Formation of Agostic Structures Driven by London Dispersion

Electron Density and Molecular Orbital Analyses of the Nature of Bonding in the η3-CCH Agostic Rhodium Complexes Preceding the C-C and C-H Bond Cleavages

In our recent work, we revisited C-H and C-C bond activation in rhodium (I) complexes of pincer ligands PCP, PCN, PCO, POCOP, and SCS. Our findings indicated that an η3-Csp2Csp3H agostic intermediate acts as a common precursor to both C-C and C-H bond activation in these systems. We explore the electronic structure and bonding nature of these precleavage complexes using electron density and molecular orbital analyses. Using NBO, IBO, and ESI-3D methods, the bonding in the η3-CCH agostic moiety is depicted by two three-center agostic bonds: Rh-Csp2-Csp3 and Rh-Csp3-H, with all three atoms datively bound to Rh(I). IBO analysis specifically highlights the involvement of three orbitals (CC→Rh and CH→Rh σ donation, plus Rh→CCH π backdonation) in both C-C and C-H bond cleavages. NCIPLOT and QTAIM analyses highlight anagostic (Rh-H) or β-agostic (Rh-Csp2-H) interactions and the absence of Rh-Csp3 interactions. QTAIM molecular graphs suggest bond path instability under dynamic conditions due to the nearness of line and ring critical points. Several low-frequency and low-force vibrational modes interconvert various bonding patterns, reinforcing the dynamic η3-CCH agostic nature. The kinetic preference for C-H bond breaking is attributed to the smaller reduced mass of C-H vibrations compared to C-C vibrations.

Theoretical Description of Hydride-hydride Interactions in Selected Hydrogen Storage Materials

In recent years there has been growing interest in the use of metal hydrides as hydrogen rich sources. The high content of hydride-hydride contacts Hδ-⋅⋅⋅δ-H in these materials appears to be relevant for hydrogen formation. At present time there is no consensus whether these contacts are attractive or repulsive. Accordingly, the main goal of this article is to shed light on physical factors which constitute homopolar hydride-hydride interactions Hδ-⋅⋅⋅δ-H in selected transition metal complexes i. e. HCoL4, L=CO,PPh3,PH3. In order to achieve this goal, the charge and energy decomposition ETS-NOCV approach along with the Interacting Quantum Atoms (IQA) and reduced density gradient (NCI) are applied for the bonded adducts L4CoH⋅⋅⋅HCoL4. Based on DFT and correlated methods it has been shown, contrary to classical interpretations, that hydride-hydride interactions might be attractive and even far stronger than classical hydrogen bonds. The stability of the adducts is increased by phosphine ligand installation: overall Hδ-⋅⋅⋅δ-H bonding energy changes in the order: CO≪PPh3~PH3. It has been revealed that depending on monomer's conformations Hδ-⋅⋅⋅δ-H bonds are dominated by charge delocalization or London dispersion forces and the electrostatic term is also relevant. The side carbonyl ligands additionally stabilize the Hδ-⋅⋅⋅δ-H bonded structures through covalent charge delocalizations and Coulombic contributors. Furthermore, the sterically crowded systems containing bulky phosphine ligands are supported by π⋅⋅⋅π stacking, C-H⋅⋅⋅π and C-H⋅⋅⋅H-Co. It is finally determined by IQA energy decomposition, that diatomic hydride-hydride interaction CoH⋅⋅⋅HCo is chameleon-like, namely, it is attractive in CO4CoH⋅⋅⋅HCoCO4 and (PH3)4CoH⋅⋅⋅HCo(PH3)4, whereas the repulsion is unveiled in (CO)3(PPh3)CoH⋅⋅⋅HCo(CO)3(PPh3) where the monomers are of Cs symmetry.

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.

Efficient Method for Numerical Calculations of Molecular Vibrational Frequencies by Exploiting Sparseness of Hessian Matrix

Molecular vibrational frequency analysis plays an important role in theoretical and computational chemistry. However, in many cases, the analytical frequencies are unavailable, whereas frequency calculations using conventional numerical methods are very expensive. In this work, we propose an efficient method to numerically calculate the frequencies. Our main strategies are to exploit the sparseness of the Hessian matrix and to construct the N-fold two-variable potential energy surfaces to fit the parabola parameters, which are later used for the construction of Hessian matrices. A set of benchmark calculations is performed for typical molecules of different sizes and complexities using the proposed method. The obtained frequencies are compared to those calculated with the analytical methods and conventional numerical methods. It is shown that the results yielded with the new method are in very good agreement with corresponding accurate values (with a maximum error of ∼20 cm-1), while the required computation resource is largely reduced compared to that required by conventional numerical methods. For medium-sized molecules, the calculational scaling is lowered to O(N1.6) (this work) from that of O(N2) (conventional numerical methods). For even larger molecules, more computational savings can be achieved, and the scaling is estimated to be quasilinear with respect to the molecular size.

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.

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.

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.

