Bonding in Classical and Nonclassical Transition Metal Carbonyls: The Interacting Quantum Atoms Perspective

The Analysis of Electron Densities: From Basics to Emergent Applications

The electron density determines all properties of a system of nuclei and electrons. It is both computable and observable. Its topology allows gaining insight into the mechanisms of bonding and other phenomena in a way that is complementary to and beyond that available from the molecular orbital picture and the formal oxidation state (FOS) formalism. The ability to derive mechanistic insight from electron density is also important with methods where orbitals are not available, such as orbital-free density functional theory (OF-DFT). While density topology-based analyses such as QTAIM (quantum theory of atoms-in-molecules) have been widely used, novel, vector-based techniques recently emerged such as next-generation (NG) QTAIM. Density-dependent quantities are also actively used in machine learning (ML)-based methods, in particular, for ML DFT functional development, including machine-learnt kinetic energy functionals. We review QTAIM and its recent extensions such as NG-QTAIM and localization-delocalization matrices (LDM) and their uses in the analysis of bonding, conformations, mechanisms of redox reactions excitations, as well as ultrafast phenomena. We review recent research showing that direct density analysis can circumvent certain pitfalls of the FOS formalism, in particular in the description of anionic redox, and of the widely used (spherically) projected density of states analysis. We discuss uses of density-based quantities for the construction of DFT functionals and prospects of applications of analyses of density topology to get mechanistic insight with OF-DFT and recently developed time-dependent OF-DFT.

Critical assessment of the x-ray restrained wave function approach: Advantages, drawbacks, and perspectives for density functional theory and periodic ab initio calculations

The x-ray restrained wave function (XRW) method is a quantum crystallographic technique to extract wave functions compatible with experimental x-ray diffraction data. The approach looks for wave functions that minimize the energies of the investigated systems and also reproduce sets of x-ray structure factors. Given the strict relationship between x-ray structure factors and electron distributions, the strategy practically allows determining wave functions that correspond to given (usually experimental) electron densities. In this work, the capabilities of the XRW approach were further tested. The aim was to evaluate whether the XRW technique could serve as a tool for suggesting new exchange-correlation functionals for density functional theory or refining existing ones. Additionally, the ability of the method to address the influences of the crystalline environment was also assessed. The outcomes of XRW computations were thus compared to those of traditional gas-phase, embedding quantum mechanics/molecular mechanics, and fully periodic calculations. The results revealed that, irrespective of the initial conditions, the XRW computations practically yield a consensus electron density, in contrast to the currently employed density functional approximations (DFAs), which tend to give a too large range of electron distributions. This is encouraging in view of exploiting the XRW technique to develop improved functionals. Conversely, the calculations also emphasized that the XRW method is limited in its ability to effectively address the influences of the crystalline environment. This underscores the need for a periodic XRW technique, which would allow further untangling the shortcomings of DFAs from those inherent to the XRW approach.

Density functional theory study of crown ether-magnesium complexes: from a solvated ion to an ion trap

Metal ion detection rests on host-guest recognition. We propose a theoretical protocol for designing an optimal trap for a desired metal cation. A host for magnesium ions was sought for among derivatives of crown ethers 12-crown-4, 15-crown-5, and 18-crown-6. Mg-crown complexes and their hydrated counterparts with water molecules bound to the cation were optimized using density functional theory. Based on specific geometric criteria, Interacting quantum atoms analysis and density functional theory-based molecular dynamics of Mg-crown complexes immersed in water, crown ethers for optimal accommodation of Mg2+ in aqueous solution were identified. Selectivity of the chosen crowns towards Na+, K+, and Ca2+ ions is addressed.

