The bacteriophages of the Cystoviridae family package their single stranded RNA genomic precursors into empty capsid (procapsids) using a hexameric packaging ATPase motor (P4). This molecular motor shares sequence and structural similarity with RecA-like hexameric helicases. A concerted structural, mutational and kinetic analysis helped to define the mechanical reaction coordinate, i.e. the conformational changes associated with RNA translocation. The results also allowed us to propose a possible scheme of coupling between ATP hydrolysis and translocation which requires the cooperative action of three consecutive subunits. Here, we first test this model by preparing hexamers with defined proportions of wild type and mutant subunits and measuring their activity. Then, we develop a stochastic kinetic model which accounts for the catalytic cooperativity of the P4 hexamer. Finally, we use the available structural information to construct a quantum-chemical model of the chemical reaction coordinate and obtain a detailed description of the electron density changes during ATP hydrolysis. The model explains the results of the mutational analyses and yields new insights into the role of several conserved residues within the ATP binding pocket. These hypotheses will guide future experimental work.