Tilting the Balance: London Dispersion Systematically Enhances Enantioselectivities in Brønsted Acid Catalyzed Transfer Hydrogenation of Imines

London dispersion (LD) is attracting more and more attention in catalysis since LD is ubiquitously present and cumulative. Since dispersion is hard to grasp, recent research has concentrated mainly on the effect of LD in individual catalytic complexes or on the impact of dispersion energy donors (DEDs) on balance systems. The systematic transfer of LD effects onto confined and more complex systems in catalysis is still in its infancy, and no general approach for using DED residues in catalysis has emerged so far. Thus, on the example of asymmetric Brønsted acid catalyzed transfer hydrogenation of imines, we translated the findings of previously isolated balance systems onto confined catalytic intermediates, resulting in a systematic enhancement of stereoselectivity when employing DED-substituted substrates. As the imine substrate is present as Z- and E-isomers, which can, respectively, be converted to R- and S-product enantiomers, implementing tert-butyl groups as DED residues led to an additional stabilization of the Z-imine by up to 4.5 kJ/mol. NMR studies revealed that this effect is transferred onto catalyst/imine and catalyst/imine/nucleophile intermediates and that the underlying reaction mechanism is not affected. A clear correlation between ee and LD stabilization was demonstrated for 3 substrates and 10 catalysts, allowing to convert moderate-good to good-excellent enantioselectivities. Our findings conceptualize a general approach on how to beneficially employ DED residues in catalysis: they clearly showcase that bulky alkyl residues such as tert-butyl groups must be considered regarding not only their repulsive steric bulk but also their attractive properties even in catalytic complexes.

Evidence for πCHR→dM bonding in transition metal carbene compounds (LnMCHR) and its decisive role in the α-agostic effect

It has been generally recognized that the α-agostic interaction (M⋯H-C) in transition metal carbene compounds L_nMCHR (R = H, Me etc.) can be interpreted with a double metal-carbon bonding model. This bonding model involves the reorganization of the σ component, which can be illustrated in terms of three-center two-electron (3c-2e) M-H-C covalent bond as in transition metal alkyl compounds. Herein, we propose an alternative partial triple metal-carbon bonding model to elucidate the agostic interaction in L_nMCHR. Apart from the well-defined σ and π bonds, there exists a seemingly weak but decisive third force, namely the π_CHR→d_M bonding between an occupied π-like symmetric CHR orbital and a vacant metal d orbital, which is the true origin of the α-agostic effect. This partial triple bonding model is authenticated on both Fischer- and Schrock-type carbenes by an ab initio valence bond (VB) method or the block-localized wavefunction (BLW) method, which has the capability to quantify this notable π bonding and further demonstrate its geometric, energetic and spectral impacts on agostic transition metal carbene compounds. We also show that ancillary ligands can modulate the π_CHR→d_M bonding through electronic and steric effects.

Coordination-Induced Weakening of a C(sp3)-H Bond: Homolytic and Heterolytic Bond Strength of a CH-Ni Agostic Interaction

The scission of a C(sp³)-H bond to form a new metal-alkyl bond is a fundamental step in coordination chemistry and catalysis. However, the extent of C-H bond weakening when this moiety interacts with a transition metal is poorly understood and quantifying this phenomenon could provide insights into designing more efficient C-H functionalization catalysts. We present a nickel complex with a robust adamantyl reporter ligand that enables the measurement of C-H acidity (pK_a) and bond dissociation free energy (BDFE) for a C(sp³)-H agostic interaction, showing a decrease in pK_a by dozens of orders of magnitude and BDFE decrease of about 30 kcal/mol upon coordination. X-ray crystallographic data is provided for all molecules, including a distorted square planar Ni^III metalloradical and "doubly agostic" Ni^II(κ²-CH₂) complex.

Identifying molecular structural features by pattern recognition methods

Identification of molecular structural features is a central part of computational chemistry. It would be beneficial if pattern recognition techniques could be incorporated to facilitate the identification. Currently, the quantification of the structural dissimilarity is mainly carried out by root-mean-square-deviation (RMSD) calculations such as in molecular dynamics simulations. However, the RMSD calculation underperforms for large molecules, showing the so-called "curse of dimensionality" problem. Also, it requires consistent ordering of atoms in two comparing structures, which needs nontrivial effort to fulfill. In this work, we propose to take advantage of the point cloud recognition using convex hulls as the basis to recognize molecular structural features. Two advantages of the method can be highlighted. First, the dimension of the input data structure is largely reduced from the number of atoms of molecules to the number of atoms of convex hulls. Therefore, the dimensionality curse problem is avoided, and the atom ordering process is saved. Second, the construction of convex hulls can be used to define new molecular descriptors, such as the contact area of molecular interactions. These new molecular descriptors have different properties from existing ones, therefore they are expected to exhibit different behaviors for certain machine learning studies. Several illustrative applications have been carried out, which provide promising results for structure-activity studies.

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.

Open-Shell Variant of the London Dispersion-Corrected Hartree-Fock Method (HFLD) for the Quantification and Analysis of Noncovalent Interaction Energies

The London dispersion (LD)-corrected Hartree–Fock (HF) method (HFLD) is an ab initio approach for the quantification and analysis of noncovalent interactions (NCIs) in large systems that is based on the domain-based local pair natural orbital coupled-cluster (DLPNO-CC) theory. In the original HFLD paper, we discussed the implementation, accuracy, and efficiency of its closed-shell variant. Herein, an extension of this method to open-shell molecular systems is presented. Its accuracy is tested on challenging benchmark sets for NCIs, using CCSD(T) energies at the estimated complete basis set limit as reference. The HFLD scheme was found to be as accurate as the best-performing dispersion-corrected exchange-correlation functionals, while being nonempirical and equally efficient. In addition, it can be combined with the well-established local energy decomposition (LED) for the analysis of NCIs, thus yielding additional physical insights.