Dual Chalcogen-Bonding Interactions for the Conformational Control of Urea

Dual chalcogen-bonding interactions is proposed as a novel means for the conformational control of urea derivatives. The formation of a chalcogen-bonding interaction at both sides of the urea carbonyl group was unambiguously confirmed by X-ray diffraction as well as computational studies including non-covalent interaction (NCI) plot index analysis, quantum theory of atoms in molecules (QTAIM) analysis, and natural bond orbital (NBO) analysis via DFT calculations. By virtue of this dual interaction, urea derivatives that bear chalcogen atoms (X=S and Se) adopt a planar structure via the carbonyl oxygen (O) with an X⋅⋅⋅O⋅⋅⋅X arrangement on the same side of the molecule. The rigidity of the conformational lock was evaluated using the molecular arrangement in the crystal and the rotational barrier of benzochalcogenophene ring, which indicated a stronger conformational lock in benzoselenophene than in benzothiophene urea derivatives. Furthermore, the acidity of the urea derivatives increases according to the Lewis-acidic properties of the chalcogen-bonding interactions, whereby benzoselenophene urea is more acidic than benzothiophene urea. Tweezer-shaped urea derivatives were prepared, and their stereostructure proved the viability of the conformational control for defining the location of the substituents on the urea framework.

Electron Density Analysis of Metal-Metal Bonding in a Ni4 Cluster Featuring Ferromagnetic Exchange

We present a combined experimental and theoretical study of the nature of the proposed metal-metal bonding in the tetranuclear cluster Ni₄(NP^tBu₃)₄, which features four nickel(I) centers engaged in strong ferromagnetic coupling. High-resolution single-crystal synchrotron X-ray diffraction data collected at 25 K provide an accurate geometrical structure and a multipole model electron density description. Topological analysis of the electron density in the Ni₄N₄ core using the quantum theory of atoms in molecules clearly identifies the bonding as an eight-membered ring of type [Ni-N-]₄ without direct Ni-Ni bonding, and this result is generally corroborated by an analysis of the energy density distribution. In contrast, the calculated bond delocalization index of ∼0.6 between neighboring Ni atoms is larger than what has been found for other bridged metal-metal bonds and implies direct Ni-Ni bonding. Similar support for the presence of direct Ni-Ni bonding is found in the interacting quantum atom approach, an energy decomposition scheme, which suggests the presence of stabilizing Ni-Ni bonding interactions with an exchange-correlation energy contribution approximately 50% of that of the Ni-N interactions. Altogether, while the direct interactions between neighboring Ni centers are too weak and sterically constrained to bear the signature of a topological bond critical point, other continuous measures clearly indicate significant Ni-Ni bonding. These metal-metal bonding interactions likely mediate direct ferromagnetic exchange, giving rise to the high-spin ground state of the molecule.

Non-innocent cyanido ligands: tetracyanidoferrate(-II) as carbonyl copycat

While a negative oxidation state occurs rarely for metals in general, this is commonly known for metal carbonyl anions, i.e. carbonyl metalates. Although CO and CN^- are isoelectronic, cyanidometalates usually do not exhibit metal centers with negative oxidation states. However, we report on the electron-rich tetrahedral tetracyanidoferrate(-II) anion [Fe(CN)₄]^6-, which was stabilized in (Sr₃N)₂[Fe(CN)₄] (space group R3c, a = 702.12(2) pm, c = 4155.5(2) pm). Microcrystalline powders were synthesized by a solid-state route, single crystals were obtained from Na metal flux. In comparison to classical cyanidometalates, C-N distances are longer and stretching frequencies are lower as indicated by X-ray diffraction, IR and Raman spectroscopy. Weak C-N, strong Fe-C bonds as well as the anion geometry resemble the isoelectronic tetrahedral carbonyl ferrate [Fe(CO)₄]^2-. ⁵⁷Fe Mössbauer spectroscopic measurements reveal a negative isomer shift in agreement with substantially delocalized d electrons due to strong π back-bonding. These results point to a very similar bonding situation of both 18e tetracyanido and tetracarbonyl ferrates including non-innocent redox-active ligands and a d¹⁰ closed shell configuration on iron. Hereby, new tetracyanidoferrate(-II) provides a missing link for a more in-depth understanding of the chemical bonding trends of highly-reduced cyanidometalates in the quest for even higher reduced transition metals in this exceptional class of compounds.

