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The structure and morphology of three polymer/graphene nanocomposites have been studied using classical molecular dynamics (MD) simulations. The simulations use 10-monomer oligomeric chains of three polymers: polyethylene (PE), polystyrene (PS) and polyvinylidene fluoride (PVDF). The structure of the polymer chains at the graphene surface has been investigated and characterized by pair correlation functions (PCF), g(r), g(ϑ) and g(r,ϑ). In addition, the influence of the temperature on the graphene/polymer interactions has been analysed for each of the three polymer/graphene nanocomposite systems. The results indicate that graphene induces order in both the PE and PVDF systems by providing a nucleation site for crystallisation, steering the growth of oligomer crystals according to the orientation of the graphene sheet, whereas the PS system remains disordered in the presence of graphene. The overall results are in line with the findings in a recent quantumchemical study by some of the present authors. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

N-fused pentaphyrins (NFP) are the stable forms of fully meso-aryl pentaphyrins(1.1.1.1.1). In order to determine the optimum conditions for viable Möbius topologies of these porphyrinoids, the conformational preferences, Hückel–Möbius interconversion pathways and aromaticity of [22] and [24]NFP have been investigated using density functional theory calculations. The conformation of the macrocycle is shown to be strongly dependent on the oxidation state and the macrocyclic aromaticity. [22]NFP prefers a highly aromatic and relatively strain-free Hückel conformation. However, antiaromatic Hückel and weakly aromatic Möbius conformers coexist in dynamic equilibrium in [24]NFP. The Hückel–Möbius aromaticity switch requires very low activation energy barriers (Ea = 3–4 kcal mol−1). Interestingly, the balance between Möbius and Hückel conformations in [24]NFP can be controlled by meso-substituents. The structure–property relationship between the molecular conformation, number of π electrons and aromaticity has been established in our study using energetic, magnetic, structural, and reactivity descriptors of aromaticity. Although the Möbius topology is indeed accessible for [24]NFP, it does not exhibit a distinct macrocyclic aromaticity mainly due to the large dihedral angles around the molecular twist. Regarding the computational methodology, B3LYP and M06 show the best overall performance for describing the experimental geometries of NFP and, importantly, our computational results support the experimental evidence available for N-fused pentaphyrins. [ABSTRACT FROM AUTHOR]

The essential aspects of zero-temperature grand-canonical ensemble density-functional theory are reviewed in the context of spin-density-functional theory and are used to highlight the assumption of symmetry between electron addition and subtraction that underlies the corrected Koopmans approach of Tozer and De Proft (TDP) for computing electron affinities. The issue of symmetry is then investigated in a systematic study of atomic electron affinities, comparing TDP affinities with those from a conventional Koopmans evaluation and electronic energy differences. Although it cannot compete with affinities determined from energy differences, the TDP expression yields results that are a significant improvement over those from the conventional Koopmans expression. Key insight into the results from both expressions is provided by an analysis of plots of the electronic energy as a function of the number of electrons, which highlight the extent of symmetry between addition and subtraction. The accuracy of the TDP affinities is closely related to the nature of the orbitals involved in the electron addition and subtraction, being particularly poor in cases where there is a change in principal quantum number, but relatively accurate within a single manifold of orbitals. The analysis is then extended to a consideration of the ground state Mulliken electronegativity and chemical hardness. The findings further emphasize the key role of symmetry in determining the quality of the results. [ABSTRACT FROM AUTHOR]

The applicability of the local hardness as defined by the derivative of the chemical potential with respect to the electron density is undermined by an essential ambiguity arising from this definition. Further, the local quantity defined in this way does not integrate to the (global) hardness—in contrast with the local softness, which integrates to the softness. It has also been shown recently that with the conventional formulae, the largest values of local hardness do not necessarily correspond to the hardest regions of a molecule. Here, in an attempt to fix these drawbacks, we propose a new approach to define and evaluate the local hardness. We define a local chemical potential, utilizing the fact that the chemical potential emerges as the additive constant term in the number-conserving functional derivative of the energy density functional. Then, differentiation of this local chemical potential with respect to the number of electrons leads to a local hardness that integrates to the hardness, and possesses a favourable property; namely, within any given electron system, it is in a local inverse relation with the Fukui function, which is known to be a proper indicator of local softness in the case of soft systems. Numerical tests for a few selected molecules and a detailed analysis, comparing the new definition of local hardness with the previous ones, show promising results. [ABSTRACT FROM AUTHOR]

