An Unsupervised Machine Learning Approach for the Automatic Construction of Local Chemical Descriptors

Condensing the many physical variables defining a chemical system into a fixed-size array poses a significant challenge in the development of chemical Machine Learning (ML). Atom Centered Symmetry Functions (ACSFs) offer an intuitive featurization approach by means of a tedious and labor-intensive selection of tunable parameters. In this work, we implement an unsupervised ML strategy relying on a Gaussian Mixture Model (GMM) to automatically optimize the ACSF parameters. GMMs effortlessly decompose the vastness of the chemical and conformational spaces into well-defined radial and angular clusters, which are then used to build tailor-made ACSFs. The unsupervised exploration of the space has demonstrated general applicability across a diverse range of systems, spanning from various unimolecular landscapes to heterogeneous databases. The impact of the sampling technique and temperature on space exploration is also addressed, highlighting the particularly advantageous role of high-temperature Molecular Dynamics (MD) simulations. The reliability of the resulting features is assessed through the estimation of the atomic charges of a prototypical capped amino acid and a heterogeneous collection of CHON molecules. The automatically constructed ACSFs serve as high-quality descriptors, consistently yielding typical prediction errors below 0.010 electrons bound for the reported atomic charges. Altering the spatial distribution of the functions with respect to the cluster highlights the critical role of symmetry rupture in achieving significantly improved features. More specifically, using two separate functions to describe the lower and upper tails of the cluster results in the best performing models with errors as low as 0.006 electrons. Finally, the effectiveness of finely tuned features was checked across different architectures, unveiling the superior performance of Gaussian Process (GP) models over Feed Forward Neural Networks (FFNNs), particularly in low-data regimes, with nearly a 2-fold increase in prediction quality. Altogether, this approach paves the way toward an easier construction of local chemical descriptors, while providing valuable insights into how radial and angular spaces should be mapped. Finally, this work opens the possibility of encoding many-body information beyond angular terms into upcoming ML features.

How electrons still guard the space: Electron number distribution functions based on QTAIM∩ELF intersections

Despite the importance of the one-particle picture provided by the orbital paradigm, a rigorous understanding of the spatial distribution of electrons in molecules is still of paramount importance to chemistry. Considerable progress has been made following the introduction of topological approaches, capable of partitioning space into chemically meaningful regions. They usually provide atomic partitions, for example, through the attraction basins of the electron density in the quantum theory of atoms in molecules (QTAIM) or electron-pair decompositions, as in the case of the electron localization function (ELF). In both cases, the so-called electron distribution functions (EDFs) provide a rich statistical description of the electron distribution in these spatial domains. Here, we take the EDF concept to a new fine-grained limit by calculating EDFs in the QTAIM ∩ ELF intersection domains. As shown in AHn systems based on main group elements, as well as in the CO, NO, and BeO molecules, this approach provides an exquisitely detailed picture of the electron distribution in molecules, allowing for an insightful combination of the distribution of electrons between Lewis entities (such as bonds and lone pairs) and atoms at the same time. Besides mean-field calculations, we also explore the impact of electron correlation through Hartree-Fock (HF), density functional theory (DFT) (B3LYP), and CASSCF calculations.

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.

Radical revelations: the pnictogen effect in linear acetylenes

Acetylenes are essential building blocks in modern chemistry due to their remarkable modularity. The introduction of heteroatoms, such as pnictogens (X), is one of the simplest approaches to altering the C≡C bond. However, the chemistry of the resultant dipnictogenoacetylenes (DXAs) is strongly dependent on the nature of X. In this work, rigorous theoretical chemistry tools are employed to shed light on the origin of these differences, providing a detailed evaluation of the impact of X on the geometrical and electronic features of DXAs. Special emphasis is made on the study of the carbene character of the systems through the analysis of the interconversion mechanism between the linear and zigzag isomers. Our results show that second-period atoms behave drastically differently to the remaining X: down the group, a zwitterionic resonance form emerges at the expense of decreasing the carbenoid role, eventually resulting in an electrostatically driven ring closure. Furthermore, our findings pave the way to potentially unveiling novel routes for the promotion of free-radical chemistry.