A fast approximate extension of the interacting quantum atoms energy decomposition to excited states

An approach is developed for the fast calculation of the interacting quantum atoms energy decomposition (IQA) from the information contained in the first order reduced density matrix only. The proposed methodology utilizes an approximate exchange-correlation density from Density Matrix Functional Theory without the need to evaluate the correlation-exchange contribution directly. Instead, weight factors are estimated to decompose the exact V_xc into atomic and pairwise contributions. In this way, the sum of the IQA contributions recovers the energy obtained from the electronic structure calculation. This method can, hence, be applied to obtain atomic contributions in excited states on the same footing as in their ground states using any method that delivers the reduced first-order density matrix. In this way, one can locate chromophores from first principles quantum chemical calculations. Test calculations on the ground and excited states of a set of small molecules indicate that the scaled atomic contributions reproduce vertical electronic transition energies calculated exactly. This approach may be useful to extend the applicability of the IQA approach in the study of large photochemical systems especially when the calculations of the second order reduced density matrices is prohibitive or not possible.

Proton leap: shuttling of protons onto benzonitrile

The detailed description of chemical transformations in the interstellar medium allows deciphering the origin of a number of small and medium - sized organic molecules. We present density functional theory analysis of proton transfer from the trihydrogen cation and the ethenium cation to benzonitrile, a recently discovered species in the Taurus Molecular Cloud 1. Detailed energy transformations along the reaction paths were analyzed using the interacting quantum atoms methodology, which elucidated how the proton carrier influences the lightness to deliver the proton to benzonitrile's nitrogen atom. The proton carriers' deformation energy represents the largest destabilizing effect, whereas a proton's promotion energy, the benzonitrile-proton Coulomb attraction, as well as non-classical benzonitrile-proton and carrier-proton interaction are the dominant stabilizing energy components. As two ion-molecule reactions proceed without energy barriers, rate constants were estimated using the classical capture theory and were found to be an order of magnitude larger for the reaction with the trihydrogen cation compared to that with the ethenium cation (∼10^-8 and 10^-9 cm³ s^-1, respectively). These results were obtained both with quantum chemical and ab initio molecular dynamics simulations (the latter performed at 10 K and 100 K), confirming that up to 100 K both systems choose energetically undemanding routes by tracking the corresponding minimum energy paths. A concept of a turning point is introduced, which is an equivalent to the transition state in barrierless reactions.

Insights into the Metal-CO Bond in O2M(η1-CO) (M = Cr, Mo, W, Nd, and U) Complexes

Investigations on the structures and bonding properties of metal carbonyl compounds provide fundamental understandings on the origin of small-molecule activations. Herein, the geometry and bonding trends of a series of isovalent metal oxocarbonyl complexes O₂M(η¹-CO) (M = Cr, Mo, W, Nd, and U) were studied by combined matrix-isolation infrared spectroscopy and advanced quantum chemical calculations. The title complexes present red shift of C-O stretching bands in the range from 122 to 244 cm^-1, indicating the difference of CO activation ability for the series of isovalent metal dioxides. Density functional theory calculations predict T-shaped structures with a C_2v symmetry for all the title molecules. O₂Nd(η¹-CO) bears little resemblance to the other complexes in bonding characters because of the weak interactions between the NdO₂ and CO moiety. For the other complexes, natural localized molecular orbital analysis reveals a gradual increase of covalent character in M-CO bonds along the metal series Cr → Mo → W→ U. Energy decomposition analysis with natural orbitals for chemical valence calculations demonstrates that the M-CO bonding patterns conform to the conventional Dewar-Chatt-Duncanson motif. The contributions from orbital interactions in total attractions increase from Cr (41.7%) to U (52.7%). The breakdown of the orbital term into pairwise interactions shows that contributions of the M ← CO σ donation decrease from Cr (59.2%) to U (28.4%), while the M → CO π* backdonation increases significantly from Cr (23.8%) to U (67.3%). The more effective overlap and the better energy matching of U 5f and U 6d valence orbitals with CO π* orbitals result in much stronger U → CO π backdonation than the other metal elements.

Metal–ligand bonding in tricarbonyliron(0) complexes bearing thiochalcone ligands

Bonding interactions between iron and thiochalcones in a series of recently synthesized complexes were analyzed using various theoretical methods.

