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Conceptual Density Functional Theory (CDFT) has been extended beyond its traditional role in elucidating chemical reactivity to the development of density functional theory methods, e.g., the investigation of the delocalization error. This delocalization error causes the dependence of the energy on the number of electrons ( N ) to deviate from its exact piecewise linear behavior, an error which is the basis of many well-known limitations of commonly used density-functional approximations (DFAs). Following our previous work on the analytical hardness η ± for pure functionals, we extend its application to hybrid and range-separated functionals. A comparison is made between the analytical hardness and the slope of the delocalization function introduced by Hait and Head-Gordon. Our results show that there is a linear relationship between its slope and the analytical hardness. An approximate scheme is presented to construct the energy vs N curve without fractional occupation number calculations. The extension to densities is discussed.

Until quite recently, Conceptual DFT (CDFT) was mainly based on the energy functional, E [ N , v ], where the number of electrons N and the external potential v are state variables. One of the strengths of CDFT, however, is the ease with which additional and/or different state variables can be incorporated. Here, the incorporation of new variables-namely temperature and external fields-is discussed, outlining the motivation for these extensions, sketching their theoretical/computational context, and presenting some elucidative examples. Using the Grand Canonical Ensemble, finite temperature can be introduced, ameliorating the N -differentiability problem and leading to new well-behaved chemical reactivity concepts. Incorporating temperature as an additional fundamental variable enables us to formulate a novel suite of "thermodynamic" reactivity descriptors, including important concepts like the heat capacity of electronic systems. The mathematical structure underpinning the set of (well-behaved) finite-temperature reactivity indices can guide the formulation of plausible definitions for local analogs of global descriptors. This endeavor is especially significant in the case of local hardness, a concept that has remained elusive since the inception of CDFT. The ever-increasing portfolio of experimental reaction conditions to creatively synthesize new molecules, needs the introduction of various external "fields" like electric and magnetic fields ( ε and B ), mechanical forces ( F ) and pressure ( P ) to describe the state of the chemical system. The conventional energy functional can be expressed in a general form, E [ N , v , X ], where X denotes the "field". Response functions to changes in the field can then be defined in analogy to classical thermodynamics. The electric field results display a case of a field-induced selectivity in a reaction channel of the Fukui function. Remarkably, atomic electronegativity and hardness in magnetic fields display a piecewise behavior in magnetic fields, associated to configurational jumps upon increasing field strength. The overall compression of their ranges for stronger fields may be insightful when investigating chemistry in extremely high fields. The electronegativity and hardness of diatomics under mechanical force can be traced back to changes in equilibrium distances in the neutral, cationic and anionic state, parallel with the evolution of an intrinsic atomic volume under pressure., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

Context: Single-atom catalytic systems constitute an intriguing research topic due to their inherently different chemical behavior as compared to classic heterogeneous catalysts. In this study, cluster systems representing single late transition metal atoms adsorbed on anatase were constructed starting from previously generated periodic models and subjected to a density functional theory (DFT) benchmark study. The ability of different density functional approximations representing all rungs of the Jacob's Ladder classification to accurately describe bond lengths and adsorption energies was assessed for these clusters with the aim of revealing the functional that allows to retain the structural characteristics of the initial periodic system, while also delivering reliable energetics. In this regard, our results indicate that optimisation of the clusters with the meta-GGA functionals TPSS or RevTPSS provides the lowest mean unsigned error and root-mean-square deviations with respect to the periodic models. Moreover, these functionals and, to a slightly lesser degree, PW91 were also found to provide adsorption energies that are statistically the least deviating from the CCSD(T) reference data. More complex hybrid functionals appear to be performing less well., Methods: Cluster geometries were determined at the Kohn-Sham DFT level using the LANL2DZ basis set for the transition metals and the Pople 6-31G(d) basis set for O and H. The density functional approximations considered were SVWN, PBE, BP86, BLYP, PW91, TPSS, RevTPSS, M06L, M11L, B3LYP, PBE0, M06, M06-2X, MN15, ωB97X-D, CAM-B3LYP, M11, and MN12-SX. Reference adsorption energies of the metals on the support cluster were obtained at the CCSD(T)/LANL2TZ (transition metals)/6-311 +  + G(d,p)//RevTPSS/LANLD2DZ (transition metals)/6-31G*. Besides the above-mentioned functionals, energy calculations using the double-hybrid functionals, DSDPBEP86, PBE0-DH, and B2PLYP, were also performed. All adsorption energy calculations were carried out on the RevTPSS geometries., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

