The mixed quantum/classical molecular dynamics with quantum transitions (MDQT) method is extended to treat the donor-acceptor vibrational motion as well as the hydrogen motion quantum mechanically for proton transfer reactions. The quantum treatment of both the hydrogen and the donor-acceptor motions requires the calculation of two-dimensional vibrational wave functions. The MDQT surface hopping method incorporates nonadiabatic transitions among these adiabatic vibrational states. This approach is applied to a model representing intramolecular proton transfer within a phenol-amine complex in liquid methyl chloride. For this model, the rates and kinetic isotope effects are the same within statistical uncertainty for simulations in