An implementation of coupled Hartree-Fock theory for static quadrupola
r perturbations is used to calculate the quadrupole polarizability C a
nd mixed dipole-quadrupole hyperpolarizability B for anions in crystal
s. The ions studied are F- in LiF and NaF, O2- in MgO, S2- in MgS, H-
in LiH, and C4- in Be2C. In-crystal compression produces a more than f
ourfold reduction in C(F-) to 9.7 a.u. in LiF and 11.6 a.u. in NaF, an
d nominally infinite reductions for O2- and S2-. Low anisotropies DELT
AC indicate retention of approximate spherical symmetry for all but C4
-. The hyperpolarizability B shows similar reductions. Implications fo
r quadrupolar shell models of Cauchy violation are discussed.