Variational studies of two- and three-dimensionalD−centers in magnetic fields

Low-lying singlet states of the ${\mathit{D}}^{\mathrm{-}}$ center, a hydrogenic donor with a second electron attached, are studied for two-dimensional and bulk three-dimensional centers in uniform applied magnetic fields. Accurate trial functions which are, at the same time, simple, physically transparent, and computationally efficient are sought. Various candidate functions are compared. The best of these produce energies for the ground state which, in three dimensions, fall within the statistical uncertainties quoted for recent ‘‘exact’’ Monte Carlo calculations at all fields tested. The ${\mathit{D}}^{\mathrm{-}}$ ground state and lowest-lying singlet p-like excited state energies are calculated versus magnetic field for two-dimensional centers. Energies of optical transitions between these two states are found to lie above the ionization energy of the center for all magnetic-field strengths greater than zero.