  We use atomistic tight-binding theory with a configuration interaction
description of Coulomb and exchange effects to describe excitons in symmetric
quantum dots in a vertical electric field. We show that field-induced
manipulation of exciton orientation and phase produces a drastic reduction of
fine structure splitting, an anticrossing, and a 90 degree rotation of
polarization, similar to experiment. An atomistic analysis is needed to explain
how exciton reorientation modifies anisotropic exchange and fine structure
splitting without significantly altering other splittings.
