Exchange spin coupling is usually evaluated in quantum chemistry from the energy difference between a high-spin determinant and a Broken-Symmetry (BS) determinant in combination with Kohn-Sham density functional theory (KS-DFT), based on the work of Noodleman. As an alternative, an efficient approximate approach relying on Green's functions has been developed by one of the authors. This approach stems from solid-state physics and has never been systematically tested for molecular systems. We rederive a version of the Green's-function approach originally suggested by Han, Ozaki, and Yu. This new derivation employs local projection operators as common in quantum chemistry for defining local properties such as partial charges, rather than using a dual basis as in the Han-Ozaki-Yu approach. The result is a simple postprocessing procedure for KS-DFT calculations, which in contrast to the BS energy-difference approach requires the electronic structure of only one spin state. We show for several representative small molecules, diradicals, and dinuclear transition metal complexes that this method gives qualitatively consistent results with the BS energy-difference approach as long as it is applied to high-spin determinants and as long as structural relaxation effects in different spin states do not play an important role.

Fully inorganic, colloidal gold nanoclusters (NCs) constitute a new class of nanomaterials that are clearly distinguishable from their commonly studied metal–organic ligand‐capped counterparts. As their synthesis by chemical methods is challenging, details about their optical properties remain widely unknown. In this work, laser fragmentation in liquids is performed to produce fully inorganic and size‐controlled colloidal gold NCs with monomodal particle size distributions and an fcc‐like structure. Results reveal that these NCs exhibit highly pronounced photoluminescence with quantum yields of 2%. The emission behavior of small (2–2.5 nm) and ultrasmall (<1 nm) NCs is significantly different and dominated by either core‐ or surface‐based emission states. It is further verified that emission intensities are a function of the surface charge density, which is easily controllable by the pH of the surrounding medium. This experimentally observed correlation between surface charge and photoluminescence emission intensity is confirmed by density functional theoretical simulations, demonstrating that fully inorganic NCs provide an appropriate material to bridge the gap between experimental and computational studies of NCs. The presented study deepens the understanding of electronic structures in fully inorganic colloidal gold NCs and how to systematically tune their optical properties via surface charge density and particle size.

Increasing interactions between spin centers in molecules and molecular materials is a desirable goal for applications such as single-molecule magnets for information storage or magnetic metal-organic frameworks for adsorptive separation and targeted drug delivery and release. To maximize these interactions, introducing unpaired spins on bridging ligands is a concept used in several areas where such interactions are otherwise quite weak, in particular, lanthanide-based molecular magnets and magnetic metal-organic frameworks. Here, we use Kohn-Sham density functional theory to study how much the ground spin state is stabilized relative to other low-lying spin states by creating an additional spin center on the bridge for a series of simple model compounds. The di- and triradical structures consist of nitronyl nitroxide (NNO) and semiquinone (SQ) radicals attached to a meta-phenylene(R) bridge (where R = -NH/-NH, -O/OH, -CH/CH). These model compounds are based on a fully characterized SQ-meta-phenylene-NNO diradical with moderately strong antiferromagnetic coupling. Replacing closed-shell substituents CH and NH with their radical counterparts CH and NH leads to an increase in stabilization of the ground state with respect to other low-lying spin states by a factor of 3-6, depending on the exchange-correlation functional. For OH compared with O substituents, no conclusions can be drawn as the spin state energetics depend strongly on the functional. This could provide a basis for constructing sensitive test systems for benchmarking theoretical methods for spin state energy splittings. Reassuringly, the stabilization found for a potentially synthesizable complex (up to a factor of 3.5) is in line with the simple model systems (where a stabilization of up to a factor of 6.2 was found). Absolute spin state energy splittings are considerably smaller for the potentially stable system than those for the model complexes, which points to a dependence on the spin delocalization from the radical substituent on the bridge.

Photoswitching is an intriguing way of incorporating functionality into molecules or their subunits. Dithienylethene switches are particularly promising, but have so far mostly been studied with five-membered ring (cyclopentenyl) backbones. We aim at comparing the switching properties of backbones with five and six carbon atoms in the ring. A major advantage is that cyclohexenyl rings offer new options for chiral functionalization. A slight change in the reaction conditions of a McMurry ring closure reaction leads to the formation of dithienyl derivatives with a cyclohexene backbone in reasonable yield. Density functional theory calculations were carried out, demonstrating the similarity of both compounds. Experimental results confirm the theoretical outcomes.