Global hardness and softness and the associated hard/soft acid/base (HSAB) principle have been used to explain many experimental observed reactivity patterns and these concepts can be found in textbooks of general, inorganic, and organic chemistry. In addition, local versions of these reactivity indices and principles have been defined to describe the regioselectivity of systems. In a very recent article (Chem.–Eur. J.2008, 14, 8652), the present authors have shown that the picture of these well-known descriptors is incomplete and that the understanding of these reactivity indices must be “reinterpreted”. In fact, the local softness and hardness contain the same “potential information” and they should be interpreted as the “local abundance” or “concentration” of their corresponding global properties. In this contribution, we analyze the implications of this new point of view for the applicability of these well-known descriptors when comparing two sites in three situations: two sites within one molecule, two sites in two different, but noninteracting molecules, and two sites in two different, but interacting, molecules. The implications on the HSAB principle are highlighted, leading to the discussion of the role of the electrostatic interaction. [ABSTRACT FROM AUTHOR]

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.)

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.

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.

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.

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.)

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.

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.

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., Competing Interests: There are no conflicts of interest to declare., (This journal is © The Royal Society of Chemistry.)

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.

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.

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.

Electrophilic aromatic sulfonation of benzene with sulfur trioxide is studied with ab initio molecular dynamics simulations in gas phase, and in explicit noncomplexing (CCl 3 F) and complexing (CH 3 NO 2 ) solvent models. We investigate different possible reaction pathways, the number of SO 3 molecules participating in the reaction, and the influence of the solvent. Our simulations confirm the existence of a low-energy concerted pathway with formation of a cyclic transition state with two SO 3 molecules. Based on the simulation results, we propose a sequence of elementary reaction steps and a kinetic model compatible with experimental data. Furthermore, a new alternative reaction pathway is proposed in complexing solvent, involving two SO 3 and one CH 3 NO 2 .

The electron density changes from reactants towards the transition state of a chemical reaction is expressed as a linear combination of the state-specific dual descriptors (SSDD) of the corresponding reactant complexes. Consequently, the SSDD can be expected to bear important resemblance to the so-called natural orbitals for chemical valence (NOCV), introduced as the orbitals that diagonalize the deformation density matrix of interacting molecules. This agreement is shown for three case studies: the complexation of a Lewis acid with a Lewis base, a SN2 nucleophilic substitution reaction and a Diels-Alder cycloaddition reaction. As such, the SSDD computed for reactant complexes are shown to provide important information about charge transfer interactions during a chemical reaction.

We have developed a simple model for incorporating the influence of external pressure and solution pH into a cluster based (i.e. comprising the central Al(3+) cation and nearest neighbor coordinating H2O and OH(-) ligands) 1st principles approach to investigate the hydrolysis equilibria of aqueous Al(3+) monomeric species in high pressure environments such as are found in the Earth's mantle. Our model is demonstrated to reproduce the well documented bulk chemistry of the aqueous Al(3+) system under ambient conditions, namely the system is dominated at low and high pH by the 6-coordinated aqua species and 4 coordinated hydroxide species, respectively, while all remaining species occupy a narrow intermediate pH range. Coupling this model to changes in solution pH is achieved by using [H3O(+)] as a parameter in the definition of the formation equilibrium constants used; the influence of external pressure is evaluated using Planck's equation. This approach predicts that changes in external pressure will induce drastic changes in the aqueous solubility of these species under high pressure conditions and moderate changes at as low as 5 GPa. Finally, some industrial and geochemical implications of this result are discussed.

