Phosphate transfer reactions are catalyzed by a large number of enzymes comprising kinases, mutases and phosphatases. These enzymes play a fundamental role in controlling numerous life processes and it is therefore important to understand the origin of their potent catalytic power. An example is the Ca²⁺-ATPase. In the E2P-state, this enzyme hydrolyses the phosphorylated amino acid, Asp351, 10⁶ to 10⁷ fold faster than when the model compound, acetyl phosphate, is hydrolyzed in in water.This thesis explores the catalytic power of Ca²⁺-ATPase using theoretical method based on quantum mechanics. The studies of this protein were made by performing quantum chemical calculations on models of phosphoric monoesters as well as on the explicit reaction pathway of the hydrolysis. The studies show the importance of electrostatic interactions as well as the role of the specific active site residue Glu183, a residue that acts as a base in the catalytic pathway. Furthermore, based on the calculations, the interpretation of the experimental infrared spectrum of the E2P-state of Ca²⁺-ATPase, could be further elucidated as well as modified.The experimental infrared spectrum of phosphoenol pyruvate in water has also been elucidated through calculations. This molecule is converted into pyruvate in the last step of the glycolytic pathway, a reaction that is catalyzed by pyruvate kinase (PK). These results further enabled the interpretation of the experimental spectrum of the PK's catalytic reaction.These two processes, the transport of Ca²⁺ into the sarcoplasmatic reticulum against a concentration gradient and the glycolysis, are two important actions of a muscle cell.