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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.

Thelinear response kernel also referred to as linear responsefunction (LRF) in the framework of conceptual density functional theoryhas gained tremendous success in time-dependent density functionaltheory. Comparatively less attention has been devoted to the LRF froma chemical reactivity perspective in its time- or frequency-independentcontext, although it has recently been used to qualitatively describeelectron delocalization, (anti-)-aromaticity, inductive and mesomericeffects, etc. Despite these successes, which were obtained by approximatingthe LRF using the independent particle approximation deriving froma coupled-perturbed Kohn-Sham computation, the robustness ofthis LRF approach needs to be assessed. In this work, we compute theLRF at four levels of approximation (independent particle approximation,random phase approximation, Hartree-Fock approximation, andthe (exact) DFT (density functional theory) expression) using functionalsfrom the first four rungs of Jacob's ladder of exchange-correlationenergy functionals. To scrutinize the impact of these approximations,new visualization strategies are discussed and systematized. The overallconclusion is that the independent particle approximation yields qualitativelycorrect results (ergo previous conceptual applications of the LRFare trustworthy), but for quantitative results, LRF expressions includingcoulomb and exchange-(-correlation) terms should be included. Withrespect to functionals, density-gradient contributions to the exchange-correlationkernel are less than 10% and may be omitted safely where that is preferablecomputationally.

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.

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 300 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 776 entries, the paper represents a broad snapshot of DFT, anno 2022.

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.

Following the recent discovery of stable octa‐coordinated alkaline earth metals with N2 and CO, the role of group II metals in the catalytic reduction of these ligands by means of density functional theory (DFT) calculations and conceptual DFT‐based reactivity indices is investigated. Cubic group IV and octahedral group VI transition metal complexes as well as the free ligands are computed for reference. The outer and most accessible atoms of N2 and CO become much more nucleophilic and electrophilic in all complexes, relevant for N2 fixation, as probed by the Fukui function and local softness. Within one row of the periodic table, the alkaline earth complexes often show the strongest activation. On the contrary, the electrostatic character is found to be virtually unaffected by complexation. Trends in the soft frontier orbital and hard electrostatic character are in agreement with calculated proton affinities and energy decomposition analyses of the protonated structures, demonstrating the dominance of the soft (HOMO–LUMO) orbital interactions., Alkaline earth complexes: The viability of alkaline earth metal‐based N2 fixation is investigated. It is shown that the activation of N2 through complexation originates from the d–π back‐donation. Within one row of the periodic table, the alkaline earth metal shows the strongest nucleophilic activation of the N2 ligand, confirming clear trends in proton affinities.

How do local reactivity descriptors, such as the Fukui function and the local spin density distribution, shape the potential energy surface (PES) associated with chemical reactions and thus govern reactivity trends and regioselective preferences? This is the question that is addressed here through a qualitative valence bond (VB) analysis. We demonstrate that common density functional theory (DFT)-based local reactivity descriptors can essentially be regarded-in one way or another-as indirect measures of delocalization, i.e., resonance stabilization, of the reactants within VB theory. The inherent connection between (spatial) delocalization and (energetic) resonance stabilization embedded in VB theory provides a natural and elegant framework for analyzing and comprehending the impact of individual local reactivity descriptors on the global PES. Our analysis provides new insights into the role played by local reactivity descriptors and illustrates under which conditions they can sometimes fail to predict reactivity trends and regioselective preferences, e.g., in the case of ambident reactivity. This treatment constitutes a first step toward a unification of VB theory and conceptual DFT.

Benziporphyrins are versatile macrocycles exhibiting aromaticity switching behaviors. The existence of both Hückel and Möbius (anti)aromaticity has been reported in these systems, whose validity is respectively governed by the [4n + 2] and [4n] π-electron rule on the macrocyclic pathway. Despite the experimental evidence on the floppiness of benziporphyrins, the switching mechanism between Hückel and Möbius structures is still not clear, as well as the factors influencing the stability of the different π-conjugation topologies. For these reasons, we performed a systematic study on A,D-di-p-benzihexaphyrins(1.1.1.1.1.1) with two redox states corresponding to [28] and [30] π-electron conjugation pathways. Whereas benzi[28]hexaphyrin obeys Möbius aromaticity, benzi[30]hexaphyrin follows Hückel aromaticity. The dynamic interconversion between Möbius and Hückel aromaticity is investigated through the rotation of a phenylene ring, which acts as the topology selector. Further analyses of the energy profiles using energy decomposition and information-theoretic approaches provide new insights into conformational stability, aromaticity and antiaromaticity for these species. Strong and opposite cross correlations between aromaticity indexes and information-theoretic quantities were found for the two macrocyclic systems with opposite global aromaticity and antiaromaticity behaviors. These results indicate that Hückel and Möbius aromaticity and antiaromaticity, though qualitatively different, are closely related and can be interchanged, and information-theoretic quantities provide a novel understanding about their relevance. Our present results should provide in-depth insights to appreciate the nature and origin about Möbius (anti)aromaticity and its close relationship with Hückel (anti)aromaticity.