Most of the work done on the linear response kernel χ(r,r') has focussed on its atom-atom condensed form χAB. Our previous work [Boisdenghien et al., J. Chem. Theory Comput., 2013, 9, 1007] was the first effort to truly focus on the non-condensed form of this function for closed (sub)shell atoms in a systematic fashion. In this work, we extend our method to the open shell case. To simplify the plotting of our results, we average our results to a symmetrical quantity χ(r,r'). This allows us to plot the linear response kernel for all elements up to and including argon and to investigate the periodicity throughout the first three rows in the periodic table and in the different representations of χ(r,r'). Within the context of Spin Polarized Conceptual Density Functional Theory, the first two-dimensional plots of spin polarized linear response functions are presented and commented on for some selected cases on the basis of the atomic ground state electronic configurations. Using the relation between the linear response kernel and the polarizability we compare the values of the polarizability tensor calculated using our method to high-level values.

We present the results of a theoretical investigation focusing on the solvent structure surrounding the -1, 0 and +1 charged species of F, Cl, Br and I halogen atoms and F2, Cl2, Br2 and I2 di-halogen molecules in a methanol solvent and its influence on the electronic structure of the solute molecules. Our results show a large stabilizing effect arising from the solute-solvent interactions. Well-formed first solvation shells are observed for all species, the structure of which is strongly influenced by the charge of the solute species. Detailed analysis reveals that coordination number, CN, solvent orientation, θ, and solute-solvent distance, d, are important structural characteristics which are coupled to changes in the electronic structure of the solute. We propose that the fundamental chemistry of any solute species is generally regulated by these solvent degrees of freedom.

The trans effect and trans influence were investigated and rationalized in the aminolysis, a typical nucleophilic substitution reaction, of trans-TPtCl2NH3 complexes (T = NH3, PH3, CO and C2H4) using energy decomposition analysis, both along the reaction paths and on the stationary points, and Natural Orbital for Chemical Valence analysis. In order to scrutinize the underlying principles and the origin of the kinetic trans effect, plausible structural constraints were introduced in the decomposition analysis, which allowed eliminating the distance dependence of the interaction energy components. It was established that the trans effect can be rationalized with the interaction of the TPtCl2 and NH3 fragments in the reactant state and TPtCl2 and (NH3)2 fragments in the transition state. It was evinced quantitatively that the σ-donor ability of T indeed controls the stability of the reactant, whereas in the case of π-acids, backdonation stabilizes the transition state, for which conceptually two mechanisms are available: intrinsic and induced π-backdonation. In the destabilization of the reactant and also in the labilization of the leaving group (trans influence) repulsion plays a more important role than orbital sharing effects, which are the cornerstones of the widely accepted interpretations of the trans influence, such as competition for donation or limitation of the donation of the leaving group by the trans ligand T. This repulsive interaction was rationalized both in terms of donated electron density and also in the molecular orbital framework. NOCV orbitals indeed clearly show that the σ-trans effect can be envisioned as a donation from the trans ligand not only to the metal but also to the σ* orbital of the metal-leaving group bond, which manifests as a repulsion between the metal and the leaving group.

We predict that electron attachment may be used with ESI-MS techniques to observe neutral Al metal aqua-oxo-hydroxo species and the complex polymerization and precipitation reactions in which they participate. Neutral aqueous metal species have, so far, been invisible to ESI-MS techniques.

Tuning the band gap of graphene nanoribbons by chemical edge functionalisation is a promising approach towards future electronic devices based on graphene. The band gap is closely related to the aromaticity distribution and therefore tailoring the aromaticity patterns is a rational way for controlling the band gap. In the present work, it is shown how the three distinct classes of aromaticity patterns already found for armchair graphene nanoribbons can be rationally tuned by chemical edge functionalisation to modify their electronic arrangement and band gap. The electronic structure and the aromaticity distribution are studied using DFT calculations and through a series of delocalisation and geometry analysis methods, like the six-centre index (SCI) and the mean bond length (MBL) geometry descriptor. Novel aromaticity patterns are found for fluorine and nitrogen functionalisation characterised as inverted incomplete-Clar, and broken-Kekulé classes, while oxygen and nitrogen functionalisation is found to cut and extend the aromatic system, respectively. All these different arrangements of aromatic rings along the structure of graphene nanoribbons are explained using Clar's sextet theory, and a mesomeric effect mechanism for fluorine and nitrogen. In all cases, the changes in the aromaticity patterns are related to changes in the band gap. The energy and stability of the different edge functionalised graphene nanoribbons are also studied. An overall picture of edge effects, aromaticity patterns, and band gap tuning is provided.

