  We report first principles density functional calculations of the Born
effective charges and electronic dielectric tensors for the relaxor PMN
(PbMg1/3Nb2/3O3). Visualization of the Born charge tensors as charge ellipsoids
have provided microscopic insights on the factors governing piezoelectric
enhancements with polarization rotation. Several 15 and 30-atom ferroelectric
and antiferroelectric supercells of PMN involving 1:2 and 1:1 chemical ordering
have been studied. A cascading set of ferroelectric phonon instabilities lead
to several low symmetry monoclinic structures. We find a ground state with a
15-atom unit cell with 1:2 chemical ordering along [111] with a monoclinic C2
structure.
