Real-Space In Situ Bond Energies: Toward A Consistent Energetic Definition of Bond Strength

First Alliance of Pyrazole and Furoxan Leading to High-Performance Energetic Materials

Nitrogen heterocyclic scaffolds retain their leading position as valuable building blocks in material science, particularly for the design of small-molecule energetic materials. However, the search for more balanced combinations of directly linked heterocyclic cores is far from being exhausted and aims to reach ideally balanced high-energy substances. Herein, we present the synthetic route to novel pyrazole-furoxan framework enriched with nitro groups and demonstrate a promising set of properties, viz., good thermal stability, acceptable mechanical sensitivity, and high detonation performance. In-depth crystal analysis showed that the isomers having lower-impact sensitivity values in both types of regioisomeric pairs are those with the exocyclic furoxan oxygen atom being closer to the pyrazole ring. Owing to the favorable combination of high crystal densities (1.83-1.93 g cm-3), positive oxygen balance to CO (up to +13.9%), and high enthalpies of formation (322-435 kJ mol-1), the synthesized compounds show high calculated detonation velocities (8.4-9.1 km s-1) and excellent metal accelerating abilities. The incorporation of the 3-nitrofuroxan moiety increases the thermal stability (by ca. 20 °C) and decreases the mechanical sensitivity of target hybrid materials in both types of regioisomeric pairs. Simultaneously, the detonation performance of 3-nitrofuroxans is almost identical to that of 4-nitrofuroxans, highlighting the potential of the regioisomeric tunability in the future design of energetic materials.

Delocalization-ratio analysis of 3-center bonding in position-space for closo-boranes and related systems: Approaching the styx picture and beyond

Closo-boron hydrides BnHn 2- (n = 5-12) are a conceptually well understood class of compounds. For these and a few related prototype compounds, both the local and the global picture of 3-center bonding are extracted from position-space quantities based on the electron density and the pair density. For this purpose, three-center delocalization indices between quantum theory of atoms in molecules (QTAIM) atoms in position space are used to develop a consistent set of local bond and triangle, and global cluster delocalization ratios (DRs), which are quantitatively compared with conceptual Γ values derived from the styx code for each cluster. Combination of the cluster DRs with associated effective numbers of skeletal electron sharing (SES) for selected cluster surface edges, triangles, or the whole cluster yields effective styx type values describing the trend and even the size of the conceptual styx codes for closo-boranes BnHn 2- and related systems with increasing cluster size n reasonably well. For nonuniform cluster topologies, the different vertex degrees are shown to cause systematic 3-center wise bond delocalization effects for the associated edges and triangles of different average vertex degrees. Extension of DR analysis beyond the styx type triangular cluster-surface bonding corresponds to a triangulation of multicentric bonding. The cluster-wise results keep indicating consistency with the mixed 2- and 3-center bonding approach. The successfully established chemical meaning of the local edge, triangle, and global cluster DRs and their associated SES values constitutes the basis for systematic investigations of mixed 2- and 3-center bonding scenarios in particular in intermetallic and related (endohedral) cluster compounds in the future.

Persistence of atoms in molecules: there is room beyond electron densities

Evidence that the electronic structure of atoms persists in molecules to a much greater extent than has been usually admitted is presented. This is achieved by resorting to N-electron real-space descriptors instead of one- or at most two-particle projections like the electron or exchange-correlation densities. Here, the 3N-dimensional maxima of the square of the wavefunction, the so-called Born maxima, are used. Since this technique is relatively unknown to the crystallographic community, a case-based approach is taken, revisiting first the Born maxima of atoms in their ground state and then some of their excited states. It is shown how they survive in molecules and that, beyond any doubt, the distribution of electrons around an atom in a molecule can be recognized as that of its isolated, in many cases excited, counterpart, relating this fact with the concept of energetic promotion. Several other cases that exemplify the applicability of the technique to solve chemical bonding conflicts and to introduce predictability in real-space analyses are also examined.