Appreciating reactivity in terms of physicochemical effects for chemical processes is one of the most important undertakings in chemistry. While transition state (TS) theory provides the framework enabling the reliable calculation of the barrier height for a given elementary step, analytical tools are necessary to gain insight into key factors governing the different processes during chemical reactions. In this contribution, we partition the potential energy surface of an elementary step along the intrinsic coordinate into three segments, the so-called Pre-TS, TS, and Post-TS regions, and then determine the most important factors dictating each segment. This analysis is based on the use of both reactivity descriptors from conceptual density functional theory and concepts from the information-theoretic approach in density functional theory. We found that in both Pre-TS and Post-TS regions, steric effects are the dominant factors, whereas in the TS region, it is the intrinsic electrophilic and nucleophilic propensity of the transition state structure that governs the reactivity. The wide applicability of our approach is shown by a validation for a total of 37 organic and inorganic reactions. Different partition approaches from density functional theory, energy decomposition analysis and wavefunction-based resonance theory are employed to support our main conclusions., (© 2024 Wiley-VCH GmbH.)

While high-pressure chemistry has a well-established history, methods to simulate pressure at the single-molecule level have been somewhat lacking. The current work aims at comparing two static models (XP-PCM and GOSTSHYP) to apply isotropic pressure to single molecules, focusing on the equilibrium bond length and electric dipole moment of diatomic molecules. Numerical challenges arising in the potential energy surface using the XP-PCM method were examined, and a pragmatic approach was followed to mitigate these. The definition of the cavity was scrutinized, and two approaches to retrieve the isotropic character that could potentially be lost when using the standard methodology were suggested. Subsequently, equilibrium bond lengths under pressure were evaluated, showing reasonable agreement between GOSTSHYP and XP-PCM, but some discrepancies persist. A Taylor series analysis introduced elsewhere was then applied to rationalize the observed trends in terms of the bond surface. Finally, the dipole moment was shown to be highly sensitive to the cavity definition, and qualitative agreement necessitates the use of our adapted procedure.

Chiral pyrrolidines are common structural motives in natural products as well as active pharmaceutical ingredients, explaining the need for methods for their enantioselective synthesis. While several, often metal-catalyzed, methods for their preparation do exist, the enantioselective synthesis of pyrrolidines containing quaternary stereocenters remains challenging. Herein, we report a Bro̷nsted acid-catalyzed intramolecular hydroamination that provides such pyrrolidines from simple starting materials in high yield and enantioselectivity. Key to an efficient reaction was the use of an electron-deficient protective group on nitrogen, the common nosyl-protecting group, to avoid deactivation of the Bro̷nsted acid by deprotonation. The reaction proceeds as a stereospecific anti -addition indicating a concerted reaction. Furthermore, kinetic studies show Michaelis-Menten behavior, suggesting the formation of a precomplex similar to those observed in enzymatic catalysis.

The extension of conceptual density-functional theory (conceptual DFT) to include external electromagnetic fields in chemical systems is utilised to investigate the effects of strong magnetic fields on the electronic charge distribution and its consequences on the reactivity of π-systems. Formaldehyde, H 2 CO, is considered as a prototypical example and current-density-functional theory (current-DFT) calculations are used to evaluate the electric dipole moment together with two principal local conceptual DFT descriptors, the electron density and the Fukui functions, which provide insight into how H 2 CO behaves chemically in a magnetic field. In particular, the symmetry properties of these quantities are analysed on the basis of group, representation, and corepresentation theories using a recently developed automatic program for symbolic symmetry analysis, QSYM 2 . This allows us to leverage the simple symmetry constraints on the macroscopic electric dipole moment components to make profound predictions on the more nuanced symmetry transformation properties of the microscopic frontier molecular orbitals (MOs), electron densities, and Fukui functions. This is especially useful for complex-valued MOs in magnetic fields whose detailed symmetry analyses lead us to define the new concepts of modular and phasal symmetry breaking . Through these concepts, the deep connection between the vanishing constraints on the electric dipole moment components and the symmetry of electron densities and Fukui functions can be formalised, and the inability of the magnetic field in all three principal orientations considered to induce asymmetry with respect to the molecular plane of H 2 CO can be understood from a molecular perspective. Furthermore, the detailed forms of the Fukui functions reveal a remarkable reversal in the direction of the dipole moment along the CO bond in the presence of a parallel or perpendicular magnetic field, the origin of which can be attributed to the mixing between the frontier MOs due to their subduced symmetries in magnetic fields. The findings in this work are also discussed in the wider context of a long-standing debate on the possibility to create enantioselectivity by external fields.