Metal-CO Bonding in Mononuclear Transition Metal Carbonyl Complexes

DFT calculations have been carried out for coordinatively saturated neutral and charged carbonyl complexes [M(CO) _n ] ^q where M is a metal atom of groups 2-10. The model compounds M(CO)₂ (M = Ca, Sr, Ba) and the experimentally observed [Ba(CO)]⁺ were also studied. The bonding situation has been analyzed with a variety of charge and energy partitioning approaches. It is shown that the Dewar-Chatt-Duncanson model in terms of M ← CO σ-donation and M → CO π-backdonation is a valid approach to explain the M-CO bonds and the trend of the CO stretching frequencies. The carbonyl ligands of the neutral complexes carry a negative charge, and the polarity of the M-CO bonds increases for the less electronegative metals, which is particularly strong for the group 4 and group 2 atoms. The NBO method delivers an unrealistic charge distribution in the carbonyl complexes, while the AIM approach gives physically reasonable partial charges that are consistent with the EDA-NOCV calculations and with the trend of the C-O stretching frequencies. The AdNDP method provides delocalized MOs which are very useful models for the carbonyl complexes. Deep insight into the nature of the metal-CO bonds and quantitative information about the strength of the [M] ← (CO)₈ σ-donation and [M(d)] → (CO)₈ π-backdonation visualized by the deformation densities are provided by the EDA-NOCV method. The large polarity of the M-CO π orbitals toward the CO end in the alkaline earth octacarbonyls M(CO)₈ (M = Ca, Sr, Ba) leads to small values for the delocalization indices δ(M-C) and δ(M···O) and significant overlap between adjacent CO groups, but the origin of the charge migration and the associated red-shift of the C-O stretching frequencies is the [M(d)] → (CO)₈ π-backdonation. The heavier alkaline earth metals calcium, strontium and barium use their s/d valence orbitals for covalent bonding. They are therefore to be assigned to the transition metals.

The significance of the metal cation in guanine-quartet – metalloporphyrin complexes

The distinct positions of the divalent metal ions with respect to the porphyrin ring are responsible for different interaction energies between metalloporphyrins and the guanine quartet.

The Nature of Nonclassical Carbonyl Ligands Explained by Kohn-Sham Molecular Orbital Theory

When carbonyl ligands coordinate to transition metals, their bond distance either increases (classical) or decreases (nonclassical) with respect to the bond length in the isolated CO molecule. C−O expansion can easily be understood by π‐back‐donation, which results in a population of the CO's π*‐antibonding orbital and hence a weakening of its bond. Nonclassical carbonyl ligands are less straightforward to explain, and their nature is still subject of an ongoing debate. In this work, we studied five isoelectronic octahedral complexes, namely Fe(CO)₆²⁺, Mn(CO)₆⁺, Cr(CO)₆, V(CO)₆⁻ and Ti(CO)₆²⁻, at the ZORA‐BLYP/TZ2P level of theory to explain this nonclassical behavior in the framework of Kohn–Sham molecular orbital theory. We show that there are two competing forces that affect the C−O bond length, namely electrostatic interactions (favoring C−O contraction) and π‐back‐donation (favoring C−O expansion). It is a balance between those two terms that determines whether the carbonyl is classical or nonclassical. By further decomposing the electrostatic interaction ΔV_elstat into four fundamental terms, we are able to rationalize why ΔV_elstat gives rise to the nonclassical behavior, leading to new insights into the driving forces behind C−O contraction.

Interacting Quantum Atoms-A Review

The aim of this review is threefold. On the one hand, we intend it to serve as a gentle introduction to the Interacting Quantum Atoms (IQA) methodology for those unfamiliar with it. Second, we expect it to act as an up-to-date reference of recent developments related to IQA. Finally, we want it to highlight a non-exhaustive, yet representative set of showcase examples about how to use IQA to shed light in different chemical problems. To accomplish this, we start by providing a brief context to justify the development of IQA as a real space alternative to other existent energy partition schemes of the non-relativistic energy of molecules. We then introduce a self-contained algebraic derivation of the methodological IQA ecosystem as well as an overview of how these formulations vary with the level of theory employed to obtain the molecular wavefunction upon which the IQA procedure relies. Finally, we review the several applications of IQA as examined by different research groups worldwide to investigate a wide variety of chemical problems.

