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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.

Radicals can be regarded as electrophilic/nucleophilic, depending on their tendency to attack sites of relatively higher/lower electron density. In this paper, an electrophilicity scale, global as well as local, and a nucleophilicity scale for 35 radicals is reported. The global electrophilicity scale correlates well with the nucleophilicity scale, suggesting that these concepts are inversely related.

A benchmark theoretical study of the electronic ground state and of the vertical and adiabatic singlet-triplet ͑ST͒ excitation energies of benzene ͑n =1͒ and n-acenes ͑C 4n+2 H 2n+4 ͒ ranging from naphthalene ͑n =2͒ to heptacene ͑n =7͒ is presented, on the ground of single-and multireference calculations based on restricted or unrestricted zero-order wave functions. High-level and large scale treatments of electronic correlation in the ground state are found to be necessary for compensating giant but unphysical symmetry-breaking effects in unrestricted single-reference treatments. The composition of multiconfigurational wave functions, the topologies of natural orbitals in symmetry-unrestricted CASSCF calculations, the T1 diagnostics of coupled cluster theory, and further energy-based criteria demonstrate that all investigated systems exhibit a 1 A g singlet closed-shell electronic ground state. Singlet-triplet ͑S 0 -T 1 ͒ energy gaps can therefore be very accurately determined by applying the principles of a focal point analysis onto the results of a series of single-point and symmetry-restricted calculations employing correlation consistent cc-pVXZ basis sets ͑X=D, T, Q, 5͒ and single-reference methods ͓HF, MP2, MP3, MP4SDQ, CCSD, CCSD͑T͔͒ of improving quality. According to our best estimates, which amount to a dual extrapolation of energy differences to the level of coupled cluster theory including single, double, and perturbative estimates of connected triple excitations ͓CCSD͑T͔͒ in the limit of an asymptotically complete basis set ͑cc-pVϱZ͒, the S 0 -T 1 vertical excitation energies of benzene ͑n =1͒ and n-acenes ͑n =2-7͒ amount to 100.79, 76.28, 56.97, 40.69, 31.51, 22.96, and 18.16 kcal/mol, respectively. Values of 87.02, 62.87, 46.22, 32.23, 24.19, 16.79, and 12.56 kcal/mol are correspondingly obtained at the CCSD͑T͒ / cc-pVϱZ level for the S 0 -T 1 adiabatic excitation energies, upon including B3LYP/cc-PVTZ corrections for zero-point vibrational energies. In line with the absence of Peierls distortions, extrapolations of results indicate a vanishingly small S 0 -T 1 energy gap of 0 to ϳ4 kcal/ mol ͑ϳ0.17 eV͒ in the limit of an infinitely large polyacene.

The applicability of the electronegativity equalization method (EEM) is investigated for the fast calculation of atomic charges in organic chemistry, with an emphasis on medicinal chemistry. A large training set of molecules was composed, comprising H, C, N, O, and F, covering a wide range of medicinal chemistry. Geometries and atomic charges are calculated at the B3LYP/6-31G* level, and from the calculated charges, effective electronegativity and hardness values are calibrated in a weighted least-squares fashion. The optimized parameter set is compared to other theoretical as well as experimental values and origins of the differences discussed. An approach toward extension of EEM to include new atoms is introduced. The quality of the EEM charges is assessed by comparison with B3LYP/6-31G* charges calculated for a set of medicinal molecules, not contained in the training set. The EEM approach is found to be a very powerful way to obtain ab initio quality charges without the computational cost of the ab initio approach.

The Woodward-Hoffmann rules for pericyclic reactions are explained entirely in terms of directly observable physical properties of molecules (specifically changes in electron density) without any recourse to model-dependent concepts, such as orbitals and aromaticity. This results in a fundamental explanation of how the physics of molecular interactions gives rise to the chemistry of pericyclic reactions. This construction removes one of the key outstanding problems in the qualitative density-functional theory of chemical reactivity (the so-called conceptual DFT). One innovation in this paper is that the link between molecular-orbital theory and conceptual DFT is treated very explicitly, revealing how molecular-orbital theory can be used to provide "back-of-the-envelope" approximations to the reactivity indicators of conceptual DFT.

The absolute hardness in density functional theory (DFT) is discussed, emphasizing the charge-transfer excitation interpretation. Direct evaluation from the computed ionization potential and electron affinity is intrinsically problematic when the affinity is negative; the calculated affinity exhibits a strong basis set dependence, becoming near zero as diffuse functions are added. An alternative Koopmans-based approximation using local functional eigenvalues uniformly and significantly underestimates the hardness. A simple correction to the Koopmans expression is highlighted on the basis of a consideration of the integer discontinuity. The resulting hardness expression does not require the explicit computation of the affinity and has a straightforward interpretation in terms of the electronegativity. The correction eliminates the underestimation and gives hardness values that do not degrade as the electron affinity becomes more negative. For systems with large negative affinities, the values are an improvement over those from the other approaches. The success can be traced to an implicit, unconventional approximation for the electron affinity, which outperforms the standard approach when the affinity is significantly negative and which does not break down as the basis set becomes more diffuse.