New measurements are presented of the electric and magnetic hyperfine constants of the I and Cl nuclei for the A((3)Pi (1)) state of (ICl)-Cl-35, nu =16-27 and 33. This extends the existing set of measurements for the A state to cover most of the vibrational levels from nu =7 to the dissociation limit. These data are inverted to provide hyperfine constants as a function of internuclear distance. The constants are found to be strongly dependent on the internuclear distance. The changing values are modeled by a separated atom (or valence-bond) model of the wave function. This model contains only eight basis states, but successfully describes the observed changes in the hyperfine constants for internuclear separations ranging from 5.5 down to 2.9 Angstrom. The model also allows the rehybridization of the bond to be described quantitatively as a function of internuclear separation. Two interesting effects of vibration are observed; first, the orientation of the unoccupied p orbitals varies considerably over the range of nuclear motion. Second, the contribution to the wave function of spin-orbit excited atomic chlorine states changes dramatically around 3.5 Angstrom. As part of this analysis we present extensions to the current methods of estimating molecular hyperfine constants from atomic properties to allow a wider range of parameters to be covered. <(C)> 2000 American Institute of Physics.