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We show that substitutional alloying during the aqueous self-assembly of layered organic-templated metal oxides produces single-phase mixed-metal hybrids. Single-crystal X-ray diffraction, bulk elemental analyses, and vibrational and electronic spectroscopies corroborate a solid solution of Mo and W atoms at lattice sites within the two-dimensional metal oxide layers. Mild postsynthetic reduction then introduces relatively delocalized electrons to afford mixed-metal hybrid bronzes. To our knowledge, this represents the first demonstration of mixed-metal alloying in a hybrid metal oxide and a rare example of solid-solution formation at low temperature. We show this approach yields mixed-metal congeners with optical band gaps over 130 meV smaller than those of single-metal analogs, while achieving activation energies (Ea) of conduction as low as 78.4(2) meV. Further, metal substitution appears to tune collective electronic phenomena by suppressing the non-Arrhenius behavior observed for Mo-based hybrids. This work considerably expands the nascent hybrid bronze platform to help address energy-related challenges and fundamental solid-state physical questions. 

Pressure-induced intermolecular coupling in 4,4′-bipyridine occursviadistinct mechanisms—dehydrogenative dimerization and sp³-hybridized oligomerization—presenting design rules for novel phases. 

We introduce the space of virtual Markov chains (VMCs) as a projective limit of the spaces of all finite state space Markov chains (MCs), in the same way that the space of virtual permutations is the projective limit of the spaces of all permutations of finite sets.We introduce the notions of virtual initial distribution (VID) and a virtual transition matrix (VTM), and we show that the law of any VMC is uniquely characterized by a pair of a VID and VTM which have to satisfy a certain compatibility condition.Lastly, we study various properties of compact convex sets associated to the theory of VMCs, including that the Birkhoff-von Neumann theorem fails in the virtual setting.