On Atoms‐in‐Molecules Energies from Kohn–Sham Calculations

Determining the Factors Accounting for Reaction Selectivity: A Relative Energy Gradient - Interacting Quantum Atoms and Natural Bonding Orbitals Study

Identifying the main physicochemical properties accounting for the course of a reaction is of utmost importance to rationalize chemical syntheses. To this aim, the relative energy gradient (REG) method is an appealing approach because it is an unbiased and automatic process to extract the most relevant pieces of energy information. Initially formulated within the interacting quantum atoms (IQA) framework for a single reaction, here we extend the REG method to natural bond orbitals (NBO) analysis and to the case of two competitive processes. This development enables the determination of the driving forces of any chemical selectivity. We illustrate the extended REG method on the case study of ring opening in cyclobutenes, which is an important instance of the so-called torquoselectivity.

Affinity of Telluronium Chalcogen Bond Donors for Lewis Bases in Solution: A Critical Experimental-Theoretical Joint Study

Telluronium salts [Ar2 MeTe]X were synthesized, and their Lewis acidic properties towards a number of Lewis bases were addressed in solution by physical and theoretical means. Structural X-ray diffraction analysis of 21 different salts revealed the electrophilicity of the Te centers in their interactions with anions. Telluroniums' propensity to form Lewis pairs was investigated with OPPh3 . Diffusion-ordered NMR spectroscopy suggested that telluroniums can bind up to three OPPh3 molecules. Isotherm titration calorimetry showed that the related heats of association in 1,2-dichloroethane depend on the electronic properties of the substituents of the aryl moiety and on the nature of the counterion. The enthalpies of first association of OPPh3 span -0.5 to -5 kcal mol-1 . Study of the affinity of telluroniums for OPPh3 by state-of-the-art DFT and ab-initio methods revealed the dominant Coulombic and dispersion interactions as well as an entropic effect favoring association in solution. Intermolecular orbital interactions between [Ar2 MeTe]+ cations and OPPh3 are deemed insufficient on their own to ensure the cohesion of [Ar2 MeTe ⋅ Bn ]+ complexes in solution (B=Lewis base). Comparison of Grimme's and Tkatchenko's DFT-D4/MBD-vdW thermodynamics of formation of higher [Ar2 MeTe ⋅ Bn ]+ complexes revealed significant molecular size-dependent divergence of the two methodologies, with MBD yielding better agreement with experiment.

Aza-Michael Addition in Explicit Solvent: A Relative Energy Gradient-Interacting Quantum Atoms Study

Aza-Michael additions are key reactions in organic synthesis. We investigate, from a theoretical and computational point of view, several examples ranging from weak to strong electrophiles in dimethylsulfoxide treated as explicit solvent. We use the REG-IQA method, which is a quantum topological energy decomposition (Interacting Quantum Atoms, IQA) coupled to a chemical-interpretation calculator (Relative Energy Gradient, REG). We focus on the rate-limiting addition step in order to unravel the different events taking place in this step, and understand the influence of solvent on the reaction, with an eye on predicting the Mayr electrophilicity. For the first time, a link is established between an REG-IQA analysis and experimental values.

Non-covalent interactions from a Quantum Chemical Topology perspective

About half a century after its little-known beginnings, the quantum topological approach called QTAIM has grown into a widespread, but still not mainstream, methodology of interpretational quantum chemistry. Although often confused in textbooks with yet another population analysis, be it perhaps an elegant but somewhat esoteric one, QTAIM has been enriched with about a dozen other research areas sharing its main mathematical language, such as Interacting Quantum Atoms (IQA) or Electron Localisation Function (ELF), to form an overarching approach called Quantum Chemical Topology (QCT). Instead of reviewing the latter’s role in understanding non-covalent interactions, we propose a number of ideas emerging from the full consequences of the space-filling nature of topological atoms, and discuss how they (will) impact on interatomic interactions, including non-covalent ones. The architecture of a force field called FFLUX, which is based on these ideas, is outlined. A new method called Relative Energy Gradient (REG) is put forward, which is able, by computation, to detect which fragments of a given molecular assembly govern the energetic behaviour of this whole assembly. This method can offer insight into the typical balance of competing atomic energies both in covalent and non-covalent case studies. A brief discussion on so-called bond critical points is given, highlighting concerns about their meaning, mainly in the arena of non-covalent interactions.

