Variational Theory of Paramagnetic Impurities in Van der Waals Crystals

A consistent method of calculating the wave functions and electron-spin-resonance properties of a dilute paramagnetic impurty in a molecular crystal is outlined, and the system of atomic hydrogen in solid argon is treated as a detailed example. Starting from a one-electron, tight-binding, static-lattice picture of the impurity-doped crystal, the crystal wave function is formed as the antisymmetrized product of atomic Hartree-Fock 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 interaction. The spin-resonance parameters are then found from the expectation value of the interaction with a magnetic field. The results lead to a reintepretation of parameters in previous theories and show that the various crystal perturbations do not add independently to give a net result when there is appreciable overlap between the impurity and host atoms. Estimates of the electronic $g$ factor for hydrogen in argon are in good agreement with experiment. The predicted hyperfine shifts for substitutional hydrogen impurities also agrees well. However, it is shown that for interstitial sites the hyperfine-shift calculations are unreliable.