Electron density-based protocol to recover the interacting quantum atoms components of intermolecular binding energy

A new approach for obtaining interacting quantum atoms-defined components of binding energy of intermolecular interactions, which bypasses the use of standard six-dimensional integrals and two-particle reduced density matrix (2-RDM) reconstruction, is proposed. To examine this approach, three datasets calculated within the density functional theory framework using the def2-TZVP basis have been explored. The first two, containing 53 weakly bound bimolecular associates and 13 molecular clusters taken from the crystal, were used in protocol refinement, and the third one containing other 20 bimolecular and three cluster systems served as a validation reference. In addition, to verify the performance of the proposed approach on an exact 2-RDM, calculations within the coupled cluster formalism were performed for part of the first set systems using the cc-pVTZ basis set. The process of optimization of the proposed parametric model is considered, and the role of various energy contributions in the formation of non-covalent interactions is discussed with regard to the obtained trends.

The effect of immediate environment on bond strength of different bond types-A valence bond study

The ability to design catalysis largely depends on our understanding of the electrostatic effect of the surrounding on the bonds participating in the reaction. Here, we used a simplistic model of point charges (PCs) to determine a set of rules guiding how to construct PC-bond arrangement that can strengthen or weaken different chemical bonds. Using valence bond theory to calculate the in situ bond energies, we show that the effect of the PC mainly depends on the bond's dipole moment irrespective of its type (being covalent or charge shift). That is, polar bonds are getting stronger or weaker depending on the sign and location of the PC, whereas non- or weakly polar bonds become stronger or weaker depending only on the location of the PC and to a smaller extent compared with polar bonds. We also show that for polar bonds, the maximal bond strengthening and weakening effect can be achieved when the PC is placed along the bond axis, as close as possible to the more and less polarizable atom/fragment, respectively. Finally, due to the stabilizing effects of polarizability, we show that, overall, it is easier to cause bond strengthening compared with bond weakening. Particularly, for polar bonds, bond strengthening is larger than bond weakening obtained by an oppositely signed PC. These rules should be useful in the future design of catalysis in, e.g., enzyme active sites.

The role of references and the elusive nature of the chemical bond

Chemical bonding theory is of utmost importance to chemistry, and a standard paradigm in which quantum mechanical interference drives the kinetic energy lowering of two approaching fragments has emerged. Here we report that both internal and external reference biases remain in this model, leaving plenty of unexplored territory. We show how the former biases affect the notion of wavefunction interference, which is purportedly recognized as the most basic bonding mechanism. The latter influence how bonding models are chosen. We demonstrate that the use of real space analyses are as reference-less as possible, advocating for their use. Delocalisation emerges as the reference-less equivalent to interference and the ultimate root of bonding. Atoms (or fragments) in molecules should be understood as a statistical mixture of components differing in electron number, spin, etc.

The theory of chemical bonding relies on arbitrary references. Here the authors report a fundamental study on the chemical bond showing that considering the binding fragments as objects in real space enables to eliminate inherent biases.

Bond Dissociation Energies Reveal the Participation of d Electrons in f-Element Halide Bonding

Bond dissociation energies (BDEs) reported in the literature for lanthanide monofluorides and lanthanide monochlorides LnX, where X = F or Cl, exhibit substantial irregular variations across the Ln series. It is demonstrated here that correlations of these variations with reported experimentally based atomic energies to prepare the Ln constituent for bonding reveal the nature of the bonding. Whereas some molecular characteristics are well understood in the context of highly ionic bonding, with LnX considered to be (Ln⁺)(X^-), some significant variations in BDEs are not well rationalized simply by ionization to convert Ln to Ln⁺ for bonding. Focusing here on lanthanide monofluorides LnF, a consideration of alternative Ln preparation schemes shows that a particularly good rationalization of BDEs is obtained by invoking the participation of a lanthanide 5d electron in bonding. This 5d participation could be in ionic (Ln⁺)(F^-) via π-donation from F^- 2p to empty Ln⁺ 5d orbitals or in covalent π-bonded Ln:F via polarization from Ln 5d to F 2p, with these ionic and polar covalent perspectives ultimately being equivalent. The inference of lanthanide 5d involvement suggests that the valence 4f and 6s electrons do not effectively participate in some key aspects of the bonding, presumably due to poor spatial overlap with F 2p orbitals. An extension to actinide monofluorides, AnF, assumes analogous ionic or polar covalent bonding involving a valence 6d electron and results in predictions for BDEs that include a general decrease from left to right across the series, except for a distinctive local minimum at AmF. Determining the BDE for AmF would serve to evaluate the predictions and the underlying assumption of 6d bonding. The BDE assessments/predictions for neutral monofluorides, LnF and AnF, are also applied to cationic LnF⁺ and AnF⁺, and it is noted that the approach can be directly extended to f-element monochlorides, monobromides, and monoiodides.

