The "invisible" 13C NMR chemical shift of the central carbon atom in [(Ph3PAu)6C]2+: a theoretical investigation

The experimental 13C NMR chemical shift of the central carbon atom in the octahedral [(Ph3PAu)6C]2+ cluster was investigated on the basis of relativistic density functional calculations. In order to arrive at independent model conclusions regarding the value of the chemical shift, a systematic study of the dependence of the cluster structure on the phosphine ligands, the chosen density functionals, and the basis set size was conducted. The best structures obtained were then used in the NMR calculations. Because of the cage-like cluster structure a pronounced deshielding of the central carbon nucleus could have been expected. However, upon comparison with the 13C NMR properties of the related complex [C{Au[P(C6H5)2(p-C6H4NMe2)]}6]2+, Schmidbaur et al. have assigned a signal at delta=135.2 ppm to the interstitial carbon atom. Our calculations confirm this value in the region of the aromatic carbon atoms of the triphenylphosphine ligands. The close-lying signals of the 108 phenyl carbon atoms can explain the difficulties of assigning them experimentally.     

Critical scaling for monodromy fields

The large scale asymptotics of the correlations for a family of two dimensional lattice field theories is calculated at the critical temperature.     

Potentiometric measurements of the first hydrolysis quotient of magnesium(II) to 250°C and 5 molal ionic strength (NaCl)

The first molal hydrolysis quotient, Q_1.1, of Mg²⁺ was measured potentiometrically from 1 to 250°C at ionic strengths of 0.11, 0.31, 1.01, and 5.0 mol-kg^-1 in an aqueous NaCl medium using a hydrogen-electrode, concentration cell. Only hydrolysis of the first four percent of the magnesium in solution could be followed before precipitation of brucite, Mg(OH)₂(cr), occurred. The log Q_1.1 values were fitted as a function of temperature and ionic strength using four adjustable parameters. The resulting constants are compared with the limited existing low temperature data. At infinite dilution and 25°C the following quantities are reported: logK _1.1 = -11.68±0.05, †H_so = 70.1±1.2 kJ-mol^-1, †S^o = 11±4 J-K^-1-mol^-1, and †C _p ^o = 0 J-K^-1-mor^-1. At each ionic strength, including the values extrapolated to infinite dilution, the heat capacity change for the hydrolysis reaction was zero,i.e., logQ _1.1 was found to be a linear function of the reciprocal temperature in Kelvin, at least over the measured range of l-250°C. The hydrolysis constants at infinite dilution were modeled to 550°C and two kbar pressure with a function incorporating solvent density using published results obtained at these extreme conditions.