Does Aromaticity Play a Role in Electronic and Structural Properties of YBn (n=2-14) Clusters?

Nanoclusters exhibit electronic, optical, and magnetic properties that differ significantly from those of extended and molecular systems with comparable stoichiometries. In this work, we examined the structural, energetic, and electronic characteristics of yttrium-doped boron clusters (YBn,  n =2-14) with robust wavefunction analysis tools. Special emphasis is placed on the elucidation of the potential aromatic character exhibited by the resultant molecules and how it can affect their chemical bonding and stability. Our results revealed that the YBn stability is governed by the maximization of the ionic Y-B interactions. This is evidenced from the lowest-energy conformations, which manifest as half-sandwich structures wherein the majority of boron atoms are bonded to yttrium. The stabilization of such chemical contacts comes at the expense of a notorious depletion of the Y local electron density, crystallizing in a considerable ionic character, close to Y2+ + Bn2-. Such a  charge transfer is coupled to the enhancement of the electron delocalization within the YBn lattice, resulting in quite remarkable local and global aromatic characters. Altogether, this study shows how the toolkit of real space chemical bonding descriptors can offer valuable insights into the structural and electronic properties,  of YBn clusters, contributing to a better understanding of their behavior.

Atoms in molecules in real space: a fertile field for chemical bonding.

In this perspective, we review some recent advances in the concept of atoms-in-molecules from a real space perspective. We first introduce the general formalism of atomic weight factors that allows unifying the treatment of fuzzy and non-fuzzy decompositions under a common algebraic umbrella. We then show how the use of reduced density matrices and their cumulants allows partitioning any quantum mechanical observable into atomic or group contributions. This circumstance provides access to electron counting as well as energy partitioning, on the same footing. We focus on how the fluctuations of atomic populations, as measured by the statistical cumulants of the electron distribution functions, are related to general multi-center bonding descriptors. Then we turn our attention to the interacting quantum atom energy partitioning, which is briefly reviewed since several general accounts on it have already appeared in the literature. More attention is paid to recent applications to large systems. Finally, we consider how a common formalism to extract electron counts and energies can be used to establish an algebraic justification for the extensively used bond order-bond energy relationships. We also briefly review a path to recover one-electron functions from real space partitions. Although most of the applications considered will be restricted to real space atoms taken from the quantum theory of atoms in molecules, arguably the most successful of all the atomic partitions devised so far, all the take-home messages from this perspective are generalizable to any real space decompositions.

A real space picture of the role of steric effects in SN 2 reactions.

Within substitution reactions, the Bimolecular Nucleophilic Substitution (SN 2) reaction mechanism is one of the most frequently found and studied ones. Among other factors, the easiness of the SN 2 pathway is classically considered to be determined by steric hindrance. However, the diffuse nature of the latter inevitably darkens these and other arguments holding the pillars of chemical intuition. In this work, we employ the steric energy (EST ) descriptor, formulated within the Interacting Quantum Atoms approach, to offer insights regarding this problem. The steric demands of the substrate, nucleophile and leaving group were studied using the gas-phase SN 2 reaction with different organic skeletons (CH3 , CH3 CH2 , (CH3 )2 CH, (CH3 )3 C, (CH3 )3 CCH2 ) and halogens (F, Cl, and Br) as test-bed systems. Our results show that, according to EST , the SH experienced along these simple reactions fits, in the general case, the trends predicted by a meticulous and rigorous application of chemical intuition. However, steric clash alone should not be considered as the only argument used to explain the easiness of the SN 2 reaction over different electrophiles.

Does Steric Hindrance Actually Govern the Competition between Bimolecular Substitution and Elimination Reactions?

Bimolecular nucleophilic substitution (SN2) and elimination (E2) reactions are prototypical examples of competing reaction mechanisms, with fundamental implications in modern chemical synthesis. Steric hindrance (SH) is often considered to be one of the dominant factors determining the most favorable reaction out of the SN2 and E2 pathways. However, the picture provided by classical chemical intuition is inevitably grounded on poorly defined bases. In this work, we try to shed light on the aforementioned problem through the analysis and comparison of the evolution of the steric energy (EST), settled within the IQA scheme and experienced along both reaction mechanisms. For such a purpose, the substitution and elimination reactions of a collection of alkyl bromides (R-Br) with the hydroxide anion (OH-) were studied in the gas phase at the M06-2X/aug-cc-pVDZ level of theory. The results show that, generally, EST recovers the appealing trends already anticipated by chemical intuition and organic chemistry, supporting the role that SH is classically claimed to play in the competition between SN2 and E2 reactions.

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.

The nature of the intermolecular interaction in (H2X)2 (X = O, S, Se).