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.

The Ehrenfest force field: A perspective based on electron density functions

The topology of the Ehrenfest force field (EhF) is investigated as a tool for describing local interactions in molecules and intermolecular complexes. The EhF is obtained by integrating the electronic force operator over the coordinates of all but one electron, which requires knowledge of both the electron density and the reduced pair density. For stationary states, the EhF can also be obtained as minus the divergence of the kinetic stress tensor, although this approach leads to well-documented erroneous asymptotic behavior at large distances from the nuclei. It is shown that these pathologies disappear using the electron density functions and that the EhF thus obtained displays the correct behavior in real space, with no spurious critical points or attractors. Therefore, its critical points can be unambiguously obtained and classified. Test cases, including strained molecules, isomerization reactions, and intermolecular interactions, were analyzed. Various chemically relevant facts are highlighted: for example, non-nuclear attractors are generally absent, potential hydrogen-hydrogen interactions are detected in crowded systems, and a bifurcation mechanism is observed in the isomerization of HCN. Moreover, the EhF atomic basins are less charged than those of the electron density. Although integration of the EhF over regions of real space can also be performed to yield the corresponding atomic forces, several numerical drawbacks still need to be solved if electron density functions are to be used for that purpose. Overall, the results obtained support the Ehrenfest force field as a reliable descriptor for the definition of atomic basins and molecular structure.

Wave function analyses of scandium-doped aluminium clusters, AlnSc (n = 1-24), and their CO2 fixation abilities

Nanoclusters represent a connection between (i) solid state systems and (ii) species in the atomic and molecular domains. Additionally, nanoclusters can also have very interesting electronic, optical and magnetic properties. For example, some aluminium clusters behave as superatoms and the doping of these clusters might strengthen their adsorption capabilities. Thus, we address herein the structural, energetic and electronic characterisation of scandium-doped aluminium clusters (Al_nSc (n = 1-24)) by means of density functional theory calculations and quantum chemical topology wave function analyses. We studied the effect of Sc-doping on the structure and charge distribution by considering pure Al clusters as well. The quantum theory of atoms in molecules (QTAIM) reveals that interior Al atoms have large negative atomic charges (≈2a.u.) and hence the atoms surrounding them are considerably electron deficient. The Interacting Quantum Atoms (IQA) energy partition allowed us to establish the nature of the interaction between the Al₁₃ superatom and the Al₁₂Sc cluster with Al to form the complexes Al₁₄ and Al₁₃Sc, respectively. We also used the IQA approach to examine (i) the influence of Sc on the geometry of the Al_nSc complexes along with (ii) the cooperative effects in the binding of Al_nSc and Al_n+1 clusters. We also exploited the QTAIM and IQA approaches to study the interaction of the electrophilic surface of the examined systems with CO₂. Overall, we observe that the investigated Sc-doped Al complexes with a marked stability towards disproportionation reactions exhibit strong adsorption energies with CO₂. Concomitantly, the carbon dioxide molecule is considerably distorted and destabilised, conditions which might prepare it for further chemical reactions. Altogether, this paper gives valuable insights on the tuning of the properties of metallic clusters for their design and exploitation in custom-made materials.

Developing a User-Friendly Code for the Fast Estimation of Well-Behaved Real-Space Partial Charges

