Metavalent or Hypervalent Bonding: Is There a Chance for Reconciliation?

A family of solids including crystalline phase change materials such as GeTe and Sb2 Te3 , topological insulators like Bi2 Se3, and halide perovskites such as CsPbI3 possesses an unconventional property portfolio that seems incompatible with ionic, metallic, or covalent bonding. Instead, evidence is found for a bonding mechanism characterized by half-filled p-bands and a competition between electron localization and delocalization. Different bonding concepts have recently been suggested based on quantum chemical bonding descriptors which either define the bonds in these solids as electron-deficient (metavalent) or electron-rich (hypervalent). This disagreement raises concerns about the accuracy of quantum-chemical bonding descriptors is showed. Here independent of the approach chosen, electron-deficient bonds govern the materials mentioned above is showed. A detailed analysis of bonding in electron-rich XeF2 and electron-deficient GeTe shows that in both cases p-electrons govern bonding, while s-electrons only play a minor role. Yet, the properties of the electron-deficient crystals are very different from molecular crystals of electron-rich XeF2 or electron-deficient B2 H6 . The unique properties of phase change materials and related solids can be attributed to an extended system of half-filled bonds, providing further arguments as to why a distinct nomenclature such as metavalent bonding is adequate and appropriate for these solids.

Calculation of the ELF in the excited state with single-determinant methods.

Since its first definition, back in 1990, the electron localization function (ELF) has settled as one of the most commonly employed techniques to characterize the nature of the chemical bond in real space. Although most of the work using the ELF has focused on the study of ground-state chemical reactivity, a growing interest has blossomed to apply these techniques to the nearly unexplored realm of excited states and photochemistry. Since accurate excited electronic states usually require to account appropriately for electron correlation, the standard single-determinant ELF formulation cannot be blindly applied to them, and it is necessary to turn to correlated ELF descriptions based on the two-particle density matrix (2-PDM). The latter requires costly wavefunction approaches, unaffordable for most of the systems of current photochemical interest. Here, we compare the exact, 2-PDM-based ELF results with those of approximate 2-PDM reconstructions taken from reduced density matrix functional theory. Our approach is put to the test in a wide variety of representative scenarios, such as those provided by the lowest-lying excited electronic states of simple diatomic and polyatomic molecules. Altogether, our results suggest that even approximate 2-PDMs are able to accurately reproduce, on a general basis, the topological and statistical features of the ELF scalar field, paving the way toward the application of cost-effective methodologies, such as time-dependent-Hartree-Fock or time-dependent density functional theory, in the accurate description of the chemical bonding in excited states of photochemical relevance.

A QCT View of the Interplay between Hydrogen Bonds and Aromaticity in Small CHON Derivatives.

The somewhat elusive concept of aromaticity plays an undeniable role in the chemical narrative, often being considered the principal cause of the unusual properties and stability exhibited by certain π skeletons. More recently, the concept of aromaticity has also been utilised to explain the modulation of the strength of non-covalent interactions (NCIs), such as hydrogen bonding (HB), paving the way towards the in silico prediction and design of tailor-made interacting systems. In this work, we try to shed light on this area by exploiting real space techniques, such as the Quantum Theory of Atoms in Molecules (QTAIM), the Interacting Quantum Atoms (IQA) approaches along with the electron delocalisation indicators Aromatic Fluctuation (FLU) and Multicenter (MCI) indices. The QTAIM and IQA methods have been proven capable of providing an unbiased and rigorous picture of NCIs in a wide variety of scenarios, whereas the FLU and MCI descriptors have been successfully exploited in the study of diverse aromatic and antiaromatic systems. We used a collection of simple archetypal examples of aromatic, non-aromatic and antiaromatic moieties within organic molecules to examine the changes in π delocalisation and aromaticity induced by the Aromaticity and Antiaromaticity Modulated Hydrogen Bonds (AMHB). We observed fundamental differences in the behaviour of systems containing the HB acceptor within and outside the ring, e.g., a destabilisation of the rings in the former as opposed to a stabilisation of the latter upon the formation of the corresponding molecular clusters. The results of this work provide a physically sound basis to rationalise the strengthening and weakening of AMHBs with respect to suitable non-cyclic non-aromatic references. We also found significant differences in the chemical bonding scenarios of aromatic and antiaromatic systems in the formation of AMHB. Altogether, our investigation provide novel, valuable insights about the complex mutual influence between hydrogen bonds and π systems.

Partition of the electronic energy of the PM7 method via the interacting quantum atoms approach.

