Thef-felectronic spectra of aD4coordination compound [Eu(III)(2,2′-bipyridine-N,N′-dioxide)4]3+and ofD3analogues indicate, on comparison, that only the ΔMJ= ±1 component of the quadrupolar Eu(III)7F0→5D2transition is active in theD4case. The intensity of a quadrupolar metal-ion transition in aD4complex is governed uniquely by a single rank-2 environmental ligand tensor, within the restriction to one-electron operators, and it generates a first order electric dipole moment solely for the ΔMJ= ± 1 transition component. A rank-2 ligand tensor cannot arise from a configurational interaction mechanism based upon a static point-charge or dipolar crystal field, nor from the dynamic ligand-polarization mechanism in the mean polarizability approximation. The extension of the latter mechanism to include the polarizability anisotropy of the ligand bonds gives a rank-2 ligand polarization field tensorF(2)0which accounts for the7F0→5D2dipole strength of theD4complex investigated.