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 B0 = ħe−1a0−2 ≈ 2.3505 × 105 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 B0. 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 B0. The insight into periodic trends in strong magnetic fields may provide a crucial starting point for predicting chemical reactivity under these exotic conditions.

In our effort to implement the mechanical force used to activate single molecules in mechanochemistry in the context of conceptual density functional theory, we present a theoretical investigation of strained alkynes for rationalizing structural trends as well as the reactivity of cyclic alkynes that are of great importance in in vivo click reactions. The strain on the triple bond in cyclic alkynes is modeled by angular constraints in a 2-butyne fragment and the corresponding bending force is calculated by means of an extended COGEF (constrained geometries simulate external forces) model. In general, the force required to bend the triple bond is smaller with electron-withdrawing groups on the propargylic C-atom, which elegantly results in smaller angles around the triple bond in cyclic alkynes with such substitution pattern. By means of conceptual DFT descriptors, the electrophilic and nucleophilic character of bent triple bonds was investigated revealing moderate activation for small distortions from the linear geometry (0° to 15°) and a drastically more reactive π-space if the triple bond is bent further. This analysis of the intrinsic reactivity of the triple bond is in line with experimental observations, explaining the reactive nature of cyclooctynes and cycloheptynes, whereas larger cyclic systems do not drastically activate the triple bond., The force required to bend alkynes increases linearly with the angle and depends on the substituent pattern. The reactivity of the triple bond does not readily increase and is less influenced by the substituent pattern for larger bends.

Linear triatomic molecules (CO2, N2O, and OCS) are scrutinized for their propensity to form perpendicular tetrel (CO2 and OCS) or pnictogen (N2O) bonds with Lewis bases (dimethyl ether and trimethyl amine) as compared with their tendency to form end-on chalcogen bonds. Comparison of the IR spectra of the complexes with the corresponding monomers in cryogenic solutions in liquid argon enables to determine the stoichiometry and the nature of the complexes. In the present cases, perpendicular tetrel and pnictogen 1:1 complexes are identified mainly on the basis of the lifting of the degenerate ν 2 bending mode with the appearance of both a blue and a red shift. Van ′t Hoff plots of equilibrium constants as a function of temperature lead to complexation enthalpies that, when converted to complexation energies, form the first series of experimental complexation energies on sp1 tetrel bonds in the literature, directly comparable to quantum-chemically obtained values. Their order of magnitude corresponds with what can be expected on the basis of experimental work on halogen and chalcogen bonds and previous computational work on tetrel bonds. Both the order of magnitude and sequence are in fair agreement with both CCSD(T) and DFA calculations, certainly when taking into account the small differences in complexation energies of the different complexes (often not more than a few kJ mol−1) and the experimental error. It should, however, be noted that the OCS chalcogen complexes are not identified experimentally, most probably owing to entropic effects. For a given Lewis base, the stability sequence of the complexes is first successfully interpreted via a classical electrostatic quadrupole–dipole moment model, highlighting the importance of the magnitude and sign of the quadrupole moment of the Lewis acid. This approach is validated by a subsequent analysis of the molecular electrostatic potential, scrutinizing the σ and π holes, as well as the evolution in preference for chalcogen versus tetrel bonds when passing to “higher” chalcogens in agreement with the evolution of the quadrupole moment. The energy decomposition analysis gives further support to the importance/dominance of electrostatic effects, as it turns out to be the largest attractive term in all cases considered, followed by the orbital interaction and the dispersion term. The natural orbitals for chemical valence highlight the sequence of charge transfer in the orbital interaction term, which is dominated by an electron-donating effect of the N or O lone-pair(s) of the base to the central atom of the triatomics, with its value being lower than in the case of comparable halogen bonding situations. The effect is appreciably larger for TMA, in line with its much higher basicity than DME, explaining the comparable complexation energies for DME and TMA despite the much larger dipole moment for DME.