Interacting Quantum Atoms Analysis of the Reaction Force: A Tool to Analyze Driving and Retarding Forces in Chemical Reactions

The analysis of the reaction force and its topology has provided a wide range of fruitful concepts in the theory of chemical reactivity over the years, allowing to identify chemically relevant regions along a reaction profile. The reaction force (RF), a projection of the Hellmann-Feynman forces acting on the nuclei of a molecular system onto a suitable reaction coordinate, is partitioned using the interacting quantum atoms approach (IQA). The exact IQA molecular energy decomposition is now shown to open a unique window to identify and quantify the chemical entities that drive or retard a chemical reaction. The RF/IQA coupling offers an extraordinarily detailed view of the type and number of elementary processes that take reactants into products, as tested on two sets of simple reactions.

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.

Relationship Investigation between C(sp2)-X and C(sp3)-X Bond Energies Based on Substituted Benzene and Methane

The C-X bonds of organic compounds between group X and a saturated or unsaturated carbon atom differ in bond energy. To identify the causes of variation is of great significance in terms of bond nature understanding and bond energy estimation. In this paper, the electronegativity χ[X] of group X was calculated by the "valence electron equalized electronegativity" method. Then, χ[X] and the electronic effect constant of the substituent were taken as variables to establish equations for quantitative correlation between C(sp³)-X and C(sp²)-X for the calculation of C-X bond energies. The aim is make comparison between substituted methane, Me-X, and substituted benzene, Ph-X, as well as that between Me-X and substituted ethylene, C₂H₃-X. We conducted calculation over 40 compounds that contain different X groups, and the results reveal that the C(sp³)-X and C(sp²)-X bond energies are under the influence of a number of factors. In addition to the covalent properties of C and X atoms and χ[X], the bond energies of C(sp²)-X (i.e., D[C(sp²)-X]) are under the influence of the field/inductive effect (σ_F[X]) and conjugated effect (σ_R[X]) of group X, with the former causing a decrease while the latter an increase of D[C(sp²)-X]. Using the acquired quantitative correlation equations and on the basis of a relatively rich set of measured D[Me-X] data, we estimated D[Ph-X] of Ph-X and D[C₂H₃-X] of C₂H₃-X, and the estimation accuracy is within experimental uncertainty. Employing the above method, the D[C(sp²)-X] of 33 substituted benzenes, 53 substituted ethenes, and 82 α-substituted naphthalenes was estimated with satisfactory outcomes.

Interatomic exchange-correlation interaction energy from a measure of quantum theory of atoms in molecules topological bonding: A diatomic case

The potential relations between the measure of topological interatomic bonding-integrals of electron density with respect to internuclear axis over the corresponding quantum theory of atoms in molecules (QTAIM)-defined interatomic surface (IAS)-and interatomic exchange-correlation contributions from the interacting quantum atoms approach are discussed. The quantum chemical computations of 38 equilibrium diatomic systems at different levels of theory (HF, MP2, MP4SDQ, and CCSD) are invoked to support abstract considerations. Parameters of excellent correlations between IAS integrals and interatomic exchange-correlation energy are found by the optimization. The performance of these trends depends on the accuracy of the electronic correlation treatment. The resulting trends are a unique feature of equilibrium states, whereas more complicated dependencies are explored for several systems at non-equilibrium conditions. The relations of established trends with other IAS-based estimations of strength of bonding interactions between topological atoms and issues explored for multiatomic systems are briefly discussed.

