The discretized flow on domains of attraction: a structural stability result

It is well known that, for stepsize sufficiently small, compactattractors of ordinary differential equations persist underdiscretization. The present paper describes the structure ofthe discrete-time dynamical system obtained via discretizationon A(M_h)\M_h where M_h is the approximate attractor and A(M_h)is its domain of attraction. The existence of a smooth embeddinginto a continuous-time parallelizable flow is proved. The constructioncan be used to define sections for discretizations and can beinterpreted as a justification of the method of modified equations.     

The Golden Pathway to Thiolate-Stabilized Nanoparticles: Following the Formation of Gold(I) Thiolate from Gold(III) Chloride

Pathways for the formation of gold thiolate complexes from gold(III) chloride precursors AuCl(4)(-) and AuCl(3) are examined. This work demonstrates that two distinct reaction pathways are possible; which pathway is accessible in a given reaction may depend on factors such as the residue group R on the incoming thiol. Density functional theory calculations using the BP86 functional and a polarized triple-ζ basis set show that the pathway resulting in gold(III) reduction is favored for R = methyl. A two-to-one ratio of thiol or thiolate to gold can reduce Au(III) to Au(I), and a three-to-one ratio can lead to polymeric Au(SR) species, which was first suggested by Schaaff et al. J. Phys. Chem. B, 1997, 101, 7885 and later confirmed by Goulet and Lennox J. Am. Chem. Soc., 2010, 132, 9582. Most transition states in the pathways examined here have reasonable barrier heights around 0.3 eV; we find two barrier heights that differ substantially from this which suggest the potential for kinetic control in the first step of thiolate-protected gold nanoparticle growth.     

Incremental binding energies of gold(I) and silver(I) thiolate clusters

Density functional theory is used to find incremental fragmentation energy, overall dissociation energy, and average monomer fragmentation energy of cyclic gold(I) thiolate clusters and anionic chain structures of gold(I) and silver(I) thiolate clusters as a measure of the relative stability of these systems. Two different functionals, BP86 and PBE, and two different basis sets, TZP and QZ4P, are employed. Anionic chains are examined with various residue groups including hydrogen, methyl, and phenyl. Hydrogen and methyl are shown to have approximately the same binding energy, which is higher than phenyl. Gold-thiolate clusters are bound more strongly than corresponding silver clusters. Lastly, binding energies are also calculated for pure Au(25)(SR)(18)(-), Ag(25)(SR)(18)(-), and mixed Au(13)(Ag(2)(SH)(3))(6)(-) and Ag(13)(Au(2)(SH)(3))(6)(-) nanoparticles.