Expanded porphyrins are currently recognized as the ideal test bed to explore the correlation between molecular properties and (anti)aromaticity since they can adopt different π-conjugation topologies and change easily the number of π-electrons along the conjugation pathway. From recent studies, aromaticity indeed emerges as the guiding concept to rationalize the spectroscopic features and the two-photon absorption cross sections in expanded porphyrins. However, from the theoretical point of view, the complex structure-property relationship between aromaticity, π-conjugation topology, and photophysical properties is not fully understood yet. To unravel such structure-property relationships, we focused on octaphyrin(1.1.1.1.1.1.1.1) macrocycles since they are flexible enough to provide twisted-Hückel, Möbius, and Hückel untwisted topologies with distinct aromaticity character. In this work, the (anti)aromaticity of the different states was first quantified using different aromaticity criteria. Second, the fingerprints of aromaticity on UV/vis spectra were elucidated. Importantly, we found that the absorption spectra of certain antiaromatic Hückel structures are characterized by more intense absorption bands than its aromatic homologues, contrary to the general statement that antiaromatic expanded porphyrins exhibit significantly attenuated absorption bands compared to aromatic ones. Finally, the role of aromaticity and π-conjugation topology on linear and nonlinear optical properties was scrutinized and our results pinpoint the importance of molecular topology and symmetry on the first and second hyperpolarizabilities. Overall, we demonstrate that expanded porphyrins upon topology interconversions can act as efficient nonlinear optical switches. ©

In molecular mechanochemistry, the chemical properties of a reactant system are modified through the absorption of mechanical energy at the single molecular level, as opposed to thermochemistry (heat), electrochemistry (electrical current) and photochemistry (light). In this proof-of-concept paper, we present a theoretical approach to rationalize and predict the change in chemical properties and concepts when an external stretching force, Fext, is applied to a chemical bond. By considering perturbations to the total molecular energy due to Fext, a series of mechanochemical response indices are obtained within the framework of conceptual density functional theory (DFT). Trends in these indices monitoring the change in hardness and electrophilicity among others, were rationalized for a number of diatomic molecules in terms of the ground-state geometry and the frontier molecular orbitals of the molecule. Finally, we present a set of rules that can be easily adopted for polyatomic molecules to predict the changing chemical reactivity of single molecules when subjected to an external force.

In this work, we report a systematic study on the global and local aromaticity of acenes using a series of model structures from 2-acene to 11-acene. A recently developed ansatz, an information-theoretic approach coached into density functional reactivity theory has been employed, which essentially provides different density functionals characterizing the molecular electron density distribution. Based on the correlation analysis of six conventional aromaticity indices with eight information-theoretic quantities, we examined the aromaticity of acenes from both global and local perspectives. From the global aromaticity viewpoint, our results suggest that different descriptors based on various physicochemical properties are intrinsically dependent. A novel laminated feature ruling local aromaticity of acenes has been unveiled, from which we found that the distance from the terminal rings plays the critical role. Based on the shape of the correlation plots between the conventional aromaticity indices and information-theoretic quantities, the latter could be separated into three subgroups. The seemingly contradictory results from global and local aromaticity perspectives not only present us the uniqueness of the acene systems but all demonstrate the effectiveness of the information-theoretic approach from density functional reactivity theory. Besides strengthening the validity of a series of new aromaticity descriptors, our results should lead to more clear insights into the chemical significance of the information-theoretic quantities.

A hitherto unexplored class of molecules for molecular force probe applications are expanded porphyrins. This work proves that mechanical force is an effective stimulus to trigger the interconversion between Hückel and Möbius topologies in [28]hexaphyrin, making these expanded porphyrins suitable to act as conformational mechanophores operating at mild (sub‐1 nn) force conditions. A straightforward approach based on distance matrices is proposed for the selection of pulling scenarios that promote either the planar Hückel topology or the three lowest lying Möbius topologies. This approach is supported by quantum mechanochemical calculations. Force distribution analyses reveal that [28]hexaphyrin selectively allocates the external mechanical energy to molecular regions that trigger Hückel–Möbius interconversions, explaining why certain pulling scenarios favor the Hückel two‐sided topology and others favor Möbius single‐sided topologies. The meso‐substitution pattern on [28]hexaphyrin determines whether the energy difference between the different topologies can be overcome by mechanical activation., Use the force: The Hückel and Möbius topology of [28]hexaphyrin can be mechanically locked by applying an external pulling force to different meso positions in a sub‐nano‐Newton force regime. The mechanical energy is distributed to a specific region in the molecule to trigger the interconversion.

