The authors use a modified form of the Stillinger-Weber potential to obtain the binding energy and geometry of a number of Si ad-dimer structures on the fully relaxed Si(001) 2*1 surface by canonical Monte Carlo simulation. At low temperatures they show the possible existence of two kinds of 'defect' ad-dimers which may hinder normal 1*2 growth. The mechanisms for both diffusion and interconversion of such dimers are then elucidated by examining their associated minimum-energy paths.