The chemical importance of the linear response kernel from conceptual Density Functional Theory (DFT) is investigated for some σ and π aromatic and anti-aromatic systems. The effect of the ring size is studied by looking at some well known aromatic and anti-aromatic molecules of different sizes, showing that the linear response is capable of correctly classifying and quantifying the aromaticity for five- to eight-membered aromatic and anti-aromatic molecules. The splitting of the linear response in σ and π contributions is introduced and its significance is illustrated using some σ-aromatic molecules. The linear response also correctly predicts the aromatic transition states of the Diels-Alder reaction and the acetylene trimerisation and shows the expected behavior along the reaction coordinate, proving that the method is accurate not only at the minimum of the potential energy surface, but also in non-equilibrium states. Finally, the reason for the close correlation between the linear response and the Para Delocalisation Index (PDI), found in previous and the present study, is proven mathematically. These results show the linear response to be a reliable DFT-index to probe the σ and π aromaticity or anti-aromaticity of a broad range of molecules.

Due to its unique mechanical properties, graphene can be applied for reinforcement in nanocomposites. We analyse the Young's modulus of graphene at the semi-empirical PM6 level of theory. The internal forces are calculated and the Young's modulus is predicted for a finite graphene sheet when external strain is applied on the system. These results are in a good agreement with theoretical and experimental results from the literature giving values of about 1 TPa for the Young's modulus. Stress-strain curves are computed for elongation up to 20%. In addition, the influence of the presence of a single vacancy, as well as for oxygenation of a vacancy, on the mechanical properties of graphene has been analysed. Our results indicate that when applying the deformation locally onto the system, higher local stress can be induced, as confirmed by Finite Element Analysis. Also, the presence of structural defects in the system will stiffen the system upon low strain, but reduces the elastic limit from more than 20% strain for pristine graphene to less than 10% strain when defects are present.

The design of molecules with optimal properties is an important challenge in chemistry because of the astronomically large number of possible stable structures that is accessible in chemical space. This obstacle can be overcome through inverse molecular design. In inverse design, one uses the computation of certain indices to design molecules with an optimal target property. In this study, for the first time, inverse design was used to optimize reactivity properties of molecules. Specifically, we optimized the acidity of substituted 2-naphthols, both in the ground and the excited state. Substituted 2-naphthols belong to the class of photoacids, showing enhanced acidity when excited from the singlet ground state to the first singlet excited state. The focus of this work is the ground state. As a measure of acidity, three different properties are optimized: the charge on the hydroxyl hydrogen atom of the acid, the charge on the negatively charged oxygen atom of the conjugate base and the energy difference between acid and conjugate base. Both the practical use of the methodology and the results for ground and excited states are discussed.

A quantitative analysis of the steric effect of aliphatic groups was carried out from first principles. An intuitive framework is proposed that allows the separation and straightforward interpretation of two contributors to the steric effect: steric strain and steric shielding (hindrance). When a sterically demanding group is introduced near a reactive center, deformation of its reactive zone will occur. By quantifying this deformation, a convincing correlation was established with Taft's steric parameters for groups of typical size, supporting the intuitive image of steric shielding; bulky groups slow down the reaction by limiting the accessibility of the reactive centre. On the other hand, the strong initial repulsion between the reactant and the substrate by means of the filled-filled orbital interaction results in the deformation of the substrate as well as a less stabilizing reaction zone, which are the manifestations of the steric strain. We thus conclude that both steric strain and steric hindrance can be derived from the Pauli repulsion evolving between the reactants in the course of the reaction.