The extension of the E = E[N, v] functional for exploring chemical reactivity in a conceptual DFT context to include external electric fields is discussed. Concentrating on the case of a homogeneous field the corresponding response functions are identified and integrated, together with the conventional response functions such as permanent dipole moment and polarizability, in an extended response function tree associated with the E = E[N, v, ϵ] functional. In a case study on the dihalogens F2, Cl2, Br2, I2 the sensitivity of condensed atomic charges (∂q/∂ϵ) is linked to the polarizability of the halogen atoms. The non-integrated (∂ρ(r)/∂ϵ) response function, directly related to the field induced density change, is at the basis of these features. It reveals symmetry breaking for a perpendicular field, not detectable in its atom condensed counterpart, and accounts for the induced dipole moment directly related to the molecular polarizability. The much higher sensitivity of the electronic chemical potential/electronegativity as compared to the chemical hardness is highlighted. The response of the condensed Fukui functions to a parallel electric field increases when going down in the periodic table and is interpreted in terms of the extension of the outer contours in the non-condensed Fukui function. In the case of a perpendicular field the (∂f(r)/∂ϵ) response function hints at stereoselectivity with a preferential side of attack which is not retrieved in its condensed form. In an application the nucleophilic attack on the carbonyl group in H2CO is discussed. Similar to the dihalogens, stereoselectivity is displayed in the Fukui function for nucleophilic attack (f+) in the case of a perpendicular electric field, and opposite to the one that would arise based on the induced density. Disentangling the expression for the evolution of the Fukui function in the presence of an electric field reveals that this difference can be traced back to local differences in the polarization or induced density between the anionic and the neutral system. This difference may be exploited, e.g. for an appropriately substituted H2CO, to generate enantioselectivity. This journal is

Metabolomics is recognized as a crucial scientific domain, promising to advance our understanding of cell biology, physiology and medicine. Tandem mass spectrometry (MS/MS) has strong potential to elucidate the metabolites in complex biological samples and to become a standard tool complementing established techniques. However, despite its potential for answering many key questions, a major challenge in the use of tandem mass spectrometry for characterizing metabolites lies in a lack of computational tools for accurate annotation and structure identification allowing us to turn complex data into molecular knowledge. Chemo-informatics and related machine-learning in silico fragmentation tools have already been established and used for different classes of metabolites. For the classes of metabolites where existing chemo-informatics approaches produce insufficiently accurate predictions a supervised machine learning based strategy can be used to predict possible molecular structures from “unassigned” experimental tandem MS data. Here, we propose a new innovative in silico approach employing quantum mechanical (QM) methods in order to predict ion formation and subsequent fragmentation patterns of arbitrary small molecules and validate putative annotations of tandem mass spectrometry (MS) data. The focus is on the evaluation of a new conceptual density functional theory (CDFT) nuclear reactivity descriptor of the nuclear Fukui function type, that characterizes the forces that the atomic nuclei experience due to proton attachment and captures the onset of the change in the nuclear positions induced by it. A series of test compounds for which high quality experimental data exist and that were investigated before in a more approximate theoretical framework have been examined. The output of these calculations provides a list of the most probable molecular structures predicted to match the experimental tandem MS spectrum (“de novo metabolite identification”).

This paper results from a round table discussion at the CCTC2018 Conference in Changsha City, Hunan, China, in December 2018. It presents a report on the status, prospects, and issues of conceptual density functional theory (CDFT). After a short exposition on the history of CDFT, its fundamentals, philosophy, and successes are highlighted. Then ten issues for reflection on the future of conceptual DFT are formulated and discussed, ending with one or more summarizing statements on the present status of various concepts/principles/practices and proposed directions for future research. The issues include the further analysis of the energy functional, E[N,v], extended to include effects of temperature, solvent, and mechanical forces, basic requirements for physically acceptable response functions as reactivity descriptors, the use of the grand canonical ensemble, the relevance of CDFT for chemical kinetics and thermodynamics, the domain of validity of CDFT-based principles, the combination of CDFT with reaction path calculations, information-theoretic descriptors, and the treatment of excited states and time dependence. The final issue advocates the transition of CDFT from an interpretative to a predictive mode; we believe this is of utmost importance for promoting CDFT as a viable alternative to wave function-based methods for the practicing chemist, a separate issue treated in the final section.

