On the role of non-equilibrium focal points as coordination devices

Considering a pure coordination game with a large number of equivalentequilibria, we argue, first, that a focal point that is itself not a Nash equilibriumand is Pareto dominated by all Nash equilibria, may attract the players'choices. Second, we argue that such a non-equilibrium focal point may act asan equilibrium selection device that the players use to coordinate on a closelyrelated small subset of Nash equilibria. We present theoretical as well asexperimental support for these two new roles of focal points as coordinationdevices.

A first-principles analysis of the magnetism of CuII polynuclear coordination complexes: the case of [Cu4(bpy)4(aspartate)2(H2O)3](ClO4)4·2.5H2O

The magnetic structure of the [Cu4(bpy)4(aspartate)2(H2O)3](ClO4)4·2.5 H2Ocrystal - using fractional coordinates determined at room-temperature ¿ has beenanalysed in detail. This analysis has been carried out by extending our first principlesbottom-up theoretical approach, which was initially designed to study through-spacemagnetic interactions, to handle through-bond magnetic interactions. The only input datarequired by this approach are the values of the computed JAB exchange parameters for allthe unique pairs of spin-containing centres. The results allow the magnetic structure ofthe crystal, which presents two types of isolated tetranuclear CuII clusters, to be definedin quantitative terms. Each of these clusters presents ferro and antiferromagneticinteractions, the former being stronger, although outnumbered by the latter. Thecomputed magnetic susceptibility curve shows the same qualitative features as theexperimental data. However, there are small differences that are presumed to beassociated with the use of room-temperature crystal coordinates.

A first-principles analysis of the magnetism of CuII polynuclear coordination complexes: the case of [Cu4(bpy)4(aspartate)2(H2O)3](ClO4)4·2.5H2O

The magnetic structure of the [Cu4(bpy)4(aspartate)2(H2O)3](ClO4)4·2.5 H2Ocrystal - using fractional coordinates determined at room-temperature ¿ has beenanalysed in detail. This analysis has been carried out by extending our first principlesbottom-up theoretical approach, which was initially designed to study through-spacemagnetic interactions, to handle through-bond magnetic interactions. The only input datarequired by this approach are the values of the computed JAB exchange parameters for allthe unique pairs of spin-containing centres. The results allow the magnetic structure ofthe crystal, which presents two types of isolated tetranuclear CuII clusters, to be definedin quantitative terms. Each of these clusters presents ferro and antiferromagneticinteractions, the former being stronger, although outnumbered by the latter. Thecomputed magnetic susceptibility curve shows the same qualitative features as theexperimental data. However, there are small differences that are presumed to beassociated with the use of room-temperature crystal coordinates.