Partial Double Metal-Carbon Bonding Model in Transition Metal Methyl Compounds

The chemical bond between a transition metal and a methyl group (M-CH₃) is typically defined as a single covalent bond, which is of fundamental significance and general interest in understanding the structural properties and reactivity of transition metal alkyl compounds. Herein, we demonstrate that the M-CH₃ bonding involves varying σ and π components and thus should be best described in terms of the partial double M═CH₃ bond. The often-neglected π bonding stems from an occupied π-symmetric orbital of the methyl group comprising all three C-H σ bonds (but one C-H' contributes more than the other two) and a vacant low-lying metal d(π) orbital, and is associated with the intramolecular C-H'···M agostic effect (i.e., an acute M-C-H' angle and a short H'···M distance), whose origin is still controversial. We quantify the geometric and energetic impacts of the π interaction involved in the M-CH₃ bond by explicitly computing the intramolecular π_CH' → d_M interaction with the ab initio valence bond (VB) theory. Our computations of the ligand-free [TiCH₃]³⁺ and a series of metallocene catalysts provide a direct proof for the presence of the π bonding in M-CH₃ bonds, which is the cause for the agostic effect. The partial double M═CH₃ bonding model is not only validated by a range of bonding analyses including VB self-consistent field (VBSCF)-based energy decomposition and quantum theory of atoms in molecules (QTAIM) but also authenticated by the specific activity of double M═CH₃ bonds in the C-H activation and olefin insertion. More importantly, the σ bond gradually switches from a classical covalent bond to a novel charge-shift bond with the π bonding becoming increasingly significant. We anticipate that the recognition of the π interaction between electrophilic metal centers and C-H bonds can benefit the understanding of the nature of metal-carbon bonds in transition metal ethyl, alkyl, and carbene compounds.

Molecular structure recognition by blob detection

Molecular structure recognition is fundamental in computational chemistry. The most common approach is to calculate the root mean square deviation (RMSD) between two sets of molecular coordinates. However, this method does not perform well for large molecules. In this work, a new method is proposed for structure comparison. Blob detection is used for recognizing structural features. Fragmentation of molecules is proposed as the pre-treatment. Mapping between blobs and atoms is developed as the post-treatment. A set of key parameters important for blob detections are determined. The dissimilarity is quantified by calculating the Euclidean metric of the blob vectors. The overall algorithm is found to be accurate to distinguish structural dissimilarity. The method has potential to be combined with other pattern recognition techniques for new chemistry discoveries.

Molecular structure recognition is fundamental in computational chemistry.

Noncovalent Interactions in Organometallic Chemistry: From Cohesion to Reactivity, a New Chapter

Noncovalent interactions (NCIs) have long interested a vast community of chemists who investigated their "canonical categories" derived from descriptive crystallography, e.g., H-bonds, π-π interactions, halogen/chalcogen/tetrel bonds, cation-π and C-H-π interactions, metallophilic interactions in the broad sense, etc. Recent developments in theoretical chemistry have enabled the treatment of noncovalent interactions under new auspices: dispersion-force-inclusive density functionals have emerged, which are reliable for modeling small to large molecular systems. It is possible to perform the full analysis of the contributions of London, Debye, and Keesom forces, i.e., the main components of van der Waals forces, by the DFT-D and ab initio methods at a reasonable computational cost. Our research has been focusing for now 15 years on the role of NCIs in the cohesion of organometallic complexes. NCIs are not only effective in Werner's secondary coordination sphere but also in the metal's primary one. The stabilization of electron-unsaturated transition metal complexes by hemichelation, metal-metal donor-acceptor complexes, and self-aggregation of cationic Rh(I) chromophores have indeed outlined the significance of the London dispersion force as an attractive force operating throughout the whole molecule or molecular assembly. The recent outburst of interest in C-H bond functionalization led us to address the broader question of reaction and catalyst engineering: although one can now satisfactorily analyze bonding and molecular cohesion in transition-metal-based organometallic systems, can modern theoretical methods guide reactivity exploration and the engineering of novel catalytic systems? We addressed this question by investigating the ambiphilic metal-ligand activation/concerted metalation-deprotonation mechanism involved in transition-metal-catalyzed directed C-H bond functionalization. This endeavor was initiated having in scope the construction of a rationale for the transposition of 4-5d metal chemistry to earth-abundant 3d metals. In this base-assisted mechanism of C-H bond metalation, agostic interactions are necessary but not sufficient because C-H bond breaking actually relies on the attractive NCI coding of a proton-transfer step and the minimization of metal-H repulsion. This Account introduces the recent shift of our research toward the construction of an NCI-inclusive paradigm of chemical reactivity engineering based on experimental efforts propped up by state-of-the-art theoretical tools.

Unveiling the complex pattern of intermolecular interactions responsible for the stability of the DNA duplex

Herein, we provide new insights into the intermolecular interactions responsible for the intrinsic stability of the duplex structure of a large portion of human B-DNA by using advanced quantum mechanical methods. Our results indicate that (i) the effect of non-neighboring bases on the inter-strand interaction is negligibly small, (ii) London dispersion effects are essential for the stability of the duplex structure, (iii) the largest contribution to the stability of the duplex structure is the Watson-Crick base pairing - consistent with previous computational investigations, (iv) the effect of stacking between adjacent bases is relatively small but still essential for the duplex structure stability and (v) there are no cooperativity effects between intra-strand stacking and inter-strand base pairing interactions. These results are consistent with atomic force microscope measurements and provide the first theoretical validation of nearest neighbor approaches for predicting thermodynamic data of arbitrary DNA sequences.