Contributions of IQA electron correlation in understanding the chemical bond and non-covalent interactions

The quantum topological energy partitioning method Interacting Quantum Atoms (IQA) has been applied for over a decade resulting in an enlightening analysis of a variety of systems. In the last three years we have enriched this analysis by incorporating into IQA the two-particle density matrix obtained from Møller–Plesset (MP) perturbation theory. This work led to a new computational and interpretational tool to generate atomistic electron correlation and thus topologically based dispersion energies. Such an analysis determines the effects of electron correlation within atoms and between atoms, which covers both bonded and non-bonded “through -space” atom–atom interactions within a molecule or molecular complex. A series of papers published by us and other groups shows that the behavior of electron correlation is deeply ingrained in structural chemistry. Some concepts that were shown to be connected to bond correlation are bond order, multiplicity, aromaticity, and hydrogen bonding. Moreover, the concepts of covalency and ionicity were shown not to be mutually excluding but to both contribute to the stability of polar bonds. The correlation energy is considerably easier to predict by machine learning (kriging) than other IQA terms. Regarding the nature of the hydrogen bond, correlation energy presents itself in an almost contradicting way: there is much localized correlation energy in a hydrogen bond system, but its overall effect is null due to internal cancelation. Furthermore, the QTAIM delocalization index has a connection with correlation energy. We also explore the role of electron correlation in protobranching, which provides an explanation for the extra stabilization present in branched alkanes compared to their linear counterparts. We hope to show the importance of understanding the true nature of the correlation energy as the foundation of a modern representation of dispersion forces for ab initio, DFT, and force field calculations.

On generalized partition methods for interaction energies

The breakdown of interaction energy has always been a very important means to understand chemical bonding and it has become a seamlessly useful tool for modern supramolecular chemistry.

Carbon monoxide adsorption at forsterite surfaces as models of interstellar dust grains: An unexpected bathochromic (red) shift of the CO stretching frequency

Carbon monoxide (CO) is one of the most abundant species in the interstellar medium (ISM). In the colder regions of the ISM, it can directly adsorb onto exposed Mg cations of forsterite (Fo, Mg₂SiO₄), one of the main constituents of the dust grains. Its energetic of adsorption can strongly influence the chemico-physical evolution of cold interstellar clouds; thus, a detailed description of this process is desirable. We recently simulated the CO adsorption on crystalline Fo surfaces by computer ab initio methods and, surprisingly, reported cases where the CO stretching frequency underwent a bathochromic (red) shift (i.e., it is lowered with respect to the CO gas phase frequency), usually not experimentally observed for CO adsorbed onto oxides with non-d cations, like the present case. Here, we elucidate in deep when and under which conditions this case may happen and concluded that this red shift may be related to peculiar surface sites occurring at the morphologically complex Fo surfaces. The reasons for the red shift are linked to both the quadrupolar nature of the CO molecule and the role of dispersion interactions with surfaces of complex morphology. The present work, albeit speculative, suggests that, at variance with CO adsorption on simple oxides like MgO, the CO spectrum may exhibit features at lower frequencies than the reference gas frequency when CO is adsorbed on complex oxides, even in the absence of transition metal ions.

Revisiting π backbonding: the influence of d orbitals on metal–CO bonds and ligand red shifts

Stronger C–O bonds are found if metal d-functions are present in carbonyl complexes, contrary to the common understanding of π-backbonding.

Unveiling the role of intra and interatomic interactions in the energetics of reaction schemes: a quantum chemical topology analysis

In this work we present a detailed analysis of selected reaction schemes in terms of the atomic components of the electronic energy defined by the quantum theory of atoms in molecules and the interacting quantum atoms method. The aim is to provide an interpretation tool for the energy change involved in a chemical reaction by means of the atomic and interaction contributions to the energies of the molecules involved. Ring strain in cyclic alkanes, the resonance energy of aromatic and antiaromatic molecules, local aromaticity in polycyclic aromatic hydrocarbons, intermolecular bonding in hydrogen fluoride clusters, and hydration of d-block metal dications were selected for the study. It was found that in addition to the changes in the strong C-C interactions in the carbon skeleton of the organic molecular rings, other contributions not usually considered to be important such as those between C and H atoms (either bonded or not) need to be considered in order to account for the net energy changes. The analysis unveils the role of the ionic and covalent contributions to the hydrogen bonding in HF clusters and the energetic origin and extent of cooperative effects involved. Moreover, the "double-hump" behavior observed for the hydration energy trend of [M(H2O)6]2+ complexes is explained in terms of the deformation energy of the metal cation and the increasingly covalent metal-water interactions. In addition, proper comparisons with the description provided by other methodologies are briefly discussed. The topological approach proposed in this contribution proves to be useful for the description of energy changes of apposite reaction schemes in chemically meaningful terms.