In recent years, a considerable interest has grown in the design of molecular nanowires with an increasing conductance with length. The development of such nanowires is highly desirable because they could play an important role in future molecular-scale circuitry. Whereas the first experimental observation of this nonclassical behavior still has to be realized, a growing number of candidate wires have been proposed theoretically. In this Letter, we point out that all the wires with an anti-Ohmic increasing conductance with length proposed so far share a common characteristic: their diradical character increases with length. The conceptual connection between diradical character and conductance enables a systematic design of such anti-Ohmic wires and explains the difficulty in their syntheses. A strategy is proposed to balance the stability and conductance so that this nonclassical phenomenon can be observed.

In this work, we explore the design of so-called "reversible bithermoelectric switches", molecules which can be switched reversibly between a positive and negative Seebeck coefficient through the application of external stimuli. We focus on heptaphyrins, a class of expanded porphyrins that can be shifted between a Hückel and Möbius topology, and demonstrate that these molecules are promising candidates for such an electronic function. Our calculations lead to the conclusion that the molecular switch between these two π-conjugation topologies causes the thermopower to change considerably from +50 μV/K to -40 μV/K, respectively. We address some of the limitations of our approach and expect that this behavior will be retrieved experimentally as well, although chemical modifications of the molecules and/or electrodes might be required. Bithermoelectric switches could potentially constitute an entirely new class of molecular switches which, instead of switching between an ON and an OFF state (the modus operandi ofmost molecular switches so far), revert the direction of the heat and/or charge transport. This could potentially lead to a wide range of novel technological applications.

Expanded porphyrins have been recently identified as promising candidates for conductance switching based on aromaticity and molecular topology changes. However, the factors that control electron transport switching across the metal-molecule-metal junction still need to be elucidated. For this reason, the transport properties of Hückel/Möbius (anti)aromatic compounds are investigated thoroughly in this work to gain qualitative understanding into the conductivity of these unique macrocycles. Starting from a polyene model, a simple counting rule is developed to predict the occurrence of quantum interference around the Fermi level at the Hückel level of theory. Next, the different approximations of Hückel theory are lifted, enabling the exploration of the influence of each of these approximations on the transport properties of expanded porphyrins. Along the way, a detailed study on the relationship between the conductance and aromaticity/topology has been undertaken. Even though it has been proposed that the π-conjugated systems of expanded porphyrins can be approximated as polyene macrocycles based on the "annulene model", it turns out that the distortion induced by the pyrrole rings to the electronic structure of the expanded porphyrins causes the simple counting rule for the prediction of quantum interference developed for polyenes to fail in some specific situations. Nevertheless, our back-of-the-envelope approach enables an intuitive rationalization of most of the transport properties of expanded porphyrins. Our conclusions cast further doubt on the proposed negative relationship between conductance and aromaticity and highlight the importance of the connectivity on determining the shape of the transmission functions of the different states. We hope that the new insights provided here will offer experimentalists a road map toward the design of functional, multidimensional electronic switches based on expanded porphyrins.

With the idea of using alchemical derivatives to explore in an efficient, computer- and cost-effective way Chemical Space was launched several years ago. In the context of Conceptual DFT response functions, these energies vs nuclear charge derivatives permit the estimatation of the energy of transmutants of a given starting or reference molecule showing different nuclear compositions. After an explorative study on small and planar molecules (Balawender et al. J. Chem. Theory Comput. 2013, 9, 5327) by the present authors of this paper, the present study fully exploits the computational advantages of the alchemical derivatives in larger three-dimensional systems. Starting from a single reference calculation on C60, the complete BN substitution pattern, from single substituted C58BN via the belt (C20(BN)20 and the ball C12(BN)24 structures to the fully substituted (BN)30, is explored. Successive and simultaneous substitution strategies are followed and compared, indicating that both techniques yield identical results up to 13 substitutions but that for higher substitutions the simultaneous approach needs to be taken. Due to the cost-efficiency of the algorithm this path can indeed be followed as opposed to earlier work in the literature where for each step a full SCF calculation was at stake leading to prohibitively large computational demands for adopting the simultaneous approach. Previously formulated rules governing the substitution pattern by Kar and co-workers are scrutinized in this context and reformulated giving chemical insight in the gradual substitution process and the relative energies of the isomers. In its present form the method offers an interesting venue to study BN substitution patterns in higher fullerenes and graphene and in general paves the way for more efficient exploration of the Chemical Space.

