The detailed mechanism of DNA hydrolysis by enzymes is of significant current interest. One of the most important questions in this respect is the catalytic role of metal ions such as Mg2+. While it is clear that divalent ions play a major role in DNA hydrolysis, it is uncertain what function such cations have in hydrolysis and why two are needed in some cases and only one in others. Experimental evaluation of the catalytic effects of the cations is problematic, since the cations are intimately involved in substrate binding. This problem is explored here by using a theoretical approach to analyze and interpret the key structural and biochemical experiments. Taking the X-ray structure of the exonuclease domain in the Klenow fragment of E. coli DNA polymerase I we use the empirical valence bond method to examine different feasible mechanisms for phosphodiester bond cleavage in the exonuclease site. This structure-function analysis is based on evaluating the activation free energies of different assumed mechanisms and comparing the calculated values to the corresponding experimentally observed activation energy for phosphodiester bond cleavage. Mechanisms whose calculated activation energies are drastically larger than the observed activation energy are eliminated and the consistency of the corresponding conclusion is examined in view of other available experimental facts including mutational and pH dependence studies. This approach indicates that phosphodiester bond hydrolysis involves catalysis by an OH- ion from aqueous solution around the protein, rather than a general base catalysis by an active site residue. The catalytic effect of two divalent metal cations in the active site is found to be primarily electrostatic.