Computational study of electronic resonances is still a very challenging topic, with the phenomenon of dissociative electron attachment (DEA) being one of the multiple features worth investigating. Recently, we extended the charge stabilization method from energies to properties of conceptual density functional theory and applied this to metastable anionic states of ethene and chlorinated ethene derivatives to study the DEA mechanism present in these compounds. We now present an extension to spatial functions, namely, the electronic Fukui function and the electron localization function. The results of our analysis show that extrapolated spatial functions are relevant and useful for more precise localization of the unbound electron. Furthermore, we report for the first time the combination of the electron localization function with Berlin's binding function for these challenging electronic states. This promising methodology allows for accurate predictions of when and where DEA will happen in the molecules studied and provides more insight into the process., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

In the context of the growing impact of conceptual density functional theory (DFT) as one of the most successful chemical reactivity theories, response functions up to second order have now been widely applied; in recent years, among others, particular attention has been focused on the linear response function and also extensions to higher order have been put forward. As the larger part of these studies have been carried using a finite difference approach to compute these concepts, we now embarked on (an extension of) an analytical approach to conceptual DFT. With the ultimate aim of providing a complete set of analytically computable second order properties, including the softness and hardness kernels, the hardness as the simplest second order response function is scrutinized again with numerical results highlighting the difference in nature between the analytical hardness (referred to as hardness condition) and the Parr-Pearson absolute chemical hardness. The hardness condition is investigated for its capability to gauge the (de)localization error of density functional approximations (DFAs). The analytical Fukui function, besides overcoming the difficulties in the finite difference approach in treating negatively charged systems, also showcases the errors of deviating from the straight-line behavior using fractional occupation number calculations. Subsequently, the softness kernel and its atom-condensed inverse, the hardness matrix, are accessed through the Berkowitz-Parr relation. Revisiting the softness kernel confirms and extends previous discussions on how Kohn's Nearsightedness of Electronic Matter principle can be retrieved and identified as the physicist's version of the chemist's "transferability of functional groups" concept. The accurate, analytical hardness matrix evaluation on the other hand provides further support for the basics of Nalewajski's charge sensitivity analysis. Based on Parr and Liu's functional expansion of the energy functional, a new energy decomposition is introduced with an order of magnitude analysis of the different terms for a series of simple molecules both at their equilibrium geometry and upon variation in bond length and dihedral angle. Finally, for the first time, the perturbation expansion of the energy functional is studied numerically up to second order now that all response functions and integration techniques are at hand. The perturbation expansion energies are in excellent agreement with those obtained directly from DFA calculations giving confidence in the convergence of the perturbation series and its use in judging the importance of the different terms in reactivity investigations.

Mechanochemistry has experienced a renaissance in recent years witnessing, at the molecular level, a remarkable interplay between theory and experiment. Molecular mechanochemistry has welcomed a broad spectrum of quantum-chemical methods to evaluate the influence of an external mechanical force on molecular properties. In this contribution, an overview is given on recent work on quantum mechanochemistry in the Brussels Quantum Chemistry group (ALGC). The effect of an external force was scrutinized both in fundamental topics, like reactivity descriptors in Conceptual DFT, and in applied topics, such as designing molecular force probes and tuning the stereoselectivity of certain types of reactions. In the conceptual part, a brief overview of the techniques introducing mechanical forces into a quantum-mechanical description of a molecule is followed by an introduction to conceptual DFT. The evolution of the electronic chemical potential (or electronegativity), chemical hardness and electrophilicity are investigated when a chemical bond in a series of diatomics is put under mechanical stress. Its counterpart, the influence of mechanical stress on bond angles, is analyzed by varying the strain present in alkyne triple bonds by applying a bending force, taking the strain promoted alkyne-azide coupling cycloaddition as an example. The increase of reactivity of the alkyne upon bending is probed by Fukui functions and the local softness. In the applied part, a new molecular force probe is presented based on an intramolecular 6π-electrocyclization in constrained polyenes operating under thermal conditions. A cyclic process is conceived where ring opening and closure are triggered by applying or removing an external pulling force. The efficiency of mechanical activation strongly depends on the magnitude of the applied force and the distance between the pulling points. The idea of pulling point distances as a tool to identify new mechanochemical processes is then tested in [28]hexaphyrins with an intricate equilibrium between Möbius aromatic and Hückel antiaromatic topologies. A mechanical force is shown to trigger the interconversion between the two topologies, using the distance matrix as a guide to select appropriate pulling points. In a final application, the Felkin-Anh model for the addition of nucleophiles to chiral carbonyls under the presence of an external mechanical force is scrutinized. By applying a force for restricting the conformational freedom of the chiral ketone, otherwise inaccessible reaction pathways are promoted on the force-modified potential energy surfaces resulting in a diastereoselectivity different from the force-free reaction.

