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

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 halolactonization reaction is one of the most common electrophilic addition reactions to alkenes. The mechanism is generally viewed as a two-step pathway, which involves the formation of an ionic intermediate, in most cases a haliranium ion. Recently, an alternative concerted mechanism was proposed, in which the nucleophile of the reaction played a key role in the rate determining step by forming a pre-polarized complex with the alkene. This pathway was coined the nucleophile-assisted alkene activation (NAAA) mechanism. Metadynamics simulations on a series of model halolactonization reactions were used to obtain the full dynamic trajectory from reactant to product and investigate the explicit role of the halogen source and solvent molecules in the mechanism. The results in this work ratify the occasional preference of a concerted mechanism over the classic two-step transformation under specific reaction conditions. Nevertheless, as the stability of both the generated substrate cation and counter-anion increase, a transition towards the classic two-step mechanism was observed. NCI analyses on the transition states revealed that the activating role of the nucleophile is independent of the formation and stability of the intermediate. Additionally, the dynamic insights obtained from the metadynamics simulations and NCI analyses employed in this work, unveiled the presence of syn -directing noncovalent interactions, such as hydrogen bonding, between the alkenoic acid and the halogen source, which rationalized the experimentally observed diastereoselectivities. Explicit noncovalent interactions between the reactants and a protic solvent or basic additive are able to disrupt these syn -directing noncovalent interactions, affecting the diastereoselective outcome of the reaction., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

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.)

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 .