Coordination of Ethylamine on Small Silver Clusters: Structural and Topological (ELF, QTAIM) Analyses

Amine ligands are expected to drive the organization of metallic centers as well as the chemical reactivity of silver clusters early growing during the very first steps of the synthesis of silver nanoparticles via an organometallic route. Density functional theory (DFT) computational studies have been performed to characterize the structure, the atomic charge distribution, and the planar two-dimensional (2D)/three-dimensional (3D) relative stability of small-size silver clusters (Ag_n, 2 ≤ n ≤ 7), with or without an ethylamine (EA) ligand coordinated to the Ag clusters. The transition from 2D to 3D structures is shifted from n = 7 to 6 in the presence of one EA coordinating ligand, and it is explained from the analysis of the Ag-N and Ag-Ag bond energies. For fully EA saturated silver clusters (Ag_n-EA_n), the effect on the 2D/3D transition is even more pronounced with a shift between n = 4 and 5. Subsequent electron localization function (ELF) and quantum theory of atoms in molecules (QTAIM) topological analyses allow for the fine characterization of the dative Ag-N and metallic Ag-Ag bonds, both in nature and in strength. Electron transfer from ethylamine to the coordinated silver atoms induces an increase of the polarization of the metallic core.

In-Situ Electronegativity and the Bridging of Chemical Bonding Concepts

One challenge in chemistry is the plethora of often disparate models for rationalizing the electronic structure of molecules. Chemical concepts abound, but their connections are often frail. This work describes a quantum‐mechanical framework that enables a combination of ideas from three approaches common for the analysis of chemical bonds: energy decomposition analysis (EDA), quantum chemical topology, and molecular orbital (MO) theory. The glue to our theory is the electron energy density, interpretable as one part electrons and one part electronegativity. We present a three‐dimensional analysis of the electron energy density and use it to redefine what constitutes an atom in a molecule. Definitions of atomic partial charge and electronegativity follow in a way that connects these concepts to the total energy of a molecule. The formation of polar bonds is predicted to cause inversion of electronegativity, and a new perspective of bonding in diborane and guanine−cytosine base‐pairing is presented. The electronegativity of atoms inside molecules is shown to be predictive of pK_a.

Cooperativity and Anticooperativity in Ion-Water Interactions: Implications for the Aqueous Solvation of Ions

Non-additive effects in hydrogen bonds (HB) take place as a consequence of electronic charge transfers. Therefore, it is natural to expect cooperativity and anticooperativity in ion-water interactions. Nevertheless, investigations on this matter are scarce. This paper addresses the interactions of (i) the cations Li⁺ , Na⁺ , K⁺ , Be²⁺ , Mg²⁺ , and Ca²⁺ together with (ii) the anions F^- , Cl^- , Br^- , NO₃ ^- and SO₄ ^2- with water clusters (H₂ O)_n , n=1-8, and the effects of these ions on the HBs within the complete molecular adducts. We used quantum chemical topology tools, specifically the quantum theory of atoms in molecules and the interacting quantum atoms energy partition to investigate non-additive effects among the interactions studied herein. Our results show a decrease on the interaction energy between ions and the first neighbouring water molecules with an increment of the coordination number. We also found strong cooperative effects in the interplay between HBs and ion-dipole interactions within the studied systems. Such cooperativity affects considerably the interactions among ions with their first and second solvation shells in aqueous environments. Overall, we believe this article provides valuable information about how ion-dipole contacts interact with each other and how they relate to other interactions, such as HBs, in the framework of non-additive effects in aqueous media.

A tool for deciphering the redox potential ranking of organic compounds: a case study of biomass-extracted quinones for sustainable energy

Carbonyl compounds have emerged as promising organic electrodes for sustainable energy storage. Accelerating the process of performant materials discovery relies on the possibility of developing methodologies to enable scanning of various sets of candidates. The genesis of this educated guess strategy must be privileged to reduce the search space of experiments, accelerate this research area and contribute to sustainable effort. To address this challenge, we built a quantitative structure-activity relationship to unveil the origin of the redox potential magnitude as a function of both structural features and complexation effects. The potential of this prediction model was demonstrated on various ortho-quinones directly derived from naturally occurring catechols. In addition to the modulation provided by substituent changes, the possibility of applying various types of alkaline(-earth)-ion electrochemistry was examined thoroughly. The power of partitioning the total molecular energy into additive atomic group contributions is highlighted, and the construction of this robust strategy provides guidance towards rational selection of the most suitable compound/metal-ion couples. An upshift/downshift of the redox potential by switching from Li to Mg/Na is revealed, while the identification of the relative role played by the various components of the systems as well as electrostatic interactions is clearly identified. These results, particularly the evidence of the different substituent effects on the single/double reduction potentials and as a function of the type of electrochemistry (Li/Na/Mg), have important implications for designing new electroactive compounds with tailored redox properties.