C-H Bond Activation by the Excited Zinc Atom: Gas-Phase Formation of Methylzinc Hydride (HZnCH3) Based on Multireference Second-Order Perturbation Theory and Coupled Cluster Calculations

The pioneering spectroscopic observations of the methylzinc hydride [HZnCH₃(X¹A₁)] molecule were reported previously by the Ziurys group [J. Am. Chem. Soc. 2010, 132, 17186-17192], and the possible formation mechanisms were suggested therein, including those with the participation of excited zinc atoms in reaction with methane. Herein, the ground singlet state and the lowest excited triplet state potential energy surfaces of the Zn + CH₄ reaction have been explored using high-level electronic structure calculations with multireference second-order perturbation theory and coupled cluster singles and doubles with perturbative triples (CCSD(T)) methods in conjunction with all-electron basis sets (up to aug-cc-pV5Z) and scalar relativistic effects incorporated via the second-order Douglas-Kroll-Hess (DK) method. Based on the ab initio results, a plausible scenario for the formation of HZnCH₃(X¹A₁) is proposed involving the activation of the C-H bond of methane by the lowest excited ³P state atomic zinc. Calculations also highlight the importance of an agostic-like Zn···H-C interactions in the pre-activation complex and good agreement between the structure of the HZnCH₃(X¹A₁) molecule predicted at the DK-CCSD(T)/aug-cc-pVQZ-DK level of theory and that derived from rotational spectroscopy, as well as the discrepancies between the ab initio and density functional theory predictions.

An isolable, crystalline complex of square-planar silicon(IV)

The structure and reactivity of silicon(IV), the second most abundant element in our Earth's crust, is determined by its invariant tetrahedral coordination geometry. Silicon(IV) with a square-planar configuration (ptSi ^IV ) represents a transition state. Quantum theory supported the feasibility of stabilizing ptSi ^IV by structural constraint, but its isolation has not been achieved yet. Here, we present the synthesis and full characterization of the first square-planar coordinated silicon(IV). The planarity provokes an extremely low-lying unoccupied molecular orbital that induces unusual silicon redox chemistry and CH-agostic interactions. The small separation of the frontier molecular orbitals enables visible-light ligand-element charge transfer and bond-activation reactivity. Previously, such characteristics have been reserved for d-block metals or low-valent p-block elements. Planarization transfers them, for the first time, to a p-block element in the normal valence state.

Solvent-Induced Formation of Novel Ni(II) Complexes Derived from Bis-Thiosemicarbazone Ligand: An Insight from Experimental and Theoretical Investigations

In this work, we report solvent-induced complexation properties of a new N₂S₂ tetradentate bis-thiosemicarbazone ligand (H₂L^I), prepared by the condensation of 4-phenylthiosemicarbazide with bis-aldehyde, namely 2,2'-(ethane-1,2-diylbis(oxy)dibenzaldehyde, towards nickel(II). Using ethanol as a reaction medium allowed the isolation of a discrete mononuclear homoleptic complex [NiL^I] (1), for which its crystal structure contains three independent molecules, namely 1-I, 1-II, and 1-III, in the asymmetric unit. The doubly deprotonated ligand L^I in the structure of 1 is coordinated in a cis-manner through the azomethine nitrogen atoms and the thiocarbonyl sulfur atoms. The coordination geometry around metal centers in all the three crystallographically independent molecules of 1 is best described as the seesaw structure. Interestingly, using methanol as a reaction medium in the same synthesis allowed for the isolation of a discrete mononuclear homoleptic complex [Ni(L^II)₂] (2), where L^II is a monodeprotonated ligand 2-(2-(2-(2-(dimethoxymethyl)phenoxy)ethoxy)benzylidene)-N-phenylhydrazine-1-carbothioamide (HL^II). The ligand L^II was formed in situ from the reaction of L^I with methanol upon coordination to the metal center under synthetic conditions. In the structure of 2, two ligands L^II are coordinated in a trans-manner through the azomethine nitrogen atom and the thiocarbonyl sulfur atom, also yielding a seesaw coordination geometry around the metal center. The charge and energy decomposition scheme ETS-NOCV allows for the conclusion that both structures are stabilized by a bunch of London dispersion-driven intermolecular interactions, including predominantly N-H∙∙∙S and N-H∙∙∙O hydrogen bonds in 1 and 2, respectively; they are further augmented by less typical C-H∙∙∙X (where X = S, N, O, π), CH∙∙∙HC, π∙∙∙π stacking and the most striking, attractive long-range intermolecular C-H∙∙∙Ni preagostic interactions. The latter are found to be determined by both stabilizing Coulomb forces and an exchange-correlation contribution as revealed by the IQA energy decomposition scheme. Interestingly, the analogous long-range C-H∙∙∙S interactions are characterized by a repulsive Coulomb contribution and the prevailing attractive exchange-correlation constituent. The electron density of the delocalized bonds (EDDB) method shows that the nickel(II) atom shares only ~0.8|e| due to the σ-conjugation with the adjacent in-plane atoms, demonstrating a very weak σ-metalloaromatic character.