Expanded porphyrins are flexible enough to switch between different π-conjugation topologies, namely Möbius, Hückel and twisted-Hückel, each with distinct electronic properties and aromaticity. Since these switches can be induced by different external stimuli, expanded porphyrins represent a promising platform to develop a novel type of molecular switch for molecular electronic devices. In this work, the feasibility of conductance switches based on topology and/or aromaticity changes in expanded porphyrins is assessed for the first time. In particular, the electron transport properties of penta-, hexa- and heptaphyrins with different π-conjugation topologies and aromaticity were carefully investigated using the nonequilibrium Green's function formalism in combination with density functional theory for various configurations of the gold contacts. Our results highlight the importance of the macrocyclic aromaticity and connectivity and, to a lesser extent, the molecular topology, in determining the transmission functions and local currents. When the electrodes are connected along the longitudinal axis of the macrocycle, we found that aromaticity of Hückel expanded porphyrins increases single-molecule junction conductance, contrary to the negative relationship between conductance and aromaticity found in single five-membered rings. For this particular connectivity, antiaromatic Hückel structures with [4n] π-electrons exhibit a sharp reduction in transmission near the Fermi level due to destructive quantum interference between the HOMO and LUMO. Belt-shaped Möbius aromatic structures exhibit a lower conductance as compared to the Hückel aromatic structures, and the current flow avoids the molecular twist. Importantly, we show that expanded porphyrins, upon redox and topology interconversions, could act as efficient three-level molecular switches with high ON/OFF ratio, up to 10

We explore a new strategy to tune the conductivity of molecular electronic devices: captodative substitution. We demonstrate that a careful design of such substitution schemes on a benzene parental structure can enhance the conductivity by almost an order of magnitude under small bias. Once this new strategy has been established, we apply it to molecular wires and demonstrate that it enables the unprecedented anti-Ohmic design of wires whose conductivity increases with the length. Overall, the captodative substitution approach provides a very promising pathway toward full chemical control of the conductivity of molecules which opens up the possibility to design molecular switches with an improved on/off ratio among others.

Using a set of state-of-the-art quantum chemical techniques we scrutinized the characteristically different reactivity of frustrated and classical Lewis pairs towards molecular hydrogen. The mechanisms and reaction profiles computed for the H2 splitting reaction of various Lewis pairs are in good agreement with the experimentally observed feasibility of H2 activation. More importantly, the analysis of activation parameters unambiguously revealed the existence of two reaction pathways through a low-energy and a high-energy transition state. An exhaustive scrutiny of these transition states, including their stability, geometry and electronic structure, reflects that the electronic rearrangement in low-energy transition states is fundamentally different from that of high-energy transition states. Our findings reveal that the widespread consensus mechanism of H2 splitting characterizes activation processes corresponding to high-energy transition states and, accordingly, is not operative for H2-activating systems. One of the criteria of H2-activation, actually, is the availability of a low-energy transition state that represents a different H2 splitting mechanism, in which the electrostatic field generated in the cavity of Lewis pair plays a critical role: to induce a strong polarization of H2 that facilities an efficient end-on acid-H2 interaction and to stabilize the charge separated “H+–H−” moiety in the transition state.

We establish the physical origins of chemical transferability from the perspective of the nearsightedness of electronic matter. To do this, we explicitly evaluate the response of electron density to a change in the system, at constant chemical potential, by computing the softness kernel, [Formula: see text] The softness kernel is nearsighted, indicating that under constant-chemical-potential conditions like dilute solutions changing the composition of the molecule at [Formula: see text] has only local effects and does not have any significant impact on the reactivity at positions [Formula: see text] far away from point [Formula: see text] This locality principle elucidates the transferability of functional groups in chemistry.

This review sets out to understand the reactivity of diradicals and how that may differ from monoradicals. In the first part of the review, we delineate the electronic structure of a diradical with its two degenerate or nearly degenerate molecular orbitals, occupied by two electrons. A classification of diradicals based on whether or not the two SOMOs can be located on different sites of the molecule is useful in determining the ground state spin. Important is a delocalized to localized orbital transformation that interchanges "closed-shell" to "open-shell" descriptions. The resulting duality is useful in understanding the dual reactivity of singlet diradicals. In the second part of the review, we examine, with a consistent level of theory, activation energies of prototypical radical reactions (dimerization, hydrogen abstraction, and addition to ethylene) for representative organic diradicals and diradicaloids in their two lowest spin states. Differences and similarities in reactivity of diradicals vs monoradicals, based on either a localized or delocalized view, whichever is suitable, are then discussed. The last part of this review begins with an extensive, comparative, and critical survey of available measures of diradical character and ends with an analysis of the consequences of diradical character for selected diradicaloids.