The HBr-assisted electrophilic aromatic bromination of benzene, anisole and nitrobenzene was investigated using static DFT calculations in gas phase and implicit apolar (CCl4) and polar (acetonitrile) solvent models at the ωB97X-D/cc-pVTZ level of theory. The reaction profiles corresponding to either a direct substitution reaction or an addition-elimination process were constructed and insight into the preferred regioselectivity was provided using a combination of conceptual DFT reactivity indices, aromaticity indices, Wiberg bond indices and the non-covalent interaction index. Our results show that under the considered reaction conditions the bromination reaction preferentially occurs through an addition-elimination mechanism and without formation of a stable charged Wheland intermediate. The ortho / para directing effect of the electron-donating methoxy-group in anisole was ascribed to a synergy between strong electron delocalisation and attractive interactions. In contrast, the preferred meta -addition on nitrobenzene could not be traced back to any of these effects, nor to the intrinsic reactivity property of the reactant. In this case, an electrostatic clash between the ipso -carbon of the ring and the nitrogen atom resulting from the later nature of the rate-determining step, with respect to anisole, appeared to play a crucial role.

Rechargeable batteries are essential to the global shift towards renewable energy sources and their storage. At present, improvements in their safety and sustainability are of great importance as part of global sustainable development goals. A major contender in this shift are rechargeable solid-state sodium batteries, as a low-cost, safe, and sustainable alternative to conventional lithium-ion batteries. Recently, solid-state electrolytes with a high ionic conductivity and low flammability have been developed. However, these still face challenges with the highly reactive sodium metal electrode. The study of these electrolyte-electrode interfaces is challenging from a computational and experimental point of view, but recent advances in molecular dynamics neural-network potentials are finally enabling access to these environments compared to more computationally expensive conventional ab-initio techniques. In this study, heteroatom-substituted Na 3 PS 3 X 1 analogues, where X is sulfur, oxygen, selenium, tellurium, nitrogen, chlorine, and fluorine, are investigated using total-trajectory analysis and neural-network molecular dynamics. It was found that inductive electron-withdrawing and electron-donating effects, alongside differences in heteroatom atomic radius, electronegativity, and valency, influenced the electrolyte reactivity. The Na 3 PS 3 O 1 oxygen analogue was found to have superior chemical stability against the sodium metal electrode, paving the way towards high-performance, long lifetime and reliable rechargeable solid-state sodium batteries., (© 2023 The Authors. ChemSusChem published by Wiley-VCH GmbH.)

The linear response kernel also referred to as linear response function (LRF) in the framework of conceptual density functional theory has gained tremendous success in time-dependent density functional theory. Comparatively less attention has been devoted to the LRF from a chemical reactivity perspective in its time- or frequency-independent context, although it has recently been used to qualitatively describe electron delocalization, (anti-)aromaticity, inductive and mesomeric effects, etc. Despite these successes, which were obtained by approximating the LRF using the independent particle approximation deriving from a coupled-perturbed Kohn-Sham computation, the robustness of this LRF approach needs to be assessed. In this work, we compute the LRF at four levels of approximation (independent particle approximation, random phase approximation, Hartree-Fock approximation, and the (exact) DFT (density functional theory) expression) using functionals from the first four rungs of Jacob's ladder of exchange-correlation energy functionals. To scrutinize the impact of these approximations, new visualization strategies are discussed and systematized. The overall conclusion is that the independent particle approximation yields qualitatively correct results (ergo previous conceptual applications of the LRF are trustworthy), but for quantitative results, LRF expressions including coulomb and exchange(-correlation) terms should be included. With respect to functionals, density-gradient contributions to the exchange-correlation kernel are less than 10% and may be omitted safely where that is preferable computationally.

The hard/soft acid/base (HSAB) principle is a cornerstone in our understanding of chemical reactivity preferences. Motivated by the success of the original ("global") version of this rule, a "local" counterpart was readily proposed to account for regioselectivity preferences, in particular, in ambident reactions. However, ample experimental evidence indicates that the local HSAB principle often fails to provide meaningful predictions. Here we examine the assumptions behind the standard proof of the local HSAB rule, showing that it is based on a flawed premise. By solving this issue, we show that it is critical to consider not only the charge transferred between the different reacting centers but also the charge reorganization within the non-reacting parts of the molecule. We propose different reorganization models and derive the corresponding regioselectivity rules for each.