Isolation of an elusive phosphatetrahedrane

This exploratory synthesis investigation was undertaken to determine the viability of replacing a single carbon vertex with another p-block element in a highly strained tetrahedrane molecule. Phosphorus was selected for this purpose because the stable molecular form of elemental phosphorus is tetrahedral. Our synthetic strategy was to generate an unsaturated phosphorus center bonded to a substituted cyclopropenyl group, a situation that could lead to closure to provide the desired phosphatetrahedrane framework. This was accomplished by dehydrofluorination of the in situ generated fluorophosphine H(F)P(C ^t Bu)₃. Tri-tert-butyl phosphatetrahedrane, P(C ^t Bu)₃, was then isolated in 19% yield as a low-melting, volatile, colorless solid and characterized spectroscopically and by a single-crystal x-ray diffraction study, confirming the tetrahedral nature of the molecule's PC₃ core. The molecule exhibits unexpected thermal stability.

Nine questions on energy decomposition analysis

The paper collects the answers of the authors to the following questions: Is the lack of precision in the definition of many chemical concepts one of the reasons for the coexistence of many partition schemes? Does the adoption of a given partition scheme imply a set of more precise definitions of the underlying chemical concepts? How can one use the results of a partition scheme to improve the clarity of definitions of concepts? Are partition schemes subject to scientific Darwinism? If so, what is the influence of a community's sociological pressure in the "natural selection" process? To what extent does/can/should investigated systems influence the choice of a particular partition scheme? Do we need more focused chemical validation of Energy Decomposition Analysis (EDA) methodology and descriptors/terms in general? Is there any interest in developing common benchmarks and test sets for cross-validation of methods? Is it possible to contemplate a unified partition scheme (let us call it the "standard model" of partitioning), that is proper for all applications in chemistry, in the foreseeable future or even in principle? In the end, science is about experiments and the real world. Can one, therefore, use any experiment or experimental data be used to favor one partition scheme over another? © 2019 Wiley Periodicals, Inc.

Is the Fluorine in Molecules Dispersive? Is Molecular Electrostatic Potential a Valid Property to Explore Fluorine-Centered Non-Covalent Interactions?

Can two sites of positive electrostatic potential localized on the outer surfaces of two halogen atoms (and especially fluorine) in different molecular domains attract each other to form a non-covalent engagement? The answer, perhaps counterintuitive, is yes as shown here using the electronic structures and binding energies of the interactions for a series of 22 binary complexes formed between identical or different atomic domains in similar or related halogen-substituted molecules containing fluorine. These were obtained using various computational approaches, including density functional and ab initio first-principles theories with M06-2X, RHF, MP2 and CCSD(T). The physical chemistry of non-covalent bonding interactions in these complexes was explored using both Quantum Theory of Atoms in Molecules and Symmetry Adapted Perturbation Theories. The surface reactivity of the 17 monomers was examined using the Molecular Electrostatic Surface Potential approach. We have demonstrated inter alia that the dispersion term, the significance of which is not always appreciated, which emerges either from an energy decomposition analysis, or from a correlated calculation, plays a structure-determining role, although other contributions arising from electrostatic, exchange-repulsion and polarization effects are also important. The 0.0010 a.u. isodensity envelope, often used for mapping the electrostatic potential is found to provide incorrect information about the complete nature of the surface reactive sites on some of the isolated monomers, and can lead to a misinterpretation of the results obtained.

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.

Reliability of HF/IQA, B3LYP/IQA, and MP2/IQA data in interpreting the nature and strength of interactions

Using CCSD/BBC1/IQA as a reference to describe interactions in glycol conformers, including O4⋯H6 and O3⋯O4 interactions, B3LYP/IQA data produced an exact qualitative picture and exceptionally reliable IQA energy changes, resulting in a perfectly comparable FAMSEC-based quantitative interpretation.

