A variational theory of paramagnetic impurities in Van der Waals crystals

Thesis (Ph.D.)--University of Rochester. College of Engineering and Applied Science. Institute of Optics, 1962.In this investigation an attempt has been made to develop a consistent method of calculating the wave function of an impurity center in a molecular crystal and from this to predict its observable electron spin resonance properties. Specifically the theory has been applied to the system of atomic hydrogen in solid argon. Starting from the one-electron, tight-binding, static-lattice picture of the impurity-doped crystal, an orthonormal set of one-electron functions for the crystal is formed by making a unitary transformation on the Hartree-Fock free atomic wave functions. The wave function for the crystal is then formed as the antisymmetrized product of these starting functions. This is modified for the interactions in the crystal by adding variational corrections for crystal field effects, the spin-orbit interaction and the Van der Waals or electron correlation effect. The variational parameters necessary for the specification of the impurity's properties are determined by minimization of the crystal energy. The spin resonance parameters may then be calculated in terms of the free atomic wave functions and the variational functions. The results show that the g-shift is the most easily calculated quantity for a paramagnetic center in a molecular crystal. It arises from the overlap of an electron centered on the impurity with atoms of the host crystal in which there is a spin-orbit interaction. The shift in the g factor is always negative. The hyperfine splitting is altered by three things: the overlap, the crystal field and the Van der Waals interaction. Generally, the overlap leads to an increase in the hyperfine splitting while the crystal field and the Van der Waals interaction tend to reduce it. At large internuclear separations the latter effects dominate giving negative shifts while at small internuclear separations the former effect dominates and leads to positive shifts. It is found that provided there is no overlap, it is a good approximation to calculate the various effects of the crystal environment on the impurity center and then add to find the net effect. However, this procedure is not justified if there is appreciable overlap. In this case, the effect of intra-atomic potentials and interatomic exchange matrix elements must be taken into account