Designing efficient and selective catalysts for carbon dioxide reduction is an intensive research area in the recent literature on homogeneous catalysis. In this work, we study the catalytic activity of a newly reported Mn(I)-PNP-pincer catalyst with an embedded aromatic ring. First, we systematically examine its capability to yield different products and highlight the importance of ligand aromaticity and steric effects on metal-ligand cooperativity. We then further conceptually probe its reactivity with descriptors from both conceptual density functional theory and an information-theoretic approach, thereby proposing a novel partitioning of the reaction coordinate into three relevant regions. Our results show that the reactivity in these different regions is governed by different properties such as steric effects, electrophilicity/nucleophilicity, or aromaticity. We anticipate that this methodology, with the analytical tools employed in this study, can be generalized and extended to other catalytic systems and find applications in designing better catalysts.

The rapidly growing interest for new heterogeneous catalytic systems providing high atomic efficiency along with high stability and reactivity triggered an impressive progress in the field of single-atom catalysis. Nevertheless, unravelling the factors governing the interaction strength between the support and the adsorbed metal atoms remains a major challenge. Based on periodic density functional theory (DFT) calculations, this paper provides insight into the adsorption of single late transition metals on a defect-free anatase surface. The obtained adsorption energies fluctuate, with the exception of Pd, between -3.11 and -3.80 eV and are indicative of a strong interaction. Depending on the considered transition metal, we could attribute the strength of this interaction with the support to i) an electron transfer towards anatase (Ru, Rh, Ni), ii) s-d orbital hybridisation effects (Pt), or iii) a synergistic effect between both factors (Fe, Co, Os, Ir). The driving forces behind the adsorption were also found to be strongly related to Klechkowsky's rule for orbital filling. In contrast, the deviating behaviour of Pd is most likely associated with the lower dissociation enthalpy of the Pd-O bond. Additionally, the reactivity of these systems was evaluated using the Fermi weighted density of states approach. The resulting softness values can be clearly related to the electron configuration of the catalytic systems as well as with the net charge on the transition metal. Finally, these indices were used to construct a model that predicts the adsorption strength of CO on these anatase-supported d-metal atoms. The values obtained from this regression model show, within a 95 % probability interval, a correlation of 84 % with the explicitly calculated CO adsorption energies., (© 2022 Wiley-VCH GmbH.)

In the current literature, many non-covalent interaction (NCI) donors have been proposed that can potentially catalyze Diels-Alder (DA) reactions. In this study, a detailed analysis of the governing factors in Lewis acid and non-covalent catalysis of three types of DA reactions was carried out, for which we selected a set of hydrogen-, halogen-, chalcogen-, and pnictogen-bond donors. We found that the more stable the NCI donor-dienophile complex, the larger the reduction in DA activation energy. We also showed that for active catalysts, a significant part of the stabilization was caused by orbital interactions, though electrostatic interactions dominated. Traditionally, DA catalysis was attributed to improved orbital interactions between the diene and dienophile. Recently, Vermeeren and co-workers applied the activation strain model (ASM) of reactivity, combined with the Ziegler-Rauk-type energy decomposition analysis (EDA), to catalyzed DA reactions in which energy contributions for the uncatalyzed and catalyzed reaction were compared at a consistent geometry. They concluded that reduced Pauli repulsion energy, and not enhanced orbital interaction energy, was responsible for the catalysis. However, when the degree of asynchronicity of the reaction is altered to a large extent, as is the case for our studied hetero-DA reactions, the ASM should be employed with caution. We therefore proposed an alternative and complementary approach, in which EDA values for the catalyzed transition-state geometry, with the catalyst present or deleted, can be compared one to one, directly measuring the effect of the catalyst on the physical factors governing the DA catalysis. We discovered that enhanced orbital interactions are often the main driver for catalysis and that Pauli repulsion plays a varying role.

Anti-Felkin-Anh diastereoselectivity can be achieved for nucleophilic additions to α-chiral ketones upon stretching the ketone with a mechanical pulling force. Herein, a mechanochemical Felkin-Anh model is proposed for predicting the outcome of a nucleophilic addition to an α-chiral ketone. Essentially, the fully stretched chiral ketone has one substituent shielding each side of the carbonyl, in contrast to the Felkin-Anh model, in which free rotation around a bond is required to achieve the two rotamers of the ketone. Depending on the pulling scenario, either Felkin-Anh or anti-Felkin-Anh diastereoselectivity is obtained. The model is entirely based on the distance between the pulling points, which is maximized in the anti-periplanar arrangement. The major diastereomer is associated with the approach with the least steric interactions. The intuitive model is validated by means of mechanochemical density functional theory calculations. Importantly, the ketone is fully stretched in the sub 1 nN force regime, thus minimizing the risk of undesired homolytic bond rupture. Moreover, the mechanical force is not used for lowering the reaction barriers associated with the nucleophilic addition; instead, it is solely applied for locking the conformation of a molecule and provoking otherwise inaccessible reaction pathways on the force-modified potential energy surface.