We have investigated aqueous Al-dimer complexes using density functional theory methods (e.g. the B3LYP exchange-correlation functional and the 6-311++G(d,p) basis set). In these calculations interactions between the Al(3+) cations and the H(2)O or OH(-) coordinating ligands are considered explicitly while the second hydration shell and remaining solvent are treated as a continuum under the IEF-PCM formalism. The Al-dimer chemical reactivity is discussed by analysis of changes in geometry, electronic structure and Gibbs free energy of formation, relative to two independent Al(H(2)O) monomers, as a function of water and hydroxide coordination. Our results indicate that the mechanism of cooperativity, i.e. decreased Al-water bond stability with increasing OH(-) coordination and increased water ligand hydrolysis as complex CN decreases, is operating on the dimer species and that, therefore, a wide variety of dimer species are available. While the stability of these species is observed to be dependent on the number of water and hydroxide ligands, the hydroxide bridging structure (singly, doubly and triply bridged species are considered) does not appear to correlate with dimer stability. Interestingly, intra-molecular H-bonds (in the form of the well known H(3)O bridge as well as two bridging structures, H(4)O(2) and H(2)O, that have not, to our knowledge, been previously considered) are observed to influence dimer stability. The evaluation of the equilibrium mole fraction of the dimer species in equilibrium with the aqueous Al(3+) monomer species of our previous study displays the qualitatively correct trend of solution composition as pH increases, namely monomeric aqueous Al(3+) and Al(OH) complexes dominate at low and high pH, respectively, and all remaining monomer and dimer species exist at intermediate pH. Further refinement of our data set by eliminating dimer complexes with OH/Al ratios greater than 2.6 brings our predicted equilibrium mole fraction distributions into excellent agreement with experimental observations. The triply bridged dimer is observed in low amounts while the singly and doubly bridged dimers dominate our model system at pH = ∼4-7.

We continue a series of papers in which the chemical importance of the linear response kernel χ(r,r') of conceptual DFT is investigated. In previous contributions (J. Chem. Theory Comput. 2010, 6, 3671; J. Phys. Chem. Lett. 2010, 1, 1228; Chem. Phys. Lett. 2010, 498, 192), two computational methodologies were presented and it was observed that the linear response kernel could serve as a measure of electron delocalisation, discerning inductive, resonance and hyperconjugation effects. This study takes the analysis one step further, linking the linear response kernel to the concept of aromaticity. Based on a detailed analysis of a series of organic and inorganic (poly)cyclic molecules, we show that the atom-condensed linear response kernel discriminates between aromatic and non-aromatic systems. Moreover, a new quantitative measure of aromaticity, termed the para linear response (PLR) index, is introduced. Its definition was inspired by the recent work published around the para delocalisation index (PDI). Both indices are shown to correlate very well, which emphasises the linear response kernel's value in the theoretical description of aromaticity.

Despite recent advances in computing negative electron affinities using density-functional theory, it is an open issue as to whether it is appropriate to use negative electron affinities, instead of zero electron affinity, to compute the chemical hardness of atoms and molecules with metastable anions. We seek to answer this question using the accepted empirical rules linking the chemical hardness to the atomic size and the polarizability; we also propose a new correlation with the C6 London dispersion coefficient. For chemical reactivity in the gas phase, it seems to make no difference whether negative, or zero, electron affinities are used for systems with metastable anions. For reactions in solution the evidence that is presently available is insufficient to establish a preference. In addressing this issue, we noted that electron affinity data from which atomic chemical hardness values are computed are out of date; an update to Pearson's classic 1988 table [Inorg. Chem., 1988, 27, 734-740] is thus provided.

We have used a potential wall method to investigate the role of d orbitals in the a(2) singly-occupied molecular orbitals of (2)A(2) negative ion states of two molecular series: pyridine, phosphabenzene, arsabenzene, stibabenzene (C(5)H(5)X, X = {N, P, As, Sb}), and furan, thiophene, selenophene, tellurophene (C(4)H(4)X, X = {O, S, Se, Te}). Unlike for the lower lying doubly occupied orbitals, heteroatom d-carbon p in-phase (bonding) interactions in these a(2) orbitals are clearly identified and explain the 0.5 eV stabilization of the (2)A(2) radical anion state in those compounds where the heteroatoms have d orbitals in the valence shell, compared to compounds where d orbitals are missing in the valence shell of the heteroatoms. The performance of both the potential wall approach and the approximate expression of Tozer and De Proft for calculating negative electron affinities has been also investigated, through a comparison with results obtained using electron-transmission spectroscopy experiments.

