Bond Fukui functions and matrices are introduced for ab initio levels of theory using a Mulliken atoms in molecules model. It is shown how these indices may be obtained from first-order density matrix derivatives without need for going to second-order density matrices as in a previous work. The importance of taking into account the nonorthogonality of the basis in ab initio calculations is shown, contrasting the present results with previous work based on Hückel theory. It is shown how the extension of Fukui functions to Fukui matrices allows getting more insight into the nature of bond Fukui functions. All presently introduced indices respect the necessary normalization conditions and include the classical single atom condensed Fukui functions. © 2013 Wiley Periodicals, Inc.