The most prominent mechanism for cell signaling, energy conversion, and the synthesis and breakdown of nucleic acids involves the transfer of phosphoryl groups. The present work applies density-functional electronic structure methods to study the model phosphoryl transfer reactions. These reactions represent reaction models for RNA catalysis (including transesterification, migration, and hydrolysis), and GTP hydrolysis in Ras and RasGAP. The effect of solvent is treated with both explicit water molecules, and self-consistently with an implicit (continuum) solvation model. Aqueous free energy barriers are calculated, and the structures and bond orders of the rate-controlling transition states are characterized. The calculated kinetic isotope effects and thio effects are consistent with available experimental data, and provide useful information for the interpretation of measured isotope and thio effects used to probe mechanism in phosphoryl transfer reactions catalyzed by enzymes and ribozymes.