Polyatomic London Dispersion Forces and NMR Gas to Liquid Chemical Shifts

Abstract

One of the most recent attempts to characterize inter-molecular dispersion forces is due to Homer and Percival, who used a modified Onsager-type reaction field approach coupled with the "buffeting" theory which accounts for the intimate effects of molecular encounters. In this thesis their overall approach is evaluated and compared with the theories of other workers that have been used to characterize NMR gas-to-solution chemical shifts. It is shown that an extended "buffeting" concept, based on their approach, renders the reaction field part of their theorem obsolete. A completely novel generalized expression for London dispersion forces is deduced by accounting for all the inter-molecular atom-atom dispersion interactions. In arriving at this expression three fundamental problems are resolved. First, a general order relationship between the mean squares of the fluctuating input and output of any system is derived to permit transformation of electrostatic expressions to electrodynamic situations. Second, a novel method is presented for characterizing the ionization potentials and polarizabilities of bonded atoms in terms of the corresponding properties of the appropriate inert atoms. Third, the average of the inverse-sixth-power of the inter-molecular atomic separation that governs dispersion forces is evaluated for molecules that are subject to random thermal motion in the liquid state; the explicit analytical expression so obtained is confirmed by the MONTE CARLO technique. The principles implicit in resolving the three stated problems are embodied in a theorem that enables the characterization of polyatomic inter-molecular mean-square fluctuating fields and the corresponding potential energies. The resulting equations are tested exhaustively and shown to enable the precise characterizations of NMR gas-to-solution shifts and latent heats of vaporization. Moreover, the equations are used to explain the relative solubilities of various gases in selected solvents and the corresponding activity coefficients. The limitations of the general approach to slowly rotating large molecules are recognized and evidence is given for the fact that for this type of molecules the inter-molecular potentials can be calculated using a simple solute~(solvent) atom additivity principle.