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Title: Some problems in the electronic structure of molecules
Author: Eisenberg, David S.
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 1964
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The greater part of this thesis is concerned with intermolecular forces in ice and some associated physical properties. Chapter I: The Dipole Moment of an Ice Molecule The average induced electric dipole moment of an ice molecule is computed. The charge distribution of an ice molecule is represented by a multipole expansion. The value of the dipole moment used in the expansion is taken from experimental measurements on water vapour, and the values of the quadrupole and octupole moments are taken from calculations on wave functions. The electric field strength of an arbitrary central molecule arising from neighbouring molecules is computed from a knowledge of the structure of ice, and the multipole expansions of the charge distributions of the neighbours. This has necessitated the development of a method for finding the probable orientation of each neighbouring molecule with respect to the fixed central molecule. The nearest 121 neighbours to the central molecule have been considered. From this electric field strength, and the value of the polarizability of ice, the dipole moment of an ice molecule is calculated. It is found to be 2.59 10-18 esu cm, a considerable increase over the dipole moment of water vapour, 1.84 10-18 esu cm. Chapter II: The Relation of Physical Quantities to the Dipole Moment of an Ice Molecule. The value of the dipole moment of an ice molecule calculated in Chapter I is related to the coulombic contribution to the energy of sublimation of ice, the dielectric constant of single crystals of ice, and the high frequency dielectric constant of ice. Treating the coulombic contribution to the energy of sublimation as the interaction of the multipole moments of the ice molecules, it is shown that neglect of the induced moments will result in an underestimate of this contribution by at least 1.8 kcal/mole of ice. Frohlich's theory of dielectrics is used to compute the dielectric constants parallel and perpendicular to the direction of the c-axis of a single ice crystal. Approximate methods are used to evaluate the expressions, and the calculated values are roughly 10% above the observed values. However, the calculated anisotropy of the dielectric constant at 0°C. agrees favourably with the experimental value. An expression is derived for the difference of the high frequency dielectric constant and the optical refractive index of ice. This difference is proportional to the square of the dipole moment of an ice molecule, inversely proportional to the force constant which describes the twisting of an ice molecule in an electric field, and independent of temperature. The expression is evaluated approximately using experimental force constants, and is found to give a value of the difference which is too small, but of the same order of magnitude as the observed value. Chapter III: Energy of Formation of Orientational Defects in Ice. Previous calculations of the energy of formation of orientational defects in ice are critically discussed. The energy of formation of Bjerrum's D-defect is calculated, assuming that bond-lengths and bond-angles in the region of the defect may be deformed. It is found that these deformations reduce the energy of formation of the D-defect from 60 to about 5 kcal/mole.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available