Small-sized aluminum clusters exhibit a possible spin competition at finite temperatures. For this reason, it is difficult to perform standard electronic structure investigations to determine the properties of the ground states of such clusters. In the particular case of Al6, a nonmagnetic ground state has been predicted at 0 K. However, singlet–triplet intercrossing could occur at laboratory temperatures, in agreement with Stern–Gerlach experiments. We have thus investigated, by means of nonadiabatic transition state theory, the possibility of such singlet–triplet spin competition. We determined the possible crossing points on the potential energy surface and then identified the most favorable minimum-energy crossing points. For these points, we evaluated the spin–orbit matrix elements, transition probabilities, and rate constants for the singlet–triplet equilibria at different temperatures using the Landau–Zener and weak-coupling formulas. The predicted equilibria at finite temperatures are consistent with previous ab initio molecular dynamics results. We point out the importance of such evaluations in determining the physical properties of these types of systems.
In metal–cumulene complexes, the metal easily slides through the double bonds of the chain. A series of late‐transition‐metal–[5]cumulene complexes has been studied by theoretical and experimental methods in order to understand the factors that control such haptotropic shifts. The bulkiness of the cumulene terminal groups plays a central role in the tautomeric preferences. The quantum theory of atoms in molecules and the electron localizability indicator show that the M–C bond closer to the terminal groups is significantly weakened by steric interactions between these groups and the rest of ligands around the metal center. The results emphasize that special attention should be paid to the orientation of both the bulky substituents at the cumulene and other voluminous ligands around the metal, because the orientation of such moieties is important in predicting the direction of the haptotropic equilibrium correctly.
We show the existence of a dynamic spin equilibrium introduced by intersystem crossing (ISC) between several spin multiplicity states in the Pt 13 cluster. Employing weak-coupling transition probabilities, nonadiabatic transition state theory, and density functional theory, we obtain rate constants for each spin transition and, from these results, we find the equilibrium populations as a function of temperature for each state. At very low temperatures, neither ground-state calculations nor Maxwell−Boltzmann distributions are able to reproduce the experimental magnetic moment of Pt 13 . The origin of such differences, as transition probabilities show, is attributed to tunneling and zero-point energy-assisted ISC, producing mixed spin vibronic states, and to the large orbital contribution to the magnetic moment confirmed by simulated X-ray magnetic circular dichroism. At low temperatures, these physical processes provide the transition mechanism, whereas as temperature increases, quantum effects are less important, and thermal hopping becomes the predominant path. These results reproduce the experimental magnetic moment found in Pt 13 and may explain the origin of anomalous magnetic properties on small metallic clusters.
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