The Quantum Theory of Atoms in Molecules (QTAIM) provides an intuitive, yet physically sound, strategy to determine the partial charges of any chemical system relying on the topology induced by the electron density ρ(r) . In a previous work [J. Chem. Phys. 2022, 156, 014112], we introduced a machine learning (ML) model for the computation of QTAIM charges of C, H, O, and N atoms at a fraction of the conventional computational cost. Unfortunately, the independent nature of the atomistic predictions implies that the raw atomic charges may not necessarily reconstruct the exact molecular charge, limiting the applicability of the latter in the chemistry realm. Trying to solve such an inconvenience, we introduce NNAIMGUI, a user-friendly code which combines the inferring abilities of ML with an equilibration strategy to afford adequately behaved partial charges. The performance of this approach is put to the test in a variety of scenarios including interpolation and extrapolation regimes (e.g chemical reactions) as well as large systems. The results of this work prove that the equilibrated charges retain the chemically accurate behavior reproduced by the ML models. Furthermore, NNAIMGUI is a fully flexible architecture allowing users to train and use tailor-made models targeted at any atomic property of choice. In this way, the GUI-interfaced code, equipped with visualization utilities, makes the computation of real-space atomic properties much more appealing and intuitive, paving the way toward the extension of QTAIM related descriptors beyond the theoretical chemistry community.

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.

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...

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.

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.

Atomic shell structure from Born probabilities: Comparison to other shell descriptors and persistence in molecules

Real space chemical bonding descriptors, such as the electron localization function or the Laplacian of the electron density, have been widely used in electronic structure theory thanks to their power to provide chemically intuitive spatial images of bonded and non-bonded interactions. This capacity stems from their ability to display the shell structure of atoms and its distortion upon molecular formation. Here, we examine the spatial position of the N electrons of an atom at the maximum of the square of the wavefunction, the so-called Born maximum, as a shell structure descriptor for ground state atoms with Z = 1-36, comparing it to other available indices. The maximization is performed with the help of variational quantum Monte Carlo calculations. We show that many electron effects (mainly Pauli driven) are non-negligible, that Born shells are closer to the nucleus than any other of the examined descriptors, and that these shells are very well preserved in simple molecules.

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

Bimolecular nucleophilic substitution (S_N2) 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 S_N2 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 (E_ST), 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, E_ST 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 S_N2 and E2 reactions.

Stronger-together: the cooperativity of aurophilic interactions

Crystallographic distances and the electron density of bi- and tri-nuclear gold(I) compounds reveal that the existence of multiple Au⋯Au interactions increases their individual strength in the order of 0.9-2.9 kcal mol^-1. We observed this behaviour both experimentally and theoretically in multinuclear systems, confirming a novel important cooperative character in aurophilic contacts.

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.

Implementation of the interacting quantum atom energy decomposition using the CASPT2 method

We present an implementation of the interacting quantum atom (IQA) energy decomposition scheme using the complete active space second-order perturbation theory (CASPT2). This combination yields a real-space interpretation tool with a proper account of the static and dynamic correlation that is particularly relevant for the description of processes in electronic excited states. The IQA/CASPT2 approach allows determination of the energy redistribution that takes place along a photophysical/photochemical deactivation path in terms of self- and interatomic contributions. The applicability of the method is illustrated by the description of representative processes spanning different bonding regimes: noble gas excimer and exciplex formation, the reaction of ozone with a chlorine atom, and the photodissociations of formaldehyde and cyclobutane. These examples show the versatility of using CASPT2 with the significant information provided by the IQA partition to describe chemical processes with a large multiconfigurational character.

Interacting Quantum Atoms Method for Crystalline Solids

An implementation of the Interacting Quantum Atoms method for crystals is presented. It provides a real space energy decomposition of the energy of crystals in which all energy components are physically meaningful. The new package ChemInt enables one to compute intra-atomic and inter-atomic energies, as well as electron population measures used for quantitative description of chemical bonds in crystals. The implementation is tested and applied to characteristic molecular and crystalline systems with different types of bonding.

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.

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.

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 E_ST . 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 E_ST here defined provides correct sterics even for hydrogen atoms, where the plain use of deformation energies leads to non-chemical results. The applicability of E_ST is validated in several chemical scenarios, going from atomic compressions to archetypal S_N2 reactions. E_ST is shown to be a robust steric hindrance descriptor.

