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You are correct in noting that there are a number of Au (II) small molecule species synthesized prior to the report of Professor Katja Heinze in 2017. The heart of the Au (II) claim by Professor Katja Heinze and team as stated in the article you referenced, see reference 1 given below, has to do with the a) relative stability of the mono-nuclear gold-...

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The rate of an $S_N1$ reaction may be increased by increasing the polarity of the solvent of reaction. Because, the more polar a solvent (as measured by the dielectric constant / relative permitivity, the easier to separate ions from each other; here: carbocation and its counter anion. Contrary to polar-aprotic solvents (think DMF, DMSO) eventually leading ...

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Depending on the constraints you impose on the system, there are different criteria for spontaneity, however, the commonly running theme is that it is related to minimizing some state function. For example, as a simple example from classical mechanics, the time evolution of the system is such that the potential energy of the mechanical bodies is minimized. ...

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Elements with just 1 or 2 electrons in the most outer $\ce{s}$ orbitals, like $\ce{K}$ or $\ce{Ca}$, have very well screened off the central charge of the kernel. As consequence, the effective charge of the kernel and related energy needed to ionize the atom are relatively low. OTOH, elements with just few missing electrons in the most outer $\ce{p}$ orbital,...

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