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Carbon-centered radicals and diradicaloids based on classical N-heterocyclic carbene (NHC) scaffolds are readily accessible as crystalline solids. The presence of an aryl (Ar) substituent at the C2-position is the key to the remarkable stability of these open-shell species as it provides appropriate room for the spin-density delocalization. Two catalytic as well as high-yielding protocols have been developed to install a suitable aryl group at the C2-position of NHCs. The spin-density in mono-radicals (NHCAr)• is mostly located on the parent carbene carbon (C2) atom. The bridging of two NHCs through a phenylene spacer (C6H4) n enables the isolation of various p-quinodimethane (p-QDM) derivatives, which may be considered as open-shell Kekulé diradicaloids. The diradical character of these NHC-analogues of Thiele (n = 1), Chichibabin (n = 2), and Müller (n = 3) hydrocarbons [(NHC)(C6H4) n (NHC)] can be tuned by a rational choice of the size and/or the topology of spacers. In this account, the synthesis, structure, and properties of this new class of radical hydrocarbons is presented.1 Introduction2 NHC-Monoradicals3 NHC-Diradicaloids4 Conclusion

Summary Donor-acceptor (DA) conjugated polymers (CPs) with narrow bandgaps and open-shell (diradical) character represent an emerging class of materials whose rich behavior emanates from their collective electronic properties and diminished electron pairing. However, the structural and electronic heterogeneities that define these materials complicate bandgap control at low energies and connections linking topology, exchange interactions, and (opto)electronic functionality remain nascent. To address these challenges, we demonstrate structurally rigid and strongly π-conjugated copolymers comprised of a solubilizing thiadiazoloquinoxaline acceptor and cyclopenta[2,1-b:3,4-b′]dithiophene or dithieno[3,2-b:2′,3′-d]thiophene donors. Atom-specific substitution modulates local aromatic character within the donor resulting in dramatic differences in structural, physicochemical, electronic, and magnetic properties of the polymers. These long-range π-mediated interactions facilitate control between low-spin aromatic and high-spin quinoidal forms. This work provides a strategy to understand the evolution of the electronic structure within DA CPs, control the ground state spin multiplicity, tune spin-spin interactions, and articulate the emergence of their novel properties.

We develop a novel method for the calculation and the analysis of the one-electron reduced densities in open-shell molecular systems using the natural orbitals and approximate spin projected occupation numbers obtained from broken symmetry (BS), i.e., spin-unrestricted (U), density functional theory (DFT) calculations. The performance of this approximate spin projection (ASP) scheme is examined for the diradical character dependence of the second hyperpolarizability (γ) using several exchange-correlation functionals, i.e., hybrid and long-range corrected UDFT schemes. It is found that the ASP-LC-UBLYP method with a range separating parameter μ = 0.47 reproduces semi-quantitatively the strongly-correlated [UCCSD(T)] result for p-quinodimethane, i.e., the γ variation as a function of the diradical character.

Using the coupled-cluster method with single and double excitations (CCSD), we investigate the relationship between the second hyperpolarizability (γ) and the diradical characters of dσ, dπ and dδ orbitals for the open-shell singlet Cr(II)-Cr(II) quadruply bonded model system, in which d 4 -d 4 interactions make one dσ, two equivalent dπ and one dδ molecular orbitals, and then these orbitals exhibit different diradical characters. The γ value is divided into the contributions of natural orbitals in order to reveal the contributions of dσ, dπ and dδ orbitals to γ. From these results, we elucidate a relationship among the orbital symmetry, diradical character and γ value, and thus we propose a guiding principle for designing open-shell singlet metal-metal multiply bonded complexes with highly efficient third-order nonlinear optical properties.