When hydroquinone meets methoxy radical: Hydrogen abstraction reaction from the viewpoint of interacting quantum atoms

Interacting Quantum Atoms methodology is used for a detailed analysis of hydrogen abstraction reaction from hydroquinone by methoxy radical. Two pathways are analyzed, which differ in the orientation of the reactants at the corresponding transition states. Although the discrepancy between the two barriers amounts to only 2 kJ/mol, which implies that the two pathways are of comparable probability, the extent of intra-atomic and inter-atomic energy changes differs considerably. We thus demonstrated that Interacting Quantum Atoms procedure can be applied to unravel distinct energy transfer routes in seemingly similar mechanisms. Identification of energy components with the greatest contribution to the variation of the overall energy (intra-atomic and inter-atomic terms that involve hydroquinone's oxygen and the carbon atom covalently bound to it, the transferring hydrogen and methoxy radical's oxygen), is performed using the Relative energy gradient method. Additionally, the Interacting Quantum Fragments approach shed light on the nature of dominant interactions among selected fragments: both Coulomb and exchange-correlation contributions are of comparable importance when considering interactions of the transferring hydrogen atom with all other atoms, whereas the exchange-correlation term dominates interaction between methoxy radical's methyl group and hydroquinone's aromatic ring. This study represents one of the first applications of Interacting Quantum Fragments approach on first order saddle points. © 2018 Wiley Periodicals, Inc.

Electron Density Analysis of Metal Clusters with Semi-Interstitial Main Group Atoms. Chemical Bonding in [Co6X(CO)16]- Species

In this work, we propose a careful and thorough analysis of the chemical bond nature in high nuclearity metal carbonyl clusters having semi-interstitial main group atoms. We investigated the species [Co₆X(CO)₁₆]^- (X = As, P), known for a rather interesting conformational flexibility of the cluster (leading to open or closed cages) and a corresponding polymorphism in the solid state (observed at least for X = As). The factors that trigger the molecular isomerism and the nature of X-Co and Co-Co interactions emerge from theoretical calculations and high resolution X-ray diffraction. Both energy and charge density atomic partitioning (QTAIM, EDA, IQA) are employed for this analysis, with the aim of revealing the stabilizing/destabilizing factors of the interaction between the cage and the semi-interstitial atoms in the various conformations.

Ligand Effect on Bonding in Gold(III) Carbonyl Complexes

We quantitatively assess the Dewar-Chatt-Duncanson (DCD) components of the Au(III)-CO bond and the charge density polarization at the CO, in a series of neutral, cationic, and dicationic bis- and monocyclometalated gold(III) complexes via charge-displacement (CD) analysis. A striking feature concerns the very small net electron charge flux from CO to the metal fragment which is unexpectedly stable toward both the charge of the complex and the oxidation state of gold (I, III). All systems exhibit a similar trend for the σ charge rearrangement in the region of the carbonyl bond, where, by contrast, the π back-donation trend variation is large, which is strictly correlated to the change in CO bond distance and the shift in CO stretching frequencies, in close analogy with the gold(I) carbonyl complexes. In the whole series of gold(III) compounds, a large Au(III) ← CO σ donation is measured (from 0.19 to 0.31 electrons), as well as a significant Au(III) → CO π back-donation (from -0.09 to -0.22 electrons), which however is not generally able to completely balance the polarization of the CO π electrons in the direction from oxygen to carbon (C ← O) induced by the presence of the metal fragment [LAu(III)]^0/+1/+2. Surprisingly, all the gold(III) complexes in the series are characterized by a very small anisotropy in the Au(III) → CO in-plane and out-of-plane π back-donation components, in sharp contrast with the marked anisotropy found before for the experimentally characterized [(C^N^C)Au(III)CO]⁺ complex. A first attempt to figure out a rationale on the bonding/reactivity relationship for Au(III)-CO is made by performing a comparative study with an isostructural [(N^N^C)Pt(II)CO]⁺ complex in a model water-gas shift (WGS) reaction.