This Perspective discusses the reduction of the electronic wave function via the second-order reduced density matrix to the electron density ρ(r), which is the key ingredient in density functional theory (DFT) as a basic carrier of information. Simplifying further, the 1-normalized density function turns out to contain essentially the same information as ρ(r) and is even of preferred use as an information carrier when discussing the periodic properties along Mendeleev's table where essentially the valence electrons are at stake. The Kullback-Leibler information deficiency turns out to be the most interesting choice to obtain information on the differences in ρ(r) or σ(r) between two systems. To put it otherwise: when looking for the construction of a functional F(AB) = F[ζ(A)(r),ζ(B)(r)] for extracting differences in information from an information carrier ζ(r) (i.e. ρ(r), σ(r)) for two systems A and B the Kullback-Leibler information measure ΔS is a particularly adequate choice. Examples are given, varying from atoms, to molecules and molecular interactions. Quantum similarity of atoms indicates that the shape function based KL information deficiency is the most appropriate tool to retrieve periodicity in the Periodic Table. The dissimilarity of enantiomers for which different information measures are presented at global and local (i.e. molecular and atomic) level leads to an extension of Mezey's holographic density theorem and shows numerical evidence that in a chiral molecule the whole molecule is pervaded by chirality. Finally Kullback-Leibler information profiles are discussed for intra- and intermolecular proton transfer reactions and a simple S(N)2 reaction indicating that the theoretical information profile can be used as a companion to the energy based Hammond postulate to discuss the early or late transition state character of a reaction. All in all this Perspective's answer is positive to the question of whether an even simpler carrier of information than the electron density function ρ(r) can be envisaged: the shape function, integrating to 1 by construction fulfils this role. On the other hand obtaining the information (or information difference) contained in one (or two) systems from ρ(r) or σ(r) can be most efficiently done by using information theory, the Kulback-Leibler information deficiency being at the moment (one of) the most advisable functionals.

Adiabatic energy differences ΔE(adiabatic) are computed at density functional theory (DFT) level for the oxidation half reaction of [M(CO)(n)L(6-n)] complexes (M = Ru(2+/3+), Os(2+/3+), Tc(2+/3+); L = CN(-), Cl(-), water, CH(3)CN, N(2) and CO). Linear trends in ΔE(adiabatic) with respect to the substitution number n(CO) support the hypothesis of additive ligand effects on the redox potential. The values of the slope of these linear regression curves are shown to be independent of metal type (Ru, Os and Tc) and can therefore act as a ligand specific parameter. Based on these parameters, a computed electrochemical series was constructed, which was in good agreement with Pickett's P(L), Lever E(L)(L) and CEP parameters. The linearity in ΔE(adiabatic) is also reflected in the structural properties such as the M-CO bond distances of [M(CO)(n)L(6-n)] complexes. An energy decomposition analysis of the bond between the metal fragment and ligand gave an additional insight into the ligand's bonding properties in terms of electrostatic and orbital contributions.

Besides chemical functionalisation, the use of surfactants can be applied to debundle and disperse carbon nanotubes before further application in polymer nanocomposites. In this work we present a theoretical analysis of the interaction between single-walled carbon nanotubes and sodium dodecyl sulfate as surfactant and/or polystyrene as polymer matrix using semi-empirical AM1 calculations. Results indicate that the use of short potassium sulfate-terminated polystyrene chains as an extra component can help to remove the surfactant from the nanotube surface within the matrix, resulting in improved electronic properties of the nanocomposite.

Although extensive theoretical and experimental research has been conducted on fluorinated fullerenes, little detailed information exists on their solubility in different solvents. However, this solubility is crucial for their processability and possible application. In this work, we predict the solubility of fluorinated C(60) in various polar and non-polar solvents, based on a correlation between experimentally measured solubilities for C(60) from the literature and theoretically predicted solubilisation energies. These solubilisation energies are predicted using the polarizable continuum model (PCM) at the ab initio Hartree-Fock 6-31+G* level of theory. In particular, the solubilities are predicted for C(60)F(2)(n) (n = 1-10) isomers, part of the addition route to saturnene C(60)F(20). An increasing solubility is found for more polar solvents with higher degree of fluorination. With these results, we can determine the minimal fluorination degree necessary for possible solubilisation in a given solvent, and offer new perspectives to separate and purify species with different degrees of fluorination.