Energetics of Electron Pairs in Electrophilic Aromatic Substitutions

The interacting quantum atoms approach (IQA) as applied to the electron-pair exhaustive partition of real space induced by the electron localization function (ELF) is used to examine candidate energetic descriptors to rationalize substituent effects in simple electrophilic aromatic substitutions. It is first shown that inductive and mesomeric effects can be recognized from the decay mode of the aromatic valence bond basin populations with the distance to the substituent, and that the fluctuation of the population of adjacent bonds holds also regioselectivity information. With this, the kinetic energy of the electrons in these aromatic basins, as well as their mutual exchange-correlation energies are proposed as suitable energetic indices containing relevant information about substituent effects. We suggest that these descriptors could be used to build future reactive force fields.

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.

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.

On the strength of hydrogen bonding within water clusters on the coordination limit

Hydrogen bonds (HB) are arguably the most important noncovalent interactions in chemistry. We study herein how differences in connectivity alter the strength of HBs within water clusters of different sizes. We used for this purpose the interacting quantum atoms energy partition, which allows for the quantification of HB formation energies within a molecular cluster. We could expand our previously reported hierarchy of HB strength in these systems (Phys. Chem. Chem. Phys., 2016, 18, 19557) to include tetracoordinated monomers. Surprisingly, the HBs between tetracoordinated water molecules are not the strongest HBs despite the widespread occurrence of these motifs (e.g., in ice I_h ). The strongest HBs within H₂ O clusters involve tricoordinated monomers. Nonetheless, HB tetracoordination is preferred in large water clusters because (a) it reduces HB anticooperativity associated with double HB donors and acceptors and (b) it results in a larger number of favorable interactions in the system. Finally, we also discuss (a) the importance of exchange-correlation to discriminate among the different examined types of HBs within H₂ O clusters, (b) the use of the above-mentioned scale to quickly assess the relative stability of different isomers of a given water cluster, and (c) how the findings of this research can be exploited to indagate about the formation of polymorphs in crystallography. Overall, we expect that this investigation will provide valuable insights into the subtle interplay of tri- and tetracoordination in HB donors and acceptors as well as the ensuing interaction energies within H₂ O clusters.

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(SR_F)(Ph₃P)] in which Ph₃P = triphenylphosphine and SR_F = 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.

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.

Assessing the Reversed Exponential Decay of the Electrical Conductance in Molecular Wires: The Undeniable Effect of Static Electron Correlation

An extraordinary new family of molecular junctions, inaccurately referred to as "anti-Ohmic" wires in the recent literature, has been proposed based on theoretical predictions. The unusual electron transport observed for these systems, characterized by a reversed exponential decay of their electrical conductance, might revolutionize the design of molecular electronic devices. This behavior, which has been associated with intrinsic diradical nature, is reexamined in this work. Since the diradical character arises from a near-degeneracy of the frontier orbitals, the employment of a multireference approach is mandatory. CASSCF calculations on a set of nanowires based on polycyclic aromatic hydrocarbons (PAHs) demonstrate that, in the frame of an appropriate multireference treatment, the ground state of these systems shows the expected exponential decay of the conductance. Interestingly, these calculations do evidence a reversed exponential decay of the conductance, although now in several excited states. Similar results have been obtained for other recently proposed candidates to "anti-Ohmic" wires. These findings open new horizons for possible applications in molecular electronics of these promising systems.

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.

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.

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.

Anti-ohmic single molecule electron transport: is it feasible?

Hitherto, only molecular wires with a regular ohmic behavior in which the electric conductance decreases with the wire length have been synthesized. Implementation of molecular conductors with reversed conductance/length trend (anti-ohmic) might revolutionize the field of molecular electronics, allowing the development of electronic devices with extraordinary properties. It is for this reason that, recently, theoretical efforts have been focused on this topic and different structures have been proposed to show reversed conductance/length behavior on the basis of density functional theory non-equilibrium Green function approach (DFT-NEGF) and topological models. From the previous works, it can be stated that an anti-ohmic molecular wire must display a very small HOMO-LUMO gap and a reversed bond alternation pattern in the case of polyenes and related conjugated systems. In this work, the pursuit of a mechanism by which the anti-ohmic electron transport may arise was carried out by studying the paradigmatic anti-ohmic p-xylylene chain (pX2) at the DFT level in combination with topological models. It has been found that the electron transport in the anti-ohmic regime is favored by a long-range superexchange mechanism, which, contrary to what is expected, is reinforced by the increase in the length of the chain. Moreover, strong links between anti-ohmic character in molecular wires and one-dimensional topological insulator models have been established. Due to the small HOMO-LUMO gap predicted at DFT level, the anti-ohmic character has been put to the proof using a multireference scenario. Preliminary results point out to the presence of different ohmic and anti-ohmic electronic states. In the particular case of pX2 the anti-ohmic states do not correspond to the ground state. These findings require a reconsideration of previous studies on the reversed conductance/length behavior using single reference methodologies.