Supramolecular structures of NiII and CuII with the sterically demanding Schiff base dyes driven by cooperative action of preagostic and other non-covalent interactions

This work reports on synthesis and extensive experimental and theoretical investigations on photophysical, structural and thermal properties of the NiII and CuII discrete mononuclear homoleptic complexes [Ni(L I,II)2] and [Cu(L I,II)2] fabricated from the Schiff base dyes o-HOC6H4-CH=N-cyclo-C6H11 (HL I) and o-HOC10H6-CH=N-cyclo-C6H11 (HL II), containing the sterically crowding cyclo-hexyl units. The six-membered metallocycles adopt a clearly defined envelope conformation in [Ni(L II)2], while they are much more planar in the structures of [Ni(L I)2] and [Cu(L I,II)2]. It has been demonstrated by in-depth bonding analyses based on the ETS-NOCV and Interacting Quantum Atoms energy-decomposition schemes that application of the bulky substituents, containing several C-H groups, has led to the formation of a set of classical and unintuitive intra- and inter-molecular interactions. All together they are responsible for the high stability of [Ni(L I,II)2] and [Cu(L I,II)2]. More specifically, London dispersion dominated intramolecular C-H⋯O, C-H⋯N and C-H⋯H-C hydrogen bonds are recognized and, importantly, the attractive, chiefly the Coulomb driven, preagostic (not repulsive anagostic) C-H⋯Ni/Cu interactions have been discovered despite their relatively long distances (∼2.8-3.1 Å). All the complexes are further stabilized by the extremely efficient intermolecular C-H⋯π(benzene) and C-H⋯π(chelate) interactions, where both the charge-delocalization and London dispersion constituents appear to be crucial for the crystal packing of the obtained complexes. All the complexes were found to be photoluminescent in CH2Cl2, with [Cu(L II)2] exhibiting the most pronounced emission - the time-dependent density-functional-theory computations revealed that it is mostly caused by metal-to-ligand charge-transfer transitions.

Hydrogen Bond and Other Lewis Acid-Lewis Base Interactions as Preliminary Stages of Chemical Reactions

Various Lewis acid-Lewis base interactions are discussed as initiating chemical reactions and processes. For example, the hydrogen bond is often a preliminary stage of the proton transfer process or the tetrel and pnicogen bonds lead sometimes to the SN2 reactions. There are numerous characteristics of interactions being first stages of reactions; one can observe a meaningful electron charge transfer from the Lewis base unit to the Lewis acid; such interactions possess at least partly covalent character, one can mention other features. The results of different methods and approaches that are applied in numerous studies to describe the character of interactions are presented here. These are, for example, the results of the Quantum Theory of Atoms in Molecules, of the decomposition of the energy of interaction or of the structure-correlation method.

Allenes for Versatile Iron-Catalyzed C-H Activation by Weak O-Coordination: Mechanistic Insights by Kinetics, Intermediate Isolation, and Computation

The iron-catalyzed hydroarylation of allenes was accomplished by weak phenone assistance. The C-H activation proceeded with excellent efficacy and high ortho-regioselectivity in proximity to the weakly coordinating carbonyl group for a range of substituted phenones and allenes. Detailed mechanistic studies, including the isolation of key intermediates, the structural characterization of an iron-metallacycle, and kinetic analysis, allowed the sound elucidation of a plausible catalytic working mode. This mechanistic rationale is supported by detailed computational density functional theory studies, which fully address multi-spin-state reactivity. Furthermore, in operando nuclear magnetic resonance monitoring of the catalytic reaction provided detailed insights into the mode of action of the iron-catalyzed C-H alkylation with allenes.

Ensembles of Metastable States Govern Heterogeneous Catalysis on Dynamic Interfaces

Heterogeneous catalysis is at the heart of the chemical industry. Being able to tune and design efficient catalysts for processes of interest is of the utmost importance, and for this, a molecular-level understanding of heterogeneous catalysts is the first step and indeed a prime focus of modern catalysis research. For a long time, the single most thermodynamically stable structure of the catalytic interface attained under the reaction conditions had been envisioned as the reactive phase. However, some catalytic interfaces continue to undergo structural dynamics in the steady state, triggered by high temperatures and pressures and binding and changing reagents. Among particularly dynamic interfaces are such widely used catalysts as crystalline and amorphous surfaced supporting (sub)nanometallic clusters. Recently, it became clear that this dynamic fluxionality causes the supported clusters to populate many distinct structural and stoichiometric states under catalytic conditions. Hence, the catalytic interface should be viewed as an evolving statistical ensemble of many structures (rather than one structure). Every member in the ensemble contributes to the properties of the catalyst differently, in proportion to its probability of being populated. This new notion flips the established paradigm and calls for a new theory, new modeling approaches, operando measurements, and updated design strategies. The statistical ensemble nature of surface-supported subnanocluster catalysts can be exemplified by oxide-supported and adsorbate-covered Pt, Pd, Cu, and CuPd clusters, which are catalytic toward oxidative and nonoxidative dehydrogenation. They have access to a variety of 3D and quasi-2D shapes. The compositions of their thermal ensembles are dependent on the cluster size, leading to size-specific catalytic activities and the famous "every atom counts" phenomenon. The support and adsorbates affect catalyst structures, and the state of the reacting species causes the ensemble to change in every reaction intermediate. The most stable member of the ensemble dominates the thermodynamic properties of the corresponding intermediate, whereas the kinetics can be determined by more active but less populated metastable catalyst states, and that suggests that many earlier studies might have overlooked the actual active sites. Both effects depend on the relative time scales of catalyst restructuring and reaction dynamics. The catalyst may routinely operate off-equilibrium. Ensemble phenomena lead to surprising exceptions from established rules of catalysis, such as scaling relations and Arrhenius behavior. Catalyst deactivation is also an ensemble property, and its extent of mitigation can be predicted through the new paradigm. These findings were enabled by advances in theory, such as global optimization and subsequent utilization of multiple local minima and pathways sampling as well as operando catalyst characterization. The fact that the per-site and per-species resolution is needed for the description and prediction of catalyst properties gives theory the central role in catalysis research, as most experiments provide ensemble-average information and cannot detect the crucial minority species that may be responsible for the catalytic activity.

