Electronic structure calculations on eight alkali fluorides and chlorides are performed in which the first shell of cations about a central anion is distorted and induced anion dipole and quadrupole moments are obtained. The charge-density overlap model used is validated against previous full-cluster calculations of distortion-induced moments and overall gives the same physical account of these properties for small anions and cations. Its use allows the calculations to be extended to RbF and RbCl. The overlap model mimics the full-cluster description of short-range damping of the multipole moments, and the induced moments are used to fit a simple model of the short-range interactions. Fitted parameter sets are shown to transfer between systems in a physically transparent manner.