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.

Quantitative Electron Delocalization in Solids from Maximally Localized Wannier Functions

Electron delocalization is the quantum-mechanical principle behind chemical concepts such as aromaticity, resonance, and bonding. A common way to measure electron delocalization in the solid state is through the visualization of maximally localized Wannier functions, a method similar to using localized orbitals in molecular quantum chemistry. Although informative, this method can only provide qualitative information and is essentially limited by the arbitrariness in the choice of orbital rotation. Quantitative orbital-independent interatomic delocalization indices can be calculated by integration inside of atomic regions of probability densities obtained from the system's wave function. In particular, Bader's delocalization indices are very informative, but typically expensive to calculate. In this article, we present a fast method to obtain the localization and delocalization indices in a periodic solid under the plane-wave/pseudopotential approximation. The efficiency of the proposed method hinges on the use of grid-based atomic integration techniques and maximally localized Wannier functions. The former enables the rapid calculation of all atomic overlap integrals required in the construction of the delocalization indices. The latter allows discarding the overlaps between maximally localized Wannier functions whose centers are far enough apart. Using the new method, all localization and delocalization indices in solids with dozens of atoms can be calculated in hours on a desktop computer. Illustrative examples are presented and studied: some simple and molecular solids, polymeric nitrogen, intermolecular delocalization in 10 phases of ice, and the self-ionization of ammonia under pressure. This work is an important step toward the quantitative description of chemical bonding in solids under pressure.

Revitalizing the concept of bond order through delocalization measures in real space

Ab initio quantum chemistry is an independent source of information supplying an ever widening group of experimental chemists. However, bridging the gap between these ab initio data and chemical insight remains a challenge. In particular, there is a need for a bond order index that characterizes novel bonding patterns in a reliable manner, while recovering the familiar effects occurring in well-known bonds. In this article, through a large body of calculations, we show how the delocalization index derived from Quantum Chemical Topology (QCT) serves as such a bond order. This index is defined in a parameter-free, intuitive and consistent manner, and with little qualitative dependency on the level of theory used. The delocalization index is also able to detect the subtler bonding effects that underpin most practical organic and inorganic chemistry. We explore and connect the properties of this index and open the door for its extensive usage in the understanding and discovery of novel chemistry.

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.

Extension of the interacting quantum atoms (IQA) approach to B3LYP level density functional theory (DFT)

An interaction between two atoms, bonded or non-bonded, consists of interatomic contributions: electrostatic energy, exchange energy and electronic correlation energy. Together with the intra-atomic energy of an atom, these contributions are the basic components of the Interacting Quantum Atom (IQA) energy decomposition scheme. Here, we investigate IQA's proper use in conjunction with an explicit implementation of the B3LYP functional. The recovery of the total molecular energy from the IQA components is emphasised, for the first time. A systematic study of three model systems of biological relevance, N-methylacetamide (NMA), the doubly capped tripeptide GlyGlyGly and an alloxan dimer, shows the stabilization effect of B3LYP on most of the interatomic exchange energies (V) compared to their Hartree-Fock values. Diagrams of exchange energies versus interatomic distance show the clustering of interactions, one cluster for each 1,n (n = 1 to 6 where the atoms are separated by n - 1 bonds). The positioning of some V values outside their expected cluster marks interesting interactions.