An improved algorithm has been designed to characterize ligand interactions in organometallic and coordination complexes in terms of the percentage of the metal coordination sphere shielded by a given ligand. The computations for ligand solid angles are performed numerically and employ introduced atomic radii that are larger than covalent but smaller than van der Waals radii. This approach enables facile evaluation of steric congestion in the metal coordination sphere, quantification of unfavorable interligand contacts, and in some cases prediction of the complex composition or ligand coordination on purely geometrical grounds.
A new method is described for the accurate measurement of quadrupole coupling parameters in liquids. Both experimental and theoretical data are given and show that for the OD deuteron in methanol the deuterium quadrupole coupling parameter xD is related to the deuterium chemical shift hD by the equation xD = 284 -15.36D; the R2 value for this correlation is 0.99. The straightforward measurement of 6D provides an accurate value for xD which in turn provides a value for the molecular correlation time. This methodology is applied to the measurement of the methanol correlation times as a function of concentration for the methanol/ CC14 system. The molecular correlation time along with a value for the solution viscosity provide an estimate of the average size for the methanol clusters present in the solution. The data reported here indicate that the average volume for the methanol clusters present in neat methanol is about 230 A', a value about midway between the volume for a cyclic pentamer (215 .k3) and a cyclic hexamer (242A').
The recently developed quantum cluster equilibrium (QCE) theory is used at the B3LYP/6-31+G* level of hybrid density functional theory to calculate the equilibrium cluster populations for formic acid vapor, whose quantitative cluster composition was determined by Coolidge and others through precise spectroscopic and vapor-density measurements over a wide range of temperature and pressure. Unlike previous experimental tests of QCE theory in which T,P-dependent cluster polpulations enter only indirectly (e.g., through convolutions with calculated cluster spectroscopic properties, yielding comparison with inhomogeneously braodened “average” spectral features), the present comparison is able to directly test the QCE population distributions. Nearly exact agreement between theory and experiment is found over the entire span of measurements, confirming that QCE theory satisfactorily predicts the T,P-dependent concentrations of individual cluster species, as well as the cruder population-weighted averages that enter less-sensitive comparisons with experiment.
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