Hydrogen bonds (HBs) are crucial non-covalent interactions in chemistry. Recently, the occurrence of an HB in (H2S)2 has been reported (Arunan et al., Angew. Chem., Int. Ed., 2018, 57, 15199), challenging the textbook view of H2S dimers as mere van der Waals clusters. We herein try to shed light on the nature of the intermolecular interactions in the H2O, H2S, and H2Se dimers via correlated electronic structure calculations, Symmetry Adapted Perturbation Theory (SAPT) and Quantum Chemical Topology (QCT). Although (H2S)2 and (H2Se)2 meet some of the criteria for the occurrence of an HB, potential energy curves as well as SAPT and QCT analyses indicate that the nature of the interaction in (H2O)2 is substantially different (e.g. more anisotropic) from that in (H2S)2 and (H2Se)2. QCT reveals that the HB in (H2O)2 includes substantial covalent, dispersion and electrostatic contributions, while the last-mentioned component plays only a minor role in (H2S)2 and (H2Se)2. The major contributions to the interactions of the dimers of H2S and H2Se are covalency and dispersion as revealed by the exchange-correlation components of QCT energy partitions. The picture yielded by SAPT is somewhat different but compatible with that offered by QCT. Overall, our results indicate that neither (H2S)2 nor (H2Se)2 are hydrogen-bonded systems, showing how the nature of intermolecular contacts involving hydrogen atoms evolves in a group down the periodic table.

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.

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.

Photochemistry in Real Space: Batho- and Hypsochromism in the Water Dimer.

Invited for the cover of this issue is Alberto Fernández-Alarcón and co-workers at The Institute of Chemistry of the National Autonomous University of Mexico and The School of Chemistry of the University of Oviedo. The image depicts the real space analysis of the excitation energies in the double blue and red shift of the water dimer. Read the full text of the article at 10.1002/chem.202002854.

Photochemistry in Real Space: Batho- and Hypsochromism in the Water Dimer.

The development of chemical intuition in photochemistry faces several difficulties that result from the inadequacy of the one-particle picture, the Born-Oppenheimer approximation, and other basic ideas used to build models. It is shown herein how real-space approaches can be efficiently used to gain valuable insights in photochemistry through a simple example of red and blue shift effects: the double hypso- and bathochromic shifts in the low-lying valence excited states of (H2 O)2 . It is demonstrated that 1) the use of these techniques allows the perturbative language used in the theory of intermolecular interactions, even in the strongly interacting short-range regime, to be maintained; 2) one and only one molecule is photoexcited in each of the addressed excited states and 3) the electrostatic interaction between the in-the-cluster molecular dipoles provides a fairly intuitive rationalisation of the observed batho- and hypsochromism. The methods exploited and illustrated herein are able to maintain the individuality and properties of the interacting entities in a molecular aggregate, and thereby they allow chemical intuition in general states, at any geometry and using a broad variety of electronic structure methods to be kept and built.

Bond Order Densities in Real Space.

In this contribution we introduce the concept of bond order density (BOD) on the basis of a previous work on natural adaptive orbitals. We show that BODs may be used to visualize both the global spatial distribution of the covalent bond order and its eigencomponents, which we call bond(ing) channels. BODs can be equally computed at correlated and noncorrelated levels of theory and in ground or excited states, thus offering an appealing description of bond-forming, bond-breaking, and bond-evolution processes. We show the power of the approach by examining a number of homo- and heterodiatomics, including the controversial existence of a fourth bonding component in dicarbon, by analyzing a few interesting bonding situations in polyatomics and chemical transformations, and by exemplifying exotic bonding behaviors in simple excited electronic states.

Partition of electronic excitation energies: the IQA/EOM-CCSD method.

Different developments in chemistry and emerging technologies have generated a renewed interest in the properties of molecular excited states. We present herein the partition of black-box, size-consistent equation-of-motion coupled cluster singles and doubles (EOM-CCSD) excitation energies within the framework of the interacting quantum atoms (IQA) formalism. We denote this method as IQA/EOM-CCSD. We illustrate this approach by considering small molecules used often in the study of excited states. This investigation shows how the combination of IQA and EOM-CCSD may provide valuable insights into the molecular changes induced by electron excitation via the real space distribution of the energy of an absorbed photon in a molecular system. Our results reveal (i) the most energetically deformed atomic basins and (ii) the most affected covalent and non-covalent interactions within a molecule due to a given photoexcitation. In other words, this kind of analysis provides insights into the spatial energetic redistribution accompanying an electronic excitation, with interesting foreseeable applications in the rational design of photoexcitations with tailored chemical effects. Altogether, we expect that the IQA/EOM-CCSD excitation energy partition will prove useful in the understanding of systems and processes of interest in photophysics and photochemistry.

