The enzyme F1-adenosine triphosphatase (ATPase) is a molecular motor that converts the chemical energy stored in the molecule adenosine triphosphate (ATP) into mechanical rotation of its gamma-subunit. During steady-state catalysis, the three catalytic sites of F1 operate in a cooperative fashion such that at every instant each site is in a different conformation corresponding to a different stage along the catalytic cycle. Notwithstanding a large amount of biochemical and, recently, structural data, we still lack an understanding of how ATP hydrolysis in F1 is coupled to mechanical motion and how the catalytic sites achieve cooperativity during rotatory catalysis. In this publication, we report combined quantum mechanical/molecular mechanical simulations of ATP hydrolysis in the betaTP and betaDP catalytic sites of F1-ATPase. Our simulations reveal a dramatic change in the reaction energetics from strongly endothermic in betaTP to approximately equienergetic in betaDP. The simulations identify the responsible protein residues, the arginine finger alphaR373 being the most important one. Similar to our earlier study of betaTP, we find a multicenter proton relay mechanism to be the energetically most favorable hydrolysis pathway. The results elucidate how cooperativity between catalytic sites might be achieved by this remarkable molecular motor.