Partitions of the electronic energy such as that provided by the Interacting Quantum Atoms (IQA) approach have given valuable insights for numerous chemical systems and processes. Unfortunately, this kind of analysis may involve the integration of scalar fields over very irregular volumes, a condition which leads to a large and often prohibitive computational effort. These circumstances have limited the use of these energy partitions to systems comprising a few tens of atoms at most. On the other hand, semiempirical methods have proved useful in the study of systems of several thousands of atoms. Therefore, the goal of this work is to carry out partitions of the semiempirical method PM7 in compliance with the IQA approach. For this purpose, we computed one- and two-atomic energetic contributions whose sum equals the PM7 electronic energy. We illustrate how one might exploit the partition of electronic energies computed via the PM7 method by considering small organic and inorganic molecules and the energetics of individual hydrogen bond interactions within several water clusters which include (H2O)30, (H2O)50 and (H2O)100. We also considered the solvation of the amphiphilic caprylate anion to exemplify how to exploit the energy partition proposed in this paper. Overall, this investigation shows how the approach put forward herein might give further insights of the interactions occurring within complex systems in physical and biological chemistry.

NNAIMQ: A neural network model for predicting QTAIM charges.

Atomic charges provide crucial information about the electronic structure of a molecular system. Among the different definitions of these descriptors, the one proposed by the Quantum Theory of Atoms in Molecules (QTAIM) is particularly attractive given its invariance against orbital transformations although the computational cost associated with their calculation limits its applicability. Given that Machine Learning (ML) techniques have been shown to accelerate orders of magnitude the computation of a number of quantum mechanical observables, in this work, we take advantage of ML knowledge to develop an intuitive and fast neural network model (NNAIMQ) for the computation of QTAIM charges for C, H, O, and N atoms with high accuracy. Our model has been trained and tested using data from quantum chemical calculations in more than 45 000 molecular environments of the near-equilibrium CHON chemical space. The reliability and performance of NNAIMQ have been analyzed in a variety of scenarios, from equilibrium geometries to molecular dynamics simulations. Altogether, NNAIMQ yields remarkably small prediction errors, well below the 0.03 electron limit in the general case, while accelerating the calculation of QTAIM charges by several orders of magnitude.

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.

On the Relationship between Hydrogen Bond Strength and the Formation Energy in Resonance-Assisted Hydrogen Bonds.

Resonance-assisted hydrogen bonds (RAHB) are intramolecular contacts that are characterised by being particularly energetic. This fact is often attributed to the delocalisation of π electrons in the system. In the present article, we assess this thesis via the examination of the effect of electron-withdrawing and electron-donating groups, namely -F, -Cl, -Br, -CF3, -N(CH3)2, -OCH3, -NHCOCH3 on the strength of the RAHB in malondialdehyde by using the Quantum Theory of Atoms in Molecules (QTAIM) and the Interacting Quantum Atoms (IQA) analyses. We show that the influence of the investigated substituents on the strength of the investigated RAHBs depends largely on its position within the π skeleton. We also examine the relationship between the formation energy of the RAHB and the hydrogen bond interaction energy as defined by the IQA method of wave function analysis. We demonstrate that these substituents can have different effects on the formation and interaction energies, casting doubts regarding the use of different parameters as indicators of the RAHB formation energies. Finally, we also demonstrate how the energy density can offer an estimation of the IQA interaction energy, and therefore of the HB strength, at a reduced computational cost for these important interactions. We expected that the results reported herein will provide a valuable understanding in the assessment of the energetics of RAHB and other intramolecular interactions.

Lewis Structures from Open Quantum Systems Natural Orbitals: Real Space Adaptive Natural Density Partitioning.

Building chemical models from state-of-the-art electronic structure calculations is not an easy task, since the high-dimensional information contained in the wave function needs to be compressed and read in terms of the accepted chemical language. We have already shown ( Phys. Chem. Chem. Phys. 2018, 20, 21368) how to access Lewis structures from general wave functions in real space by reformulating the adaptive natural density partitioning (AdNDP) method proposed by Zubarev and Boldyrev ( Phys. Chem. Chem. Phys. 2008, 10, 5207). This provides intuitive Lewis descriptions from fully orbital invariant position space descriptors but depends on not immediately accessible higher order cumulant density matrices. By using an open quantum systems (OQS) perspective, we here show that the rigorously defined OQS fragment natural orbitals can be used to build a consistent real space adaptive natural density partitioning based only on spatial information and the system's one-particle density matrix. We show that this rs-AdNDP approach is a cheap, efficient, and robust technique that immerses electron counting arguments fully in the real space realm.

Energetic Descriptors of Steric Hindrance in Real Space: An Improved IQA Picture*.

