The solvation of Mg2+ with gas-phase clusters composed of alcohol molecules

The dication Mg2+ has been clustered with a range of different alcohols to form [Mg(ROH)N]2+ complexes, where N lies in the range 2-10. Observations on the chemistry of the complexes reveal two separate patterns of behavior: (i) unimolecular metastable decay, where at small values of N the complexes undergo rapid charge separation via Coulomb explosion; and (ii) electron capture-induced decay, where collisional activation promotes bond-breaking processes via charge reduction. For the latter it has been possible to identify a generic set of reactions that are common to all of the different [Mg(ROH)N]2+ complexes; however, there are examples of reactions that are specific to individual alcohols and values of N. For metastable decay, it is shown that there is a clear correlation between the value of N at which a complex ceases to be metastable and the ionization energy of R, the radical that forms the complementary ion in the Coulomb explosion step. Metastable decay in two of the [Mg(ROH)N]2+ complexes follows a very different pathway that eventually results in proton abstraction. It is suggested that this difference is due to the precursor complexes adopting geometries that have at least one ROH molecule in a secondary solvation shell.     

Stable [Pb(ROH)(N)](2+) complexes in the gas phase: softening the base to match the Lewis acid

Experiments have been performed in the gas phase to investigate the stability of complexes of the general form [Pb(ROH)(N)](2+). With water as a solvent, there is no evidence of [Pb(H(2)O)(N)](2+); instead [PbOH(H(2)O)(N-1)](+) is observed, where lead is considered to be held formally in a +2 oxidation state by the formation of a hydroxide core. As the polarizability of the solvating ligands is increased through the use of straight chain alcohols, ROH, solvation of Pb(2+) is observed without proton transfer when R >or= CH(3)CH(2)CH(2)-. The relative stabilities of [Pb(ROH)(4)](2+) complexes with respect to proton transfer are further investigated through the application of density functional theory to examples where R = H, methyl, ethyl, and 1-propyl. Of three trial structures examined for [Pb(ROH)(4)](2+) complexes, in all cases those with the lowest energy comprised of three solvent molecules were directly bound to the central cation, with the fourth molecule held in a secondary shell by hydrogen bonds. The implications of this arrangement as a favorable starting structure for proton transfer are discussed. Conditions for the stability of particular Pb(II)/ligand combinations are also discussed in terms of the hard-soft acid-base principle. Charge population densities calculated for the central lead cation and oxygen donor atoms across the ROH range are used to support the proposal that proton transfer occurs when a ligand is hard. Stability of the [Pb(ROH)(4)](2+) unit is commensurate with a decrease in the ionic character of the bond between Pb(2+) and a ligand; this in turn reflects a softening of the ligand as the alkyl chain increases in length. From the calculations, the most favorable protonated product is, in all cases, (ROH)(2)H(+). The trends observed with lead are compared with Cu(II), which is capable of forming stable gas-phase complexes with water and all of the alcohols considered here.     

NONCOOPERATIVE MANAGEMENT OF THE NORTHEAST ATLANTIC COD FISHERY: A FIRST MOVER ADVANTAGE

The point of departure for this analysis is Bjørndal and Lindroos [2012], who developed an empirical bioeconomic model to analyze cooperative and noncooperative management of Northeast Atlantic cod. In their analysis, only constant strategies were analyzed for noncooperative games. In this paper, nonconstant strategies are considered. Moreover, the fishery in question is characterized by cooperative management. What may happen in the real world is that one nation breaks the cooperative agreement by fishing in excess of its quota. Often, it takes time for the other agent to detect this and respond. In this paper, we allow this kind of delayed response into a two‐agent noncooperative game so that, if country 2 exceeds its quota, there will be a time lag before this is detected by country 1; moreover, there may also be a delay until country 1 is able to respond. Results show that the outcome critically depends on the length of these two lags as well as initial conditions.