RESUMO
The Wigner 9j symbols of the first kind-also known as Fano X-coefficients-serve to connect different addition schemes of four angular momenta, widely known examples being the LS and the jj couplings in atomic, molecular, and nuclear spectroscopies. Here, we also consider alternative sequences of binary couplings of four angular momenta, which are dealt through the 9j symbols of the second kind, and are explicitly given by the pentagonal (or Biedenharn-Elliott) identity. These coefficients are essential ingredients in the quantum-mechanical treatments of rotational and polarization phenomena in reaction dynamics and photoinduced processes. We also emphasize the combinatorial structure underlying the extended construction of a previously introduced truncated icosahedral "abacus", and provide extensions useful for algebraical manipulations, semiclassical interpretations, and computational applications, including all the 120 addition schemes.
RESUMO
The secondary interaction between a polarized chalcogen atom and different Lewis bases, either anionic or neutral, has been studied by charge displacement analysis. Using charge displacement analysis, the charge rearrangement in the adduct upon the formation of the interaction has been quantified and described in great detail. By comparing the theoretical results with the experimental association constants, two linear correlations can be found for anionic and neutral bases. Such correlations can be used to reliably predict the association constants of adducts for which experimental data are not available yet.