A new theory is presented to explain the conductivity maxima of molten salts (versus temperature and pressure). In the new theory, conductivity is due to ions hopping from counterion to counterion, and its temperature dependence can be explained with an ordinary Arrhenius equation in which the frequency prefactor A (for hopping opportunities) and activation energy E(a) (for hopping) are density dependent. The conductivity maximum is due to competing effects: as density decreases, the frequency of opportunities for hopping increases, but the probability that an opportunity is successfully hopped decreases due to rising E(a) caused by the increased hopping distance. The theory is successfully applied to molten bismuth (III) chloride, and supported by density-functional based molecular dynamics simulations which not only reproduce the conductivity maximum, but disprove the long-standing conjecture that this liquid features an equilibrium between BiCl(3) molecules, and BiCl(2)(+) and BiCl(4)(-) ions that shifts to the left with increasing temperature.

Ab initio (coupled-cluster and density-functional) calculations of Gibbs reaction energies in solution, with new entropy-of-solvation damping terms, were performed for the ether-catalyzed hydroboration of alkenes. The goal was to test the accuracy of continuum-solvation models for reactions of neutral species in nonaqueous solvents, and the hope was to achieve an accuracy sufficient to address the mechanism in the "Pasto case": B2H6 + alkene in THF solvent. Brown's SN2/SN1 "dissociative" mechanism, of SN2 formation of borane-ether adducts followed by SN1 alkene attack, was at odds with Pasto's original SN2/SN2 hypothesis, and while Brown could prove his mechanism for a variety of cases, he could not perform the experimental test with THF adducts in THF solvent, where the higher THF concentrations might favor an SN2 second step. Two diboranes were tested: B2H6, used by Pasto, and (9BBN)2 (9BBN = 9-borabicyclo[3.3.1]nonane, C8H15B), used by Brown. The new entropy terms resulted in improved accuracy vs traditional techniques (∼2 kcal mol(-1)), but this accuracy was not sufficient to resolve the mechanism in the Pasto case.

The phenomenon of electrical conductivity maxima of molten salts versus temperature during orthobaric (closed-vessel) conditions is further examined via ab initio simulations. Previously, in a study of molten BiCl3, a new theory was offered in which the conductivity falloff at high temperatures is due not to traditional ion association, but to a rise in the activation energy for atomic ions hopping from counterion to counterion. Here this theory is further tested on two more inorganic melts which exhibit conductivity maxima: another high-conducting melt (SnCl2, σmax = 2.81 Ω(-1) cm(-1)) and a low-conducting one (HgBr2, σmax = 4.06 × 10(-4) Ω(-1) cm(-1)). First, ab initio molecular dynamics simulations were performed and again appear successful in reproducing the maxima for both these liquids. Second, analysis of the simulated liquid structure (radial distributions, species concentrations) was performed. In the HgBr2 case, a very molecular liquid like water, a clear Grotthuss chain of bromide transfers was observed in simulation when seeding the system with a HgBr(+) cation and HgBr3 (-) anion. The first conclusion is that the hopping mechanism offered for molten BiCl3 is simply the Grotthuss mechanism for conduction, applicable not just to H(+) ions, but also to halide ions in post-transition-metal halide melts. Second, it is conjectured that the conductivity maximum is due to rising activation energy in network-covalent (halide-bridging) melts (BiCl3, SnCl2, PbCl2), but possibly a falling Arrhenius prefactor (collision frequency) for molecular melts (HgBr2).

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The phenomenon of electrical conductivity maxima of molten salts versus temperature during orthobaric (closed-vessel) conditions is further examined. First, we summarize results from densityfunctional-based molecular dynamics simulations of molten SnCl 2 and HgBr 2 , which provided structural information but also succeeded in reproducing (i) previously published experimental conductivities to within an order of magnitude, and (ii) the conductivity maxima. The "hopping" mechanism we previously proposed is now termed a Grotthuss mechanism, which became quite clear in the simulations of the molecular liquid HgBr 2 which exhibited Grotthuss chains of bromide transfers. Second, we fit the experimental conductivities of 12 different molten salts with the equation