Density functional theory calculations have been carried out to investigate the possible reaction mechanisms for the reversible dihydrogen activation catalyzed by a phosphine-borane compound, (C6H2Me3)2P(C6F4)B(C6F5)2 (Welch, G. C.; Juan, R. R. S; Masuda, J. D.; Stephan, D. W. Science. 2006, 314, 1124-1126). The present calculations show that an unusual concerted Lewis acid-Lewis base mechanism is more favorable than the proton transfer or hydride transfer mechanisms suggested previously. In the concerted Lewis acid-Lewis base mechanism, the H-H heterolytic cleavage is achieved through the simultaneous electron transfer from the lone-pair orbital of the Lewis base P center to the sigma* orbital of H2 and from the sigma orbital of H2 to the empty orbital of the Lewis acid B center. The solvent is found to dramatically change the potential energy surface. The proposed mechanism can account well for the bimolecular H-D exchange process observed in deuteration experiments and the experimental fact that the H2 activation is reversible at mild conditions.