Origin of Hydrocarbons Stability from a Computational Perspective: A Case Study of Ortho-Xylene Isomers

It is shown herein that intuitive and text-book steric-clash based interpretation of the higher energy "in-in" xylene isomer (as arising solely from the repulsive CH⋅⋅⋅HC contact) with respect to the corresponding global-minimum "out-out" configuration (where the clashing C-H bonds are tilted out) is misleading. It is demonstrated that the two hydrogen atoms engaged in the CH⋅⋅⋅HC contact in "in-in" are involved in attractive interaction so they cannot explain the lower stability of this isomer. We have proven, based on the arsenal of modern bonding descriptors (EDDB, HOMA, NICS, FALDI, ETS-NOCV, DAFH, FAMSEC, IQA), that in order to understand the relative stability of "in-in" versus "out-out" xylenes isomers one must consider the changes in the electronic structure encompassing the entire molecules as arising from the cooperative action of hyperconjugation, aromaticity and unintuitive London dispersion plus charge delocalization based intra-molecular CH⋅⋅⋅HC interactions.

HFLD: A Nonempirical London Dispersion-Corrected Hartree-Fock Method for the Quantification and Analysis of Noncovalent Interaction Energies of Large Molecular Systems †

A nonempirical quantum mechanical method for the efficient and accurate quantification and analysis of intermolecular interactions is presented and tested on existing benchmark sets. The leading idea here is to focus on the intermolecular part of the correlation energy that contains the all-important London dispersion (LD) interaction. To keep the cost of the method low, essentially at the level of a Hartree-Fock (HF) calculation, the intramolecular part of the correlation energy is neglected. We also neglect the nondispersive parts of the intermolecular correlation energy. This scheme that we denote as Hartree-Fock plus London dispersion (HFLD) can be readily realized on the basis of the recently reported multilevel implementation of the domain-based local pair natural orbital coupled-cluster (DLPNO-CC) theory in conjunction with the well-established local energy decomposition (LED) analysis. The accuracy and efficiency of the HFLD method are evaluated on rare gas dimers, on the S66 and L7 benchmark sets of noncovalent interactions, and on an additional set (LP14) consisting of bulky Lewis pairs held together by intermolecular interactions of various strengths, with interaction energies ranging from -8 to -107 kcal/mol. It is first shown that the LD energy calculated with this approach is essentially identical to that obtained from the full DLPNO-CCSD(T)/LED calculation, with a mean absolute error of 0.2 kcal/mol on the S66 benchmark set. Moreover, in terms of the overall interaction energies, the HFLD method shows an efficiency that is comparable to that of the HF method, while retaining an accuracy between that of the DLPNO-CCSD and DLPNO-CCSD(T) schemes. Since the underlying DLPNO-CCSD method is linear scaling with respect to the system size, the HFLD approach also does not lead to new bottlenecks for large systems. As an illustrative example of its efficiency, the HFLD scheme was applied to the interaction between the substrate and the residues in the active site of the cyclohexanone monooxygenase enzyme. The excellent cost/performance ratio indicates that the HFLD method opens new avenues for the accurate calculation and analysis of noncovalent interaction energies in large molecular systems.

Physical Nature of Differential Spin-State Stabilization of Carbenes by Hydrogen and Halogen Bonding: A Domain-Based Pair Natural Orbital Coupled Cluster Study

The variation in the singlet-triplet energy gap of diphenylcarbene (DPC) upon interaction with hydrogen (water and methanol) or halogen bond (XCF3, X = Cl, Br, I) donors to form van der Waals (vdW) complexes is investigated in relation to the electrostatic and dispersion components of such intermolecular interactions. The domain-based local pair natural orbital coupled cluster method, DLPNO-CCSD(T), is used for calculating accurate single-triplet energy gaps and interaction energies for both spin states. The local energy decomposition scheme is used to provide an accurate quantification to the various interaction energy components at the DLPNO-CCSD(T) level. It is shown that the formation of vdW adducts stabilizes the singlet state of DPC, and in the case of water, methanol, and ICF3, it reverses the ground state from triplet to singlet. Electrostatic interactions are significant in both spin states, but preferentially stabilize the singlet state. For methanol and ClCF3, London dispersion forces have the opposite effect, stabilizing preferentially the triplet state. The quantification of the energetic components of the interactions through the local energy decomposition analysis correlates well with experimental findings and provides the basis for more elaborate treatments of microsolvation in carbenes.