When a molecule is placed as a guest inside a zeolite pore, its electronic structure will be altered, among others by the effect of the so-called "confinement". It has been established that the compression of the molecular orbitals influences a system's reactivity. In this work we use a simple potential barrier method to quantify the importance of confinement effects on chemical reactivity. In the first part, excitation energies and molecular orbital energy gaps are evaluated for molecules placed in cavities of different sizes, resembling a zeolite pore. Our results for ethylene and formaldehyde reveal an increase in excitation energy and the gap between the occupied and the unoccupied levels. In the case of the larger molecules naphthalene and anthracene, the HOMO-LUMO gap shows very little sensitivity to the confinement. To investigate the role of confinement effects on local aspects of chemical reactivity and on regioselectivity, we evaluated its effect on the Fukui function and the molecular electrostatic potential, reactivity indices that are central in the description of orbital and charge controlled reactions. The results indicate that confinement can influence the regioselectivity and that the reactivity of anions is expected to change, due to the artificial binding of the excess electron.

The Kullback-Leibler information deficiency is evaluated along molecular internal rotational or vibrational coordinates and along the intrinsic reaction coordinate for several reactions (intra- and intermolecular proton transfer and SN2 reaction). For the first time an in depth analysis of the information deficiency along the reaction path is reported. The results are consistent with the Hammond postulate, indicating that the information profiles contain relevant chemical information. A local version of the information deficiency is defined by considering Hirshfeld's partitioning of atoms in molecules. The analysis of the local information profiles permits the identification of the atoms taking part in the electron reorganization processes.

In recent years conceptual density functional theory offered a perspective for the interpretation/prediction of experimental/theoretical reactivity data on the basis of a series of response functions to perturbations in the number of electrons and/or external potential. This approach has enabled the sharp definition and computation, from first principles, of a series of well-known but sometimes vaguely defined chemical concepts such as electronegativity and hardness. In this contribution, a short overview of the shortcomings of the simplest, first order response functions is illustrated leading to a description of chemical bonding in a covalent interaction in terms of interacting atoms or groups, governed by electrostatics with the tendency to polarize bonds on the basis of electronegativity differences. The second order approach, well known until now, introduces the hardness/softness and Fukui function concepts related to polarizability and frontier MO theory, respectively. The introduction of polarizability/softness is also considered in a historical perspective in which polarizability was, with some exceptions, mainly put forward in non covalent interactions. A particular series of response functions, arising when the changes in the external potential are solely provoked by changes in nuclear configurations (the "R-analogues") are also systematically considered. The main part of the contribution is devoted to third order response functions which, at first sight, may be expected not to yield chemically significant information, as turns out to be for the hyperhardness. A counterexample is the dual descriptor and its R analogue, the initial hardness response, which turns out to yield a firm basis to regain the Woodward-Hoffmann rules for pericyclic reactions based on a density-only basis, i.e. without involving the phase, sign, symmetry of the wavefunction. Even the second order nonlinear response functions are shown possibly to bear interesting information, e.g. on the local and global polarizability. Its derivatives may govern the influence of charge on the polarizability, the R-analogues being the nuclear Fukui function and the quadratic and cubic force constants. Although some of the higher order derivatives may be difficult to evaluate a comparison with the energy expansion used in spectroscopy in terms of nuclear displacements, nuclear magnetic moments, electric and magnetic fields leads to the conjecture that, certainly cross terms may contain new, intricate information for understanding chemical reactivity.

Spatial confinement of atoms and molecules influences electronic structures, energy spectra, and chemical reactivity. A simple potential barrier approach involving a single parameter is used to study confinement in both atoms and molecules, focusing on the reactivity of the systems through the HOMO-LUMO gap, which is linked to the global chemical hardness. Both atoms and molecules are shown to respond with an increase in hardness when confined. The results suggest that previous observations of a HOMO-LUMO gap decrease for guest molecules in zeolites cannot be assigned exclusively to electron confinement.