A relative energy gradient (REG) study of the planar and perpendicular torsional energy barriers in biphenyl

Biphenyl is a prototype molecule, the study of which is important for a proper understanding of stereo-electronic effects. In the gas phase it has an equilibrium central torsion angle of ~ 45° and shows both a planar (0°) and a perpendicular (90°) torsional energy barrier. The latter is analysed for the first time. We use the newly proposed REG method, which is an exhaustive procedure that automatically ranks atomic energy contributions according to their importance in explaining the energy profile of a total system. Here, the REG method operates on energy contributions computed by the interacting quantum atoms method. This method is minimal in architecture and provides a crisp picture of well-defined and well-separated electrostatic, steric and exchange (covalent) energies at atomistic level. It is shown that the bond critical point occurring between the ortho-hydrogens in the planar geometry has been wrongly interpreted as a sign of repulsive interaction. A convenient metaphor of analysing football matches is introduced to clarify the role of a REG analysis.

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.

Can Combined Electrostatic and Polarization Effects Alone Explain the F···F Negative-Negative Bonding in Simple Fluoro-Substituted Benzene Derivatives? A First-Principles Perspective

The divergence of fluorine-based systems and significance of their nascent non-covalent chemistry in molecular assemblies are presented in a brief review of the field. Emphasis has been placed to show that type-I and -II halogen-centered F···F long-ranged intermolecular distances viable between the entirely negative fluorine atoms in some fluoro-substituted dimers of C6H6 can be regarded as the consequence of significant non-covalent attractive interactions. Such attractive interactions observed in the solid-state structures of C6F6 and other similar fluorine-substituted aromatic compounds have frequently been underappreciated. While these are often ascribed to crystal packing effects, we show using first-principles level calculations that these are much more fundamental in nature. The stability and reliability of these interactions are supported by their negative binding energies that emerge from a supermolecular procedure using MP2 (second-order Møller-Plesset perturbation theory), and from the Symmetry Adapted Perturbation Theory, in which the latter does not determine the interaction energy by computing the total energy of the monomers or dimer. Quantum Theory of Atoms in Molecules and Reduced Density Gradient Non-Covalent Index charge-density-based approaches confirm the F···F contacts are a consequence of attraction by their unified bond path (and bond critical point) and isosurface charge density topologies, respectively. These interactions can be explained neither by the so-called molecular electrostatic surface potential (MESP) model approach that often demonstrates attraction between sites of opposite electrostatic surface potential by means of Coulomb’s law of electrostatics, nor purely by the effect of electrostatic polarization. We provide evidence against the standalone use of this approach and the overlooking of other approaches, as the former does not allow for the calculation of the electrostatic potential on the surfaces of the overlapping atoms on the monomers as in the equilibrium geometry of a complex. This study thus provides unequivocal evidence of the limitation of the MESP approach for its use in gaining insight into the nature of reactivity of overlapped interacting atoms and the intermolecular interactions involved.

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.

Revealing Factors Influencing the Fluorine-Centered Non-Covalent Interactions in Some Fluorine-Substituted Molecular Complexes: Insights from First-Principles Studies

We examine the equilibrium structure and properties of six fully or partially fluorinated hydrocarbons and several of their binary complexes using computational methods. In the monomers, the electrostatic surface of the fluorine is predicted to be either entirely negative or weakly positive. However, its lateral sites are always negative. This enables the fluorine to display an anisotropic distribution of charge density on its electrostatic surface. While this is the electrostatic surface scenario of the fluorine atom, its negative sites in some of these monomers are shown to have the potential to engage in attractive engagements with the negative site(s) on the same atom in another molecule of the same type, or a molecule of a different type, to form bimolecular complexes. This is revealed by analyzing the results of current state-of-the-art computational approaches such as DFT, together with those obtained from the quantum theory of atoms in molecules, molecular electrostatic surface potential and symmetry adapted perturbation theories. We demonstrate that the intermolecular interaction energy arising in part from the universal London dispersion, which has been underappreciated for decades, is an essential factor in explaining the attraction between the negative sites, although energy arising from polarization strengthens the extent of the intermolecular interactions in these complexes.