Structure-directing sulfur...metal noncovalent semicoordination bonding

The abundance and geometric features of nonbonding contacts between metal centers and `soft' sulfur atoms bound to a non-metal substituent R were analyzed by processing data from the Cambridge Structural Database. The angular arrangement of M, S and R atoms with ∠(R-S...M) down to 150° was a common feature of the late transition metal complexes exhibiting shortened R-S...M contacts. Several model nickel(II), palladium(II), platinum(II) and gold(I) complexes were chosen for a theoretical analysis of R-S...M interactions using the DFT method applied to (equilibrium) isolated systems. A combination of the real-space approaches, such as Quantum Theory of Atoms in Molecules (QTAIM), noncovalent interaction index (NCI), electron localization function (ELF) and Interacting Quantum Atoms (IQA), and orbital (Natural Bond Orbitals, NBO) methods was used to provide insights into the nature and energetics of R-S...M interactions with respect to the metal atom identity and its coordination environment. The explored features of the R-S...M interactions support the trends observed by inspecting the CSD statistics, and indicate a predominant contribution of semicoordination bonds between nucleophilic sites of the sulfur atom and electrophilic sites of the metal. A contribution of chalcogen bonding (that is formally opposite to semicoordination) was also recognized, although it was significantly smaller in magnitude. The analysis of R-S...M interaction strengths was performed and the structure-directing role of the intramolecular R-S...M interactions in stabilizing certain conformations of metal complexes was revealed.

Tetrel Interactions from an Interacting Quantum Atoms Perspective

Tetrel bonds, the purportedly non-covalent interaction between a molecule that contains an atom of group 14 and an anion or (more generally) an atom or molecule with lone electron pairs, are under intense scrutiny. In this work, we perform an interacting quantum atoms (IQA) analysis of several simple complexes formed between an electrophilic fragment (A) (CH₃F, CH₄, CO₂, CS₂, SiO₂, SiH₃F, SiH₄, GeH₃F, GeO₂, and GeH₄) and an electron-pair-rich system (B) (NCH, NCO-, OCN-, F-, Br-, CN-, CO, CS, Kr, NC-, NH₃, OC, OH₂, SH-, and N₃-) at the aug-cc-pvtz coupled cluster singles and doubles (CCSD) level of calculation. The binding energy ( E bind AB ) is separated into intrafragment and inter-fragment components, and the latter in turn split into classical and covalent contributions. It is shown that the three terms are important in determining E bind AB , with absolute values that increase in passing from electrophilic fragments containing C, Ge, and Si. The degree of covalency between A and B is measured through the real space bond order known as the delocalization index ( δ AB ). Finally, a good linear correlation is found between δ AB and E xc AB , the exchange correlation (xc) or covalent contribution to E bind AB .

On Electrostatics, Covalency, and Chemical Dashes: Physical Interactions versus Chemical Bonds

The increasing availability of real-space interaction energies between quantum atoms or fragments that provide a chemically intuitive decomposition of intrinsic bond energies into electrostatic and covalent terms [see, for instance, Chem. Eur. J. 2018, 24, 9101] provides evidence for differences between the physicist's concept of interaction and the chemist's concept of a bond. Herein, it is argued that, for the former, all types of interactions are treated equally, whereas, for the latter, only the covalent short-range interactions have actually been used to build intuition about chemical graphs and chemical bonds. This has led to the bonding role of long-range Coulombic terms in molecular chemistry being overlooked. Simultaneously, blind consideration of electrostatic terms in chemical bonding parlance may lead to confusion. The relationship between these concepts is examined herein, and some notes of caution on how to merge them are proposed.

Real space bond orders are energetic descriptors

Orbital invariant position space techniques are used to show a theoretical link between the conventional concept of bond order and the energetics of chemical interactions.