The necessity of the recent incorporation of new external variables in the context of conceptual DFT (CDFT) is discussed based on the ever-increasing portfolio of experimental reaction conditions in the endeavor of experimentalists to synthesize new molecules with unprecedented properties. Electric and magnetic fields (ε and B), mechanical forces (F), and confinement are proposed as valuable new variables, extending conventional CDFT and its associated response functions. A finite field approach is used to calculate the evolution of both global and local descriptors in a selected series of atomic and molecular applications, and from it derive new response function involving, with one exception, the first derivative to the field considered. The electric field results, displaying, for example, a case of a field-induced enantioselectivity in the Fukui function, may be instrumental in the recent upsurge of chemistry in oriented external electric fields. The study of atomic electronegativity and hardness in magnetic fields displays a piecewise behavior, associated to configurational jumps upon increasing field strength and reveals an overall compression of their ranges for stronger fields, which may be guiding upon investigating chemistry in extremely high fields like in white dwarfs. The evolution of the electronegativity and hardness of diatomics under mechanical force can elegantly be traced back to differences in their equilibrium distance in the neutral, cationic, and anionic state. The well-known reduction of the polarizability under confinement can be seen as a fore-runner of the increasing hardness of atoms under pressure, presently under investigation. Periodicity showing up in a spontaneous way in the variety of properties is a leitmotiv in this study, as well as the interconnections/analogies between the different response functions., (© 2022 Wiley Periodicals LLC.)

The halogen bond complexes CF3X⋯Y and C2F3X⋯Y, with Y = furan, thiophene, selenophene and X = Cl, Br, I, have been studied by using DFT and CCSD(T) in order to understand which factors govern the interaction between the halogen atom X and the aromatic ring. We found that PBE0-dDsC/QZ4P gives an adequate description of the interaction energies in these complexes, compared to CCSD(T) and experimental results. The interaction between the halogen atom X and the π-bonds in perpendicular orientation is stronger than the interaction with the in-plane lone pairs of the heteroatom of the aromatic cycle. The strength of the interaction follows the trend Cl < Br < I; the chalcogenide in the aromatic ring nor the hybridization of the C−X bond play a decisive role. The energy decomposition analysis shows that the interaction energy is dominated by all three contributions, viz., the electrostatic, orbital, and dispersion interactions: not one factor dominates the interaction energy. The aromaticity of the ring is undisturbed upon halogen bond formation: the π-ring current remains equally strong and diatropic in the complex as it is for the free aromatic ring. However, the spin-orbit coupling between the singlet and triplet π→π* states is increased upon halogen bond formation and a faster intersystem crossing between these states is therefore expected.

The supramolecular gelation of small molecules is typically preceded by an external stimulus to trigger the self-assembly. The need for this trigger stems from the metastable nature of most supramolecular gels and can limit their applicability. Herein, we present a small urea-based molecule that spontaneously forms a stable hydrogel by simple mixing without the addition of an external trigger. Single particle tracking experiments and observations made from scanning electron microscopy indicated that triggerless gelation occurred in a similar fashion as the archetypical heat-triggered gelation. These results could stimulate the search for other supramolecular hydrogels that can be obtained by simple mixing. Furthermore, the mechanism of the heat-triggered supramolecular gelation was elucidated by a combination of molecular dynamics simulations and quantitative NMR experiments. Surprisingly, hydrogelation seemingly occurs via a stepwise self-assembly in which spherical nanoparticles mature into an entangled fibrillary network.

The charge stabilization method has often been used before for obtaining energies of temporary anions. Herein, we combine this method for the first time with conceptual density functional theory (DFT) and quantum theory of atoms in molecules by extending it to the study of nuclear Fukui functions, atom-condensed electronic Fukui functions, and bond critical points. This is applied to temporary anions of ethene and chlorinated ethene compounds, which are known to undergo dissociative electron attachment (DEA). It appears that the method is able to detect multiple valence resonance states in the same molecule, namely, a Π and a Σ state. The obtained nuclear and atom-condensed electronic Fukui functions are interpreted as nuclear forces and electron distributions, respectively, and show clear differences between the Π and Σ states. This enables a more profound characterization and understanding of how the DEA process proceeds. The conclusions are in line with findings from earlier publications, proving that the combination of conceptual DFT with the charge stabilization method yields reasonable results at rather low computational cost.