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

A rigorous definition of intrinsic bond strength based on the partitioning of a molecule into real-space fragments is presented. Using the domains provided by the quantum theory of atoms-in-molecules (QTAIM) together with the interacting quantum atoms (IQA) energetic decomposition, we show how an in situ bond strength, matching all the requirements of an intrinsic bond energy, can be defined between each pair of fragments. Total atomization or fragmentation energies are shown to be equal to the sum of these in situ bond energies (ISBEs) if the energies of the fragments are measured with respect to their in-the-molecule state. These energies usually lie above the ground state of the isolated fragments by quantities identified with the standard fragment relaxation or deformation energies, which are also provided by the protocol. Deformation energies bridge dissociation energies with ISBEs, and can be dissected by using well-known tools of real-space theories of chemical bonding. Similarly, ISBEs can be partitioned into ionic and covalent contributions, and this feature adds to the chemical appeal of the procedure. All the energetic quantities examined are observable and amenable, in principle, to experimental determination. Several systems, exemplifying the role of each energetic term presented herein, are used to show the power of the approach.

Halogen Bonds in Clathrate Cages: A Real Space Perspective.

In this paper we present real space analyses of the nature of the dihalogen-water cage interactions in the 512 and 512 62 clathrate cages containing chlorine and bromine, respectively. Our Quantum Theory of Atoms in Molecules and Interacting Quantum Atoms results provide strong indications that halogen bonding is present even though the lone pairs of water molecules are already engaged in hydrogen bonding interactions.

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.

A multipolar approach to the interatomic covalent interaction energy.

Interatomic exchange-correlation energies correspond to the covalent energetic contributions to an interatomic interaction in real space theories of the chemical bond, but their widespread use is severely limited due to their computationally intensive character. In the same way as the multipolar (mp) expansion is customary used in biomolecular modeling to approximate the classical Coulomb interaction between two charge densities ρA(r) and ρB(r), we examine in this work the mp approach to approximate the interatomic exchange-correlation (xc) energies of the Interacting Quantum Atoms method. We show that the full xc mp series is quickly divergent for directly bonded atoms (1-2 pairs) albeit it works reasonably well most times for 1- n (n > 2) interactions. As with conventional perturbation theory, we show numerically that the xc series is asymptotically convergent and that, a truncated xc mp approximation retaining terms up to l1+l2=2 usually gives relatively accurate results, sometimes even for directly bonded atoms. Our findings are supported by extensive numerical analyses on a variety of systems that range from several standard hydrogen bonded dimers to typically covalent or aromatic molecules. The exact algebraic relationship between the monopole-monopole xc mp term and the inter-atomic bond order, as measured by the delocalization index of the quantum theory of atoms in molecules, is also established. © 2017 Wiley Periodicals, Inc.

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.

The nature of resonance-assisted hydrogen bonds: a quantum chemical topology perspective.

Resonance Assisted Hydrogen Bonds (RAHBs) are particularly strong H-Bonds (HBs) which are relevant in several fields of chemistry. The traditional explanation for the occurrence of these HBs is built on mesomeric structures evocative of electron delocalisation in the system. Nonetheless, there are several theoretical studies which have found no evidence of such electron delocalisation. We considered the origin of RAHBs by employing Quantum Chemical Topology tools, more specifically, the Quantum Theory of Atoms in Molecules (QTAIM) and the Interacting Quantum Atoms energy partition. Our results indicate that the π-conjugated bonds allow for a larger adjustment of electron density throughout the H-bonded system as compared with non-conjugated carbonyl molecules. This rearrangement of charge distribution is a response to the electric field due to the H atom involved in the hydrogen bonding of the considered compounds. As opposed to the usual description of RAHB interactions, these HBs lead to a larger electron localisation in the system, and concomitantly to larger QTAIM charges which in turn lead to stronger electrostatic, polarization and charge transfer components of the interaction. Overall, the results presented here offer a new perspective on the cause of strengthening of these important interactions.

On the interpretation of domain averaged Fermi hole analyses of correlated wavefunctions.

Few methods allow for a physically sound analysis of chemical bonds in cases where electron correlation may be a relevant factor. The domain averaged Fermi hole (DAFH) analysis, a tool firstly proposed by Robert Ponec in the 1990's to provide interpretations of the chemical bonding existing between two fragments Ω and Ω' that divide the real space exhaustively, is one of them. This method allows for a partition of the delocalization index or bond order between Ω and Ω' into one electron contributions, but the chemical interpretation of its parameters has been firmly established only for single determinant wavefunctions. In this paper we report a general interpretation based on the concept of excluded density that is also valid for correlated descriptions. Both analytical models and actual computations on a set of simple molecules (H2, N2, LiH, and CO) are discussed, and a classification of the possible DAFH situations is presented. Our results show that this kind of analysis may reveal several correlated assisted bonding patterns that might be difficult to detect using other methods. In agreement with previous knowledge, we find that the effective bond order in covalent links decreases due to localization of electrons driven by Coulomb correlation.