the Au → C back-donation and depressing the C → Au σ donation. On the contrary, the hexafluorophosphate depresses both the Se → Au and C → Au σ donations.

Lewis Base Activation of Lewis Acid: A Detailed Bond Analysis

The effect of a Lewis base (LB) on the nucleophilic attack on chalcogeniranium (chalcogen = sulfur and selenium) cations, the so-called LB activation of a Lewis acid, has been studied coupling natural orbital for chemical valence decomposition of the orbital interaction energy with charge displacement analysis. This methodology provides a detailed and accurate description of all the interactions (LB···chalcogen, chalcogen···olefin and olefin···ammonia) present in the system and leads to a deeper understanding of how they influence each other at all stages of the reaction: reactant complex, transition state, and product complex. In particular, the bond between the chalcogen and the olefin has been decomposed in terms of σ donation/π back-donation and the bond components quantified. This allowed determination of a linear relationship between the activation barrier of the nucleophilic attack and the net amount of charge donated by the olefin to the chalcogen.

Energy Decomposition Analysis with a Stable Charge-Transfer Term for Interpreting Intermolecular Interactions

Many schemes for decomposing quantum-chemical calculations of intermolecular interaction energies into physically meaningful components can be found in the literature, but the definition of the charge-transfer (CT) contribution has proven particularly vexing to define in a satisfactory way and typically depends strongly on the choice of basis set. This is problematic, especially in cases of dative bonding and for open-shell complexes involving cation radicals, for which one might expect significant CT. Here, we analyze CT interactions predicted by several popular energy decomposition analyses and ultimately recommend the definition afforded by constrained density functional theory (cDFT), as it is scarcely dependent on basis set and provides results that are in accord with chemical intuition in simple cases, and in quantitative agreement with experimental estimates of the CT energy, where available. For open-shell complexes, the cDFT approach affords CT energies that are in line with trends expected based on ionization potentials and electron affinities whereas some other definitions afford unreasonably large CT energies in large-gap systems, which are sometimes artificially offset by underestimation of van der Waals interactions by density functional theory. Our recommended energy decomposition analysis is a composite approach, in which cDFT is used to define the CT component of the interaction energy and symmetry-adapted perturbation theory (SAPT) defines the electrostatic, polarization, Pauli repulsion, and van der Waals contributions. SAPT/cDFT provides a stable and physically motivated energy decomposition that, when combined with a new implementation of open-shell SAPT, can be applied to supramolecular complexes involving molecules, ions, and/or radicals.