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

The molecular titanium-oxo cluster [Ti 6 O 6 (O i Pr) 6 (O 2 C t Bu) 6 ] (1) can be photoactivated by UV light, resulting in a deeply coloured mixed valent (photoreduced) Ti (iii/iv) cluster, alongside alcohol and ketone (photooxidised) organic products. Mechanistic studies indicate that a two-electron (not free-radical) mechanism occurs in this process, which utilises the cluster structure to facilitate multielectron reactions. The photoreduced products [Ti 6 O 6 (O i Pr) 4 (O 2 C t Bu) 6 (sol) 2 ], sol = i PrOH (2) or pyridine (3), can be isolated in good yield and are structurally characterized, each with two, uniquely arranged, antiferromagnetically coupled d-electrons. 2 and 3 undergo onward oxidation under air, with 3 cleanly transforming into peroxide complex, [Ti 6 O 6 (O i Pr) 4 (O 2 C t Bu) 6 (py)(O 2 )] (5). 5 reacts with isopropanol to regenerate the initial cluster (1) completing a closed cycle, and suggesting opportunities for the deployment of these easily made and tuneable clusters for sustainable photocatalytic processes using air and light. The redox reactivity described here is only possible in a cluster with multiple Ti sites, which can perform multi-electron processes and can adjust its shape to accommodate changes in electron density., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

The dissociation of environmentally hazardous NO through dissociative adsorption on metallic clusters supported by oxides, is receiving growing attention. Building on previous research on monometallic M 13 clusters [The Journal of Physical Chemistry C 2019, 123 (33), 20314-20318], this work considers bimetallic Pt 12 M (M=Rh, Ru or Ir) clusters. The adsorption energy and activation energy of NO dissociation on the clusters have been calculated in vacuum using Kohn-Sham DFT, while their trends were rationalized using reactivity indices such as molecular electrostatic potential and global Fermi softness. The results show that doping of the Pt clusters lowered the adsorption energy as well as the activation energy for NO dissociation. Furthermore, reactivity indices were calculated as a first estimate of the performance of the clusters in realistic amorphous silica pores (MCM-41) through ab initio molecular dynamics simulations., (© 2022 Wiley-VCH GmbH.)

An overview of mathematical properties of the non-local second order derivatives of the canonical, grand canonical, isomorphic, and grand isomorphic ensembles is given. The significance of their positive or negative semidefiniteness and the implications of these properties for atoms and molecules are discussed. Based on this property, many other interesting properties can be derived, such as the expansion in eigenfunctions, bounds on the diagonal and off-diagonal elements, and the eigenvalues of these kernels. We also prove Kato's theorem for the softness kernel and linear response and the dissociation limit of the linear responses as the sum of the linear responses of the individual fragments when dissociating a system into two non-interacting molecular fragments. Finally, strategies for the practical calculation of these kernels, their eigenfunctions, and their eigenvalues are discussed.

The dissimilatory sulfite reductase enzyme has very characteristic active site where the substrate binds to an iron site, ligated by a siroheme macrocycle and a thiol directly connected to a [Fe 4 S 4 ] cluster. This arrangement gives the enzyme remarkable efficiency in reducing sulfite and nitrite all the way to hydrogen sulfide and ammonia. For the first time we present a theoretical study where substrate binding modalities and activation are elucidated using active site models containing proton supply side chains and the [Fe 4 S 4 ] cluster. Density functional theory (DFT) was deployed in conjunction with the energy decomposition scheme (as implemented in AMS), the quantum theory of atoms in molecules (QTAIM), and conceptual DFT (cDFT) descriptors. We quantified the role of the electrostatic interactions inside the active site created by the side chains as well as the influence of the [Fe 4 S 4 ] cluster on the substrate binding. Furthermore, using conceptual DFT results we shed light of the activation process, thus, laying foundation for further mechanistic studies. We found that the bonding of the ligands to the iron complex is dominated by electrostatic interactions, but the presence of the [Fe 4 S 4 ] cubane leads to substantial changes in electronic interaction. The spin state of the cubane, however, affects the binding energy only marginally. The conceptual DFT results show that the presence of the [Fe 4 S 4 ] cubane affects the reactivity of the active site as it is involved in electron transfer. This is corroborated by an increase in the electrophilicity index, thus making the active site more prone to react with the ligands. The interaction energies between the ligand and the siroheme group are also increased upon the presence of the cubane group, thus, suggesting that the siroheme group is not an innocent spectator but plays an active role in the reactivity of the dSIR active site.