Steric hindrance (SH) plays a central role in the modern chemical narrative, lying at the core of chemical intuition. As it however happens with many successful chemical concepts, SH lacks an underlying physically sound root, and multiple mutually inconsistent approximations have been devised to relate this fuzzy concept to computationally derivable descriptors. We here argue that being SH related to spatial as well as energetic features of interacting systems, SH can be properly handled if we chose a real space energetic stance like the Interacting Quantum Atoms (IQA) approach. Drawing on previous work by Popelier and coworkers (ChemistryOpen 8, 560, 2019) we build an energetic estimator of SH, referred to as EST . We show that the rise in the self-energy of a fragment that accompanies steric congestion is a faithful proxy for the chemist's SH concept if we remove the effect of charge transfer. This can be done rigorously, and the EST here defined provides correct sterics even for hydrogen atoms, where the plain use of deformation energies leads to non-chemical results. The applicability of EST is validated in several chemical scenarios, going from atomic compressions to archetypal SN2 reactions. EST is shown to be a robust steric hindrance descriptor.

Directing the Crystal Packing in Triphenylphosphine Gold(I) Thiolates by Ligand Fluorination.

We explore herein the supramolecular interactions that control the crystalline packing in a series of fluorothiolate triphenylphosphine gold(I) compounds with the general formula [Au(SRF)(Ph3P)] in which Ph3P = triphenylphosphine and SRF = SC6F5, SC6HF4-4, SC6F4(CF3)-4, SC6H3F2-2,4, SC6H3F2-3,4, SC6H3F2-3,5, SC6H4(CF3)-2, SC6H4F-2, SC6H4F-3, SC6H4F-4, SCF3, and SCH2CF3. We use for this purpose (i) DFT electronic structure calculations and (ii) the quantum theory of atoms in molecules and the non-covalent interactions index methods of wave function analyses. Our combined experimental and computational approach yields a general understanding of the effects of ligand fluorination in the crystalline self-assembly of the examined systems, in particular, about the relative force of aurophilic contacts compared with other supramolecular interactions. We expect this information to be useful in the design of materials based on gold coordination compounds.

Laplacian of the Hamiltonian Kinetic Energy Density as an Indicator of Binding and Weak Interactions.

The kinetic energy is the center of a controversy between two opposite points of view about its role in the formation of a chemical bond. One school states that a lowering of the kinetic energy associated with electron delocalization is the key stabilization mechanism of covalent bonding. In contrast, the opposite school holds that a chemical bond is formed by a decrease in the potential energy due to a concentration of electron density within the binding region. In this work, a topographic analysis of the Hamiltonian Kinetic Energy Density (KED) and its laplacian is presented to gain more insight into the role of the kinetic energy within chemical interactions. This study is focused on atoms, diatomic and organic molecules, along with their dimers. In addition, it is shown that the laplacian of the Hamiltonian KED exhibits a shell structure in atoms and that their outermost shell merge when a molecule is formed. A covalent bond is characterized by a concentration of kinetic energy, potential energy and electron densities along the internuclear axis, whereas a charge-shift bond is characterized by a fusion of external concentration shells and a depletion in the bonding region. In the case of weak intermolecular interactions, the external shell of the molecules merge into each other resulting in an intermolecular surface comparable to that obtained by the Non-covalent interaction (NCI) analysis.

Exotic Bonding Regimes Uncovered in Excited States.

Real-space tools were employed to show that the chemical bonding scenario used routinely to understand ground states lacks the necessary flexibility in excited states. It is shown that, even for two-center, two-electron bonds, the real-space bond orders have exotic values that have never been reported. The nature of these situations was uncovered by using electron-counting techniques that provide an appealing statistical interpretation of bonding descriptors, together with simple physical models. Bond orders greater than one as well as negative bond orders for a single bonding electron pair emerge in situations in which the electrons in the pair show a gregarious (bosonic) instead of the usual lonely (fermionic) behavior. In the first case the gregarious pair is intra-atomic, whereas the coupling is interatomic in the second. A number of examples are used to substantiate these claims.

Chemical Bonding from the Statistics of the Electron Distribution.

An introduction to the theory of chemical bonding from the point of view of the statistics of the electron distribution is presented. When atoms bind to form a molecule, their originally fixed number of electrons ceases to be a well-defined observable, and this implies that their in-the-molecule electron populations fluctuate. If a chemically meaningful definition of an atom in a molecule is assumed, the probabilities of finding a given number of electrons in each of the atoms comprising the molecule can be computed. We show in this review how the complete electron distribution function (EDF) can be used to reconstruct the basic concepts and quantities used in chemical bonding without recourse to the orbital paradigm. From the statistical point of view, which inherits Born's probabilistic interpretation of quantum mechanics, a set of atoms are bonded when their electron populations are mutually dependent. We quantify this statistical dependence by the cumulant moments of the EDF, which provide a consistent description of both two- and multi-center bonding. Particular attention is paid to building EDFs from model wavefunctions. With this, a simple bridge with orbital thinking is built. The statistical interpretation allows to easily classify all possible bonds of a given kind. We show that there are vast unexplored territories that should receive due consideration. Although building EDFs from models is easy and very instructive, the contrary is considerably more difficult. Recipes to extract chemical information from computed EDFs are also reviewed and, in all the cases, simple toy systems are used to show how the methodology works, allowing non-experts to follow easily the presentation.

