A density functional theory study of the cleavage of a DNA model [p-nitrophenyl methyl phosphate (2)] and two RNA models [p-nitrophenyl 2-hydroxypropyl phosphate (3) and phenyl 2-hydroxypropyl phosphate (4)] promoted by the dinuclear Zn((II)) complex of 1,3-bis(1,5,9-triazacyclododec-1-yl)propane formulated with a bridging methoxide (1a) was undertaken to determine possible mechanisms for the transesterification processes that are consistent with experimental data. The initial substrate-bound state of 2:1a or 3:1a has the two phosphoryl oxygens bridging Zn((II))1 and Zn((II))2. For each of 2 and 3, four possible mechanisms were investigated, three of which were consistent with the overall free energy for the catalytic cleavage step for each substrate. The computations revealed various roles for the metal ions in the three mechanisms. These encompass concerted or stepwise processes, where the two metal ions with associated alkoxy groups [Zn((II))1:((-)OCH3) and Zn((II))1:((-)O-propyl)] play the role of a direct nucleophile (on 2 and 3, respectively) or where Zn((II))1:((-)OCH3) can act as a general base to deprotonate an attacking solvent molecule in the case of 2 or the attacking 2-hydroxypropyl group in the case of 3. The Zn((II))2 ion can serve as a spectator (after exerting a Lewis acid role in binding one of the phosphates' oxygens) or play active additional roles in providing direct coordination of the departing aryloxy group or positioning a hydrogen-bonding solvent to assist the departure of the leaving group. An important finding revealed by the calculations is the flexibility of the ligand system that allows the Zn-Zn distance to expand from ~3.6 Å in 1a to over 5 Å in the transforming 2:1a and 3:1a complexes during the catalytic event.