Non-covalent π-π stacking interactions often play a key role in the stability of the secondary and tertiary structures of peptides and proteins, respectively, and can be a means of ensuring the binding of ligands within protein and enzyme binding sites. It is generally accepted that minor structural changes to the aromatic ring, such as substitution, can have a large influence on these interactions. Nevertheless, a thorough understanding of underpinning phenomena guiding these key interactions is still limited. This is especially true for larger aromatic structures. To expand upon this knowledge, elaborate ab initio calculations were performed to investigate the effect of halogenation on the stability of 3-methylindole stacking. 3-Methylindole served as a representation of the tryptophan side chain, and is a frequently used motif in drug design and development. Moreover, an expression is derived that is able to accurately predict the interaction stability of stacked halogenated 3-methylindole dimers as well as halogenated toluene dimers, based on monomer level calculated DFT descriptors. We aim for this expression to provide the field with a straightforward and reliable method to assess the effect of halogenation on the π-π stacking interactions between aromatic scaffolds.

An extension of conceptual DFT to include the influence of an external magnetic field is proposed in the context of a program set up to cope with the ever increasing variability of reaction conditions and concomitant reactivity. The two simplest global reactivity descriptors, the electronic chemical potential ( μ ) and the hardness ( η ), are considered for the main group atoms H-Kr using current density-functional theory. The magnetic field strength, | B |, is varied between 0.0 and 1.0 B 0 = ħe -1 a 0 -2 ≈ 2.3505 × 10 5 T, encompassing the Coulomb and intermediate regimes. The carbon atom is studied as an exemplar system to gain insight into the behaviour of the neutral, cationic and anionic species under these conditions. Their electronic configurations change with increasing | B |, leading to a piecewise behaviour of the ionization energy ( I ) and electron affinity ( A ) values as a function of | B |. This results in complex behaviour of properties such as the electronegativity χ = -1/2( I + A ) = - μ and hardness η = 1/2( I - A ). This raises an interesting question: to what extent are atomic properties periodic in the presence of a magnetic field? In the Coulomb regime, close to | B | = 0, we find the familiar periodicity of the atomic properties, and make the connections to response functions central to conceptual DFT. However, as the field increases in the intermediate regime configurational changes of the atomic species lead to discontinuous changes in their properties; fundamentally changing their behaviour, which is illustrated by constructing a periodic table of χ and η values at | B | = 0.5 B 0 . These values tend to increase for groups 1-2 and decrease for groups 16-18, leading to a narrower range overall and suggesting substantial changes in the chemistry of the main group elements. Changes within each group are also examined as a function of | B |. These are more complex to interpret due to the larger number of configurations accessible to heavier elements at high field. This is illustrated for group 17 where Cl and Br have qualitatively different configurations to their lighter cogener at | B | = 0.5 B 0 . The insight into periodic trends in strong magnetic fields may provide a crucial starting point for predicting chemical reactivity under these exotic conditions., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

Zeolite-catalyzed benzene ethylation is an important industrial reaction, as it is the first step in the production of styrene for polymer manufacturing. Furthermore, it is a prototypical example of aromatic electrophilic substitution, a key reaction in the synthesis of many bulk and fine chemicals. Despite extensive research, the reaction mechanism and the nature of elusive intermediates at realistic operating conditions is not properly understood. More in detail, the existence of the elusive arenium ion (better known as Wheland complex) formed upon electrophilic attack on the aromatic ring is still a matter of debate. Temperature effects and the presence of protic guest molecules such as water are expected to impact the reaction mechanism and lifetime of the reaction intermediates. Herein, we used enhanced sampling ab initio molecular dynamics simulations to investigate the complete mechanism of benzene ethylation with ethene and ethanol in the H-ZSM-5 zeolite. We show that both the stepwise and concerted mechanisms are active at reaction conditions and that the Wheland intermediate spontaneously appears as a shallow minimum in the free energy surface after the electrophilic attack on the benzene ring. Addition of water enhances the protonation kinetics by about 1 order of magnitude at coverages of one water molecule per Brønsted acidic site. In the fully solvated regime, an overstabilization of the BAS as hydronium ion occurs and the rate enhancement disappears. The obtained results give critical atomistic insights in the role of water to selectively tune the kinetics of protonation reactions in zeolites., Competing Interests: The authors declare no competing financial interest., (© 2022 The Authors. Published by American Chemical Society.)