Agostic Interactions in Early Transition-Metal Complexes: Roles of Hyperconjugation, Dispersion, and Steric Effect

The agostic interaction is a ubiquitous phenomenon in catalytic processes and transition-metal complexes, and hyperconjugation has been well recognized as its origin. Yet, recent studies showed that either short-range London dispersion or structural constraints could be the driving force, although proper evaluation of the role of hyperconjugation therein is needed. Herein, a simple variant of valence bond theory was employed to study a few exemplary Ti complexes with α- or β-agostic interactions and interpret the agostic effect in terms of the steric effect, hyperconjugation, and dispersion. For the complexes [MeTiCl₃ (dmpe)] and [MeTiCl₃ (dhpe)] with α-agostic interactions, hyperconjugation plays the dominant role with comparable magnitudes in both systems, but dispersion is solely responsible for the stronger agostic interaction in the former compared with the latter. For the complexes [EtTiCl₃ (dmpe)] and [EtTiCl₃ (dhpe)] with β-agostic interactions, however, hyperconjugation and dispersion play comparable roles, and the weaker steric repulsion leads to a stronger agostic effect in the former than in the latter. Thus, the present study clarifies the variable and sensitive roles of steric, hyperconjugative, and dispersion interactions in the agostic interaction.

Local Energy Decomposition of Open-Shell Molecular Systems in the Domain-Based Local Pair Natural Orbital Coupled Cluster Framework

Local energy decomposition (LED) analysis decomposes the interaction energy between two fragments calculated at the domain-based local pair natural orbital CCSD(T) (DLPNO-CCSD(T)) level of theory into a series of chemically meaningful contributions and has found widespread applications in the study of noncovalent interactions. Herein, an extension of this scheme that allows for the analysis of interaction energies of open-shell molecular systems calculated at the UHF-DLPNO-CCSD(T) level is presented. The new scheme is illustrated through applications to the CH₂···X (X = He, Ne, Ar, Kr, and water) and heme···CO interactions in the low-lying singlet and triplet spin states. The results are used to discuss the mechanism that governs the change in the singlet–triplet energy gap of methylene and heme upon adduct formation.

Chemistry and Quantum Mechanics in 2019: Give Us Insight and Numbers

This Perspective revisits Charles Coulson’s famous statement from 1959 “give us insight not numbers” in which he pointed out that accurate computations and chemical understanding often do not go hand in hand. We argue that today, accurate wave function based first-principle calculations can be performed on large molecular systems, while tools are available to interpret the results of these calculations in chemical language. This leads us to modify Coulson’s statement to “give us insight and numbers”. Examples from organic, inorganic, organometallic and surface chemistry as well as molecular magnetism illustrate the points made.

A noncovalent interaction insight onto the concerted metallation deprotonation mechanism

The CMD/AMLA mechanisms of cyclopalladation and the parent fictitious cyclonickelation of N,N-dimethylbenzylamine have been investigated by joint DFT-D and DLPNO-CCSD(T) methods assisted by QTAIM.

Structural versatility of the quasi-aromatic Möbius type zinc(ii)-pseudohalide complexes – experimental and theoretical investigations

In this contribution we report for the first time fabrication, isolation, structural and theoretical characterization of the quasi-aromatic Möbius complexes [Zn(NCS)₂L^I] (1), [Zn₂(μ_1,1-N₃)₂(L^I)₂][ZnCl₃(MeOH)]₂·6MeOH (2) and [Zn(NCS)L^II]₂[Zn(NCS)₄]·MeOH (3), constructed from 1,2-diphenyl-1,2-bis((phenyl(pyridin-2-yl)methylene)hydrazono)ethane (L^I) or benzilbis(acetylpyridin-2-yl)methylidenehydrazone (L^II), respectively, and ZnCl₂ mixed with NH₄NCS or NaN₃. Structures 1–3 are dictated by both the bulkiness of the organic ligand and the nature of the inorganic counter ion. As evidenced from single crystal X-ray diffraction data species 1 has a neutral discrete heteroleptic mononuclear structure, whereas, complexes 2 and 3 exhibit a salt-like structure. Each structure contains a Zn^II atom chelated by one tetradentate twisted ligand L^I creating the unusual Möbius type topology. Theoretical investigations based on the EDDB method allowed us to determine that it constitutes the quasi-aromatic Möbius motif where a metal only induces the π-delocalization solely within the ligand part: 2.44|e| in 3, 3.14|e| in 2 and 3.44|e| in 1. It is found, that the degree of quasi-aromatic π-delocalization in the case of zinc species is significantly weaker (by ∼50%) than the corresponding estimations for cadmium systems – it is associated with the Zn–N bonds being more polar than the related Cd–N connections. The ETS-NOCV showed, that the monomers in 1 are bonded primarily through London dispersion forces, whereas long-range electrostatic stabilization is crucial in 2 and 3. A number of non-covalent interactions are additionally identified in the lattices of 1–3.

Interplay between various types of non-covalent interactions allowed for isolation of rare examples of Zn(ii) based quasi-aromatic Möbius type species.

London dispersion effects in the coordination and activation of alkanes in σ-complexes: a local energy decomposition study

The coupled-cluster-based local energy decomposition (LED) analysis is used to elucidate the nature of the TM–alkane interaction in alkane σ-complexes.