Analyzing Fluxional Molecules Using DORI

The Density Overlap Region Indicator (DORI) is a density-based scalar field that reveals covalent bonding patterns and noncovalent interactions in the same value range. This work goes beyond the traditional static quantum chemistry use of scalar fields and illustrates the suitability of DORI for analyzing geometrical and electronic signatures in highly fluxional molecular systems. Examples include a dithiocyclophane, which possesses multiple local minima with differing extents of π-stacking interactions and a temperature dependent rotation of a molecular rotor, where the descriptor is employed to capture fingerprints of CH-π and π-π interactions. Finally, DORI serves to examine the fluctuating π-conjugation pathway of a photochromic torsional switch (PTS). Attention is also placed on postprocessing the large amount of generated data and juxtaposing DORI with a data-driven low-dimensional representation of the structural landscape.

A fully analytical integration of properties over the 3D volume of the β sphere in topological atoms

Atomic multipole moments associated with a spherical volume fully residing within a topological atom (i.e., the β sphere) can be obtained analytically. Such an integration is thus free of quadrature grids. A general formula for an arbitrary rank spherical harmonic multipole moment is derived, for an electron density comprising Gaussian primitives of arbitrary angular momentum. The closed expressions derived here are also sufficient to calculate the electrostatic potential, the two types of kinetic energy, as well as the potential energy between atoms. Some integrals have not been solved explicitly before but through recursion and substitution are broken down to more elementary listed integrals. The proposed method is based on a central formula that shifts Gaussian primitives from one center to another, which can be derived from the well-known plane-wave expansion (or Rayleigh equation). © 2018 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

An interacting quantum atom study of model SN 2 reactions (X- ···CH3 X, X = F, Cl, Br, and I)

The quantum chemical topology method has been used to analyze the energetic profiles in the X-  + CH3 X → XCH3  + X- SN 2 reactions, with X = F, Cl, Br, and I. The evolution of the electron density properties at the BCPs along the reaction coordinate has been analysed. The interacting quantum atoms (IQA) method has been used to evaluate the intra-atomic and interatomic energy variations along the reaction path. The different energetic terms have been examined by the relative energy gradient method and the ANANKE program, which enables automatic and unbiased IQA analysis. Four of the six most important IQA energy contributions were needed to reproduce the reaction barrier common to all reactions. The four reactions considered share many common characteristics but when X = F a number of particularities occur. © 2017 Wiley Periodicals, Inc.

Understanding the reaction mechanism of the oxidative addition of ammonia by (PXP)Ir(i) complexes: the role of the X group

An analysis of the electronic rearrangements for the oxidative addition of ammonia to a set of five representative (PXP)Ir pincer complexes (X = B, CH, O, N, SiH) is performed. We aim to understand the factors controlling the activation and reaction energies of this process by combining different theoretical strategies based on DFT calculations. Interestingly, complexes featuring higher activation barriers yield more exothermic reactions. The analysis of the reaction path using the bonding evolution theory shows that the main chemical events, N-H bond cleavage and Ir-H bond formation, take place before the transition structure is reached. Metal oxidation implies an electron density transfer from non-shared Ir pairs to the Ir-N bond. This decrement in the atomic charge of the metal provokes different effects in the ionic contribution of the Ir-X bonding depending on the nature of the X atom as shown by the interacting quantum atoms methodology.

Torquoselectivity in Cyclobutene Ring Openings and the Interatomic Interactions That Control Them

Torquoselectivity has explained diasteromeric preferences of a number electrocyclic ring openings. The quantum theory of atoms in molecules (QTAIM), the electron localizability indicator (ELI-D), and the interacting quantum atoms (IQA) energy partition method are used to evaluate qualitatively and quantitatively the atomic interactions behind the torquoselectivity of a series of 3-substituted cyclobutenes. ELI-D topology and IQA energies show that the interaction between the distal terminus carbon atom of cyclobutene (C4) with the substituent at C3 (R5) in the transition state governs torquoselectivities. In the case of 3-borylcyclobutene, this interaction is so strong that a protocovalent bond is actually formed between B5 and C4. The evaluation of the interatomic energies allowed us to identify an additional interaction that contribute to a minor extent to the stabilization of the TS. Despite the fact that C4,R5 interaction is the main cause of the torquoselectivity, a bonding path (BP) between these two atoms was not observed. However, the lack of a BP between C4 and R5 does not mean that the topology of the electron density was not affected by the interaction of these two atoms. Surprisingly, we found a strong correlation between the density at the bond critical point (BCP) and the BP shape of C3-C4 breaking bond with the observed activation energies and torquoselectivities.