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 .

Mimicking Enzymes: Asymmetric Induction inside a Carbamate-Based Steroidal Cleft.

Cholic acid has been elaborated into a carbamate-based tripodal architecture, which is able to promote an asymmetric organic transformation inside its chiral cavity. The nature of this steroidal catalyst has been disclosed by quantum-chemical calculations. It comprises the preorganization and confinement of the reagents within the cavity of the steroid to form a supramolecular complex held together by means of cooperative H-bond contacts. This operational mode resembles that of some enzymes.

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.

Beryllium Bonding in the Light of Modern Quantum Chemical Topology Tools.

We apply several modern quantum chemical topology (QCT) tools to explore the chemical bonding in well established beryllium bonds. By using the interacting quantum atoms (IQA) approach together with electron distribution functions (EDF) and the natural adaptive orbitals (NAdOs) picture, we show that, in agreement with orbital-based analyses, the interaction in simple σ and π complexes formed by BeX2 (X = H, F, Cl) with water, ammonia, ethylene, and acetylene is dominated by electrostatic terms, albeit covalent contributions cannot be ignored. Our detailed analysis proves that several σ back-donation channels are relevant in these dimers, actually controlling the conformational preference in the π adducts. A number of one-electron beryllium bonds are also studied. Orbital invariant real space arguments clearly show that the role of covalency and charge transfer cannot be ignored.

The bifunctional catalytic role of water clusters in the formation of acid rain.

State-of-the-art chemical bonding analyses show that water clusters have a bifunctional catalytic role in the formation of H2SO4 in acid rain. The embedded H2O monomers mitigate the change in the chemical bonding scenario of the rate-limiting step, reducing thereby the corresponding activation energy in accordance with Hammond's postulate. We expect that the insights given herein will prove useful in the elucidation of the catalytic mechanisms of water in inorganic and organic aqueous chemistry.

An unexpected bridge between chemical bonding indicators and electrical conductivity through the localization tensor.

While the modern theory of the insulating state shows that the conducting or insulating properties of a system can be extracted solely from the ground state properties via the so-called localization tensor (LT), no chemical reading of this important quantity has ever been offered. Here, a remarkable link between the LT and the bond orders as described by the delocalization indices (DIs) of chemical bonding theory is reported. This is achieved through a real space partition of the LT into intra- and interatomic contributions. We show that the convergence or divergence of the LT in the thermodynamic limit, which signals the insulating or conducting nature of an extended system, respectively, can be nailed down to DIs. This allows for the exploitation of traditional chemical intuition to identify essential and spectator atomic groups in determining electrical conductivity. The thermodynamic limit of the LT is controlled by the spatial decay rate of the interatomic DIs, exponential in insulators and power-law in conductors. Computational data of a few selected toy systems corroborate our results.

Cooperative and anticooperative effects in resonance assisted hydrogen bonds in merged structures of malondialdehyde.

We analyzed non-additive effects in resonance assisted hydrogen bonds (RAHBs) in different ß-enolones, which are archetypal compounds of these types of interactions. For this purpose, we used (i) potential energy curves to compute the formation energy, ΔE, of the RAHBs of interest in different circumstances along with (ii) tools offered by quantum chemical topology, namely, the Quantum Theory of Atoms In Molecules (QTAIM) and the Interacting Quantum Atoms (IQA) electronic energy partition. We established the effect that a given H-bond exerts over ΔE associated with another RAHB, determining in this way the cooperativity or the anticooperativity of these interactions. The mesomeric structures and the QTAIM delocalisation indices are consistent with the determined cooperative or anticooperative character of two given RAHBs. The HB cooperativity and anticooperativity studied herein are directly reflected in the IQA interaction energy E, but they are modulated by the surrounding hydrocarbon chain. The IQA decomposition of ΔEcoop, a measure of the cooperativity between a pair of interacting RAHBs, indicates that the analyzed H-bond cooperative/anticooperative effects are associated with greater/smaller (i) strengthening of the pseudo-bicyclic structure of the compounds of interest and (ii) electron localisations with its corresponding changes in the intra and intermolecular exchange-correlation contributions to ΔE. Overall, we expect that this investigation will provide valuable insights into the interplay among hydrogen bonded atoms and the π system in RAHBs contributing in this way to the understanding of the general features of H-bonds.