Effect of Electron Correlation on Intermolecular Interactions: A Pair Natural Orbitals Coupled Cluster Based Local Energy Decomposition Study

The development of post-Hartree-Fock (post-HF) energy decomposition schemes that are able to decompose the HF and correlation components of the interaction energy into chemically meaningful contributions is a very active field of research. One of the challenges is to provide a clear-cut quantification to the elusive London dispersion component of the intermolecular interaction. London dispersion is well-known to be a pure correlation effect, and as such it is not properly described by mean field theories. In this context, we have recently developed the local energy decomposition (LED) analysis, which provides a chemically meaningful decomposition of the interaction energy between two or more fragments computed at the domain-based local pair natural orbitals coupled cluster (DLPNO-CCSD(T)) level of theory. In this work, this scheme is used in conjunction with other interpretation tools to study a series of molecular adducts held together by intermolecular interactions of different natures. The HF and correlation components of the interaction energy are thus decomposed into a series of chemically meaningful contributions. Emphasis is placed on discussing the physical effects associated with the inclusion of electron correlation. It is found that four distinct physical effects can contribute to the magnitude of the correlation part of intermolecular binding energies (Δ E_int^C): (i) London dispersion, (ii) the correlation correction to the reference induction energy, (iii) the correlation correction to the electron sharing process, and (iv) the correlation correction to the permanent electrostatics. As expected, the largest contribution to the correlation binding energy of neutral, apolar molecules is London dispersion, as in the argon dimer case. In contrast, the correction for the HF induction energy dominates Δ E_int^C in systems in which an apolar molecule interacts with charged or strongly polar species, as in Ar-Li⁺. This effect has its origin in the systematic underestimation of polarizabilities at the HF level of theory. For similar reasons, electron sharing largely contributes to the correlation binding energy of covalently bound molecules, as in the beryllium dimer case. Finally, the correction for HF permanent electrostatics significantly contributes to Δ E_int^C in molecules with strong dipoles, such as water and hydrogen fluoride dimers. This effect originates from the characteristic overestimation of dipole moments at the HF level of theory, leading in some cases to positive Δ E_int^C values. Our results are apparently in contrast to the widely accepted view that Δ E_int^C is typically dominated by London dispersion, at least, in the strongly interacting region. Clearly, post-HF energy decomposition schemes are very powerful tools to analyze, categorize, and understand the various contributions to the intermolecular interaction energy. Hopefully, this will eventually lead to insights that are helpful in designing systems with tailored properties. All analysis tools presented in this work will be available free of charge in the next release of the ORCA program package.

Modulation of σ-Alkane Interactions in [Rh(L2)(alkane)]+ Solid-State Molecular Organometallic (SMOM) Systems by Variation of the Chelating Phosphine and Alkane: Access to η2,η2-σ-Alkane Rh(I), η1-σ-Alkane Rh(III) Complexes, and Alkane Encapsulation

Solid/gas single-crystal to single-crystal (SC-SC) hydrogenation of appropriate diene precursors forms the corresponding σ-alkane complexes [Rh(Cy₂P(CH₂) _nPCy₂)(L)][BAr^F₄] ( n = 3, 4) and [ RhH(Cy₂P(CH₂)₂( CH)(CH₂)₂PCy₂)(L)][BAr^F₄] ( n = 5, L = norbornane, NBA; cyclooctane, COA). Their structures, as determined by single-crystal X-ray diffraction, have cations exhibiting Rh···H-C σ-interactions which are modulated by both the chelating ligand and the identity of the alkane, while all sit in an octahedral anion microenvironment. These range from chelating η²,η² Rh···H-C (e.g., [Rh(Cy₂P(CH₂) _nPCy₂)(η²η²-NBA)][BAr^F₄], n = 3 and 4), through to more weakly bound η¹ Rh···H-C in which C-H activation of the chelate backbone has also occurred (e.g., [ RhH(Cy₂P(CH₂)₂( CH)(CH₂)₂PCy₂)(η¹-COA)][BAr^F₄]) and ultimately to systems where the alkane is not ligated with the metal center, but sits encapsulated in the supporting anion microenvironment, [Rh(Cy₂P(CH₂)₃PCy₂)][COA⊂BAr^F₄], in which the metal center instead forms two intramolecular agostic η¹ Rh···H-C interactions with the phosphine cyclohexyl groups. CH₂Cl₂ adducts formed by displacement of the η¹-alkanes in solution ( n = 5; L = NBA, COA), [ RhH(Cy₂P(CH₂)₂( CH)(CH₂)₂PCy₂)(κ¹-ClCH₂Cl)][BAr^F₄], are characterized crystallographically. Analyses via periodic DFT, QTAIM, NBO, and NCI calculations, alongside variable temperature solid-state NMR spectroscopy, provide snapshots marking the onset of Rh···alkane interactions along a C-H activation trajectory. These are negligible in [Rh(Cy₂P(CH₂)₃PCy₂)][COA⊂BAr^F₄]; in [ RhH(Cy₂P(CH₂)₂( CH)(CH₂)₂PCy₂)(η¹-COA)][BAr^F₄], σ_C-H → Rh σ-donation is supported by Rh → σ*_C-H "pregostic" donation, and in [Rh(Cy₂P(CH₂) _nPCy₂)(η²η²-NBA)][BAr^F₄] ( n = 2-4), σ-donation dominates, supported by classical Rh(dπ) → σ*_C-H π-back-donation. Dispersive interactions with the [BAr^F₄]^- anions and Cy substituents further stabilize the alkanes within the binding pocket.