Nature of intramolecular interactions of vitamin C in view of interacting quantum atoms: the role of hydrogen bond cooperativity on geometry

The conformational analysis of six dihedral angles was calculated by second-order Moller-Plesset perturbation theory (MP2) with the correlation-consistent aug-cc-pVDZ basis set. The quantum theory of atoms in molecules (QTAIM) was applied to gain a description of the atoms and chemical bonds. A high content of hydroxyl groups in vitamin C's (VC) structure leads to a wide range of intramolecular interactions. The nature of these interactions within the selected VC conformers was studied in view of the interacting quantum atom (IQA) approach. Complete IQA analysis of the atomic and interatomic interaction energies indicated hydrogen bond formation was responsible for the stability of most of the local minima in the potential energy surface. In these conformers, the tandem participation of interactions was operating by way of two- or three-centered (bifurcated) cooperative networks. For the intramolecular hydrogen bond interplay in cooperativity, changes of the IQA atomic and interatomic interaction energies of the participant interactions were monitored during the formation of cooperative networks. The results of the intramolecular cooperativity were evaluated with changes of the delocalization index and bond distances.

How π back-donation quantitatively controls the CO stretching response in classical and non-classical metal carbonyl complexes

The CO stretching response upon coordination to a metal M to form [(L) n M(CO)] m complexes (L is an auxiliary ligand) is investigated in relation to the σ donation and π back-donation components of the M-CO bond and to the electrostatic effect exerted by the ligand-metal fragment. Our analysis encompasses over 30 carbonyls, in which the relative importance of donation, back-donation and electrostatics are varied either through the ligand in a series of [(L)Au(CO)]0/+ gold(i) complexes, or through the metal in a series of anionic, neutral and cationic homoleptic carbonyls. Charge-displacement analysis is used to obtain well-defined, consistent measures of σ donation and π back-donation charges, as well as to quantify the σ and π components of CO polarization. It is found that all complexes feature a comparable charge flow of σ symmetry (both in the M-CO bonding region and in the CO fragment itself), which is therefore largely uncorrelated to CO response. By contrast, π back-donation is exceptionally variable and is found to correlate tightly with the change in CO bond distance, with the shift in CO stretching frequency, and with the extent and direction (C → O or C ← O) of the CO π polarization. As a result, we conclusively show that π back-donation can be an important bond component also in non-classical carbonyls and we provide the framework in which the spectroscopic data on coordinated CO can be used to extract quantitative information on the π donor properties of metal-ligand moieties.

Hydrogen bond cooperativity and anticooperativity within the water hexamer

We propose a hierarchy of H-bond strength in terms of the single and double character of the involved donor and acceptors within different structures of (H₂O)₆.

First principles static and dynamic calculations for the transition metal hydride series MH4L3 (M = Fe, Ru and Os; L = NH3, PH3 and PF3)

We present a first principles static and dynamical study of the transition metal hydride series MH4L3 (M = Fe, Ru and Os; L = NH3, PH3 and PF3), with a view to arriving at an understanding of how the variation in the electronic properties of the metal sites and ligands can influence the dynamics of the resulting complexes. A broad range of behaviour was observed, encompassing stable classical minima (M = Os, L = NH3 and M = Ru, L = PH3) to stable η(2)-H2 non-classical minima (M = Fe, L = PF3 and M = Ru, L = PH3 or PF3), with the other structures exhibiting dynamical behaviour that spontaneously converted between the classical and non-classical states during the molecular dynamics simulations. The importance of a small L(axial)-M-L(axial) angle in stabilising the non-classical state is highlighted, as is a short η(2)-H2···H(cis) distance in non-classical complexes that spontaneously convert to the classical form. We also investigated the changes in the electronic structure of the complex FeH4(PH3)3 during a η(2)-H2 bond breaking/bond making reaction and observed direct evidence of the 'cis effect', whereby a neighbouring hydride ligand acts to stabilise the intermediate classical state.