Sodium and lithium hexatitanates (A2B6O13, where A = Li or Na, B = Ti or Sn) have been considered as anode materials in batteries. In this work, the Li- and Na-ion migration energies of Li2Ti6O13, Li2Sn6O13 and Na2Ti6O13 are explored using atomistic simulations. Alkali-ion transport is explored using a validated forcefield with nudged elastic band and synchronous transition state calculations. The results show that Li-ion migration exhibits activation energies of 0.47 and 0.52 eV for Li2Ti6O13 and Li2Sn6O13, respectively. In addition, Na-ion migration in Na2Ti6O13 has the lowest activation energy of 0.17 eV. Sodium and lithium can also be accommodated into the Li2Ti6O13, Li2Sn6O13 and Na2Ti6O13 structures. Li-ion migration through the channel of Na2Ti6O13 has an activation energy of 0.39 eV, while Na-ion migration in Li2Sn6O13 and Li2Ti6O13 has values of 0.95 and 1.16 eV, respectively. The Li-ion migration barrier in Na2Ti6O13 is lower than that for Li2Sn6O13 and Li2Ti6O13 because of the lower electrostatic interactions in the NaO8 channels. The presence of quasi-transition state structures for the diffusion path impacts on the reduction of the energy barrier to reach the transition state structure, providing the low barriers for Na and Li ions in Na2Ti6O13 lattice structure. The calculated defect energetics reveal that there is a viable incorporation mechanism, without the involvement of Ti4+ to Ti3+ reduction, as reported in the literature, which describes the defect behavior and the reversible insertion of Li+ and Na+ ions in these tunnel structures.

Alchemical derivatives have been used in recent years to obtain essentially qualitative information about transformations in which the number of electrons is unchanged. Within the context of Conceptual DFT, we present a systematic approach for combining changes in both the number of electrons and the nuclear charge so that for example one can navigate from one neutral atom to another. A general formalism is presented for transformations involving changes both in or , where Parr's parabolic approach for the dependence is considered as one particular case and the ensemble description in the 0 K limit as the second case. The B3LYP functional in its CAMB3LYP version combined with the aug-cc-pCVQZ basis has been chosen to perform Coupled Perturbed Kohn Sham calculations of the alchemical derivatives. The monotonic behaviour of the alchemical potential is scrutinised. The order of magnitude analysis of the derivatives preludes convergence at third order. These results are injected in two strategies for obtaining transmutation energies from neutral atoms to a neighbouring neutral atom: one road moving along the diagonal, the other one walking along a pure alchemical road after ionisation or electron attachment. Roads involving the anion of the reference atom are much less successful than those involving its cation. The transmutation energy for the cationic pathway displays chemical accuracy when the procedure is carried at third order in . The difficulties inherent to an accurate description of the anion and its response functions are responsible for the shortcomings along the anionic paths. As a direct application Ionization Energies (IE) and Electron Affinities (EA) are evaluated showing an almost perfect agreement with the direct evaluation and a difference with experimental values less than 0.5 eV for the IE. For the first EA reasonable agreement is obtained with direct and experimental values whereas the second EAs for atoms with stable mono-anions show a remarkable agreement with literature data. Besides proof of concept that with the information content of an atom one can get accurate energetics of its neighbours, the results indicate that alchemical derivatives are capable to yield quantitative information when navigating through Chemical Compound Space.

Several expanded porphyrins switch between Hückel, Möbius and twisted-Hückel topologies, encoding different aromaticity and NLO properties. Since the topological switch can be induced by different external stimuli, expanded porphyrins represent a promising platform to develop molecular switches for molecular electronic devices. In order to determine the optimum conditions for efficient molecular switches from octaphyrins, we have carried out a comprehensive quantum chemical study focusing on the conformational preferences and aromaticity of [36]octaphyrins. Different external stimuli for triggering the topological switch have been considered in our work, such as protonation and redox reactions. Importantly, the structure–property relationships between the molecular conformation, the number of π-electrons and aromaticity in octaphyrins have been established by using energetic, magnetic, structural and reactivity descriptors. Remarkably, we found that the aromaticity of octaphyrins is highly dependent on the π-conjugation topology and the number of π-electrons and it can be modulated by protonation and redox reactions. A non-aromatic figure-eight conformation is strongly preferred by neutral [36]octaphyrins that switches to a Möbius aromatic conformation upon protonation. Such a change of topology involves an aromaticity switch in a single molecule and is accompanied by a drastic change in the NLO properties. In contrast, the twisted-Hückel topology remains the most stable one in the oxidized and reduced species, but the aromaticity is totally reversed upon redox reactions. Aromaticity is shown to be a key concept in expanded porphyrins, determining the electronic, magnetic and NLO properties of these macrocycles.

“The periodic table of the elements is one of the most powerful icons in science: a single document that captures the essence of chemistry in an elegant pattern.” This statement taken from Eric Scerri’s marvelous book The Periodic Table: Its Story and Its Significance (Scerri 2007) grasps in one simple sentence the status that the periodic table has acquired in chemistry, but not only in chemistry: every person all over the world who took high school chemistry remembers for the rest of his/her life at least one thing from it (and from science courses in general): this mysterious table of the elements omnipresent in all books and documents, often decorating the classroom. Why? Although the answer is not easy it is probably because a whole discipline of science is condensed in a simple table or scheme offering at one glimpse the essence (and the beauty) of a part of science which for the rest of the lives of many students will remain unexplored—and even for which these students will create an aversion among others in view of the “polluting role” of chemistry. Nevertheless at some moment in their lives these students felt “something” that was remarkable and which they always remember, as witnessed by their comments when visiting their old school of university with their children. In the hierarchy of the sciences chemistry is often considered, mainly by physicists, as the “physics of the outer shell.” It is sometimes said that chemistry, as also quoted by Scerri (2007), has no deep ideas, not a few fundamental laws like in physics or biology (such as those governing quantum mechanics, relativity and evolution), but the not-so-distant observer will disagree: chemical periodicity as precisely reflected in the periodic table is in my view not only the most fundamental law of chemistry, but is a law or if you want an “organizing principle” with the same status as these famous laws in adjacent disciplines! Chemical periodicity is at the heart of reducing an astonishing amount of experimental data (and nowadays theoretical data as well) to a limited number of patterns often with common origin, enabling one to understand and interpret the properties of the now more-than 50 million compounds registered in the databases of the Chemical Abstracts Services (Toussant, 2009).

In view of its use as reactivity theory, Conceptual Density Functional Theory (DFT), introduced by Parret al., has mainly concentrated up to now on theE=E[N,v]functional. However, different ensemble representations can be used involving other variables also, such asρandμ. In this study, these different ensemble representations (E, Ω,F, andR) are briefly reviewed. Particular attention is then given to the corresponding second-order (functional) derivatives, and their analogies with the second-order derivatives of thermodynamic state functionsU,F,H, andG, which are related to each otherviaLegendre transformations, just as the DFT functionals (Nalewajski and Parr, 1982). Starting from an analysis of the convexity/concavity of the DFT functionals, for which explicit proofs are discussed for some cases, the positive/negative definiteness of the associated kernels is derived and a detailed comparison is made with the thermodynamic derivatives. The stability conditions in thermodynamics are similar in structure to the convexity/concavity conditions for the DFT functionals. Thus, the DFT functionals are scrutinized based on the convexity/concavity of their two variables, to yield the possibility of establishing a relationship between the three second-order reactivity descriptors derived from the considered functional. Considering two ensemble representations,FandΩ,Fis eliminated as it has two dependent (extensive) variables,Nandρ. ForΩ, on the other hand, which is concave for both of its intensive variables (μandυ), an inequality is derived from its three second-order (functional) derivatives: the global softness, the local softness, and the softness kernel. Combined with the negative value of the diagonal element of the linear response function, this inequality is shown to be compatible with the Berkowitz-Parr relationship, which relates the functional derivatives ofρwithυ, at constantNandμ. This was recently at stake upon quantifying Kohn’s Nearsightedness of Electronic Matter. The analogy of the resulting inequality and the thermodynamic inequality for theGderivatives is highlighted. Potential research paths for this study are briefly addressed; the analogies between finite-temperature DFT response functions and their thermodynamic counterparts and the quest for analogous relationships, as derived in this paper, for DFT functionals that are analogues of entropy-dimensioned thermodynamic functions such as the Massieu function.

With the idea of using alchemical derivatives to explore in an efficient, computer- and cost-effective way Chemical Space was launched several years ago. In the context of Conceptual DFT response functions, these energies vs nuclear charge derivatives permit the estimatation of the energy of transmutants of a given starting or reference molecule showing different nuclear compositions. After an explorative study on small and planar molecules ( Balawender et al. J. Chem. Theory Comput. 2013 , 9 , 5327 ) by the present authors of this paper, the present study fully exploits the computational advantages of the alchemical derivatives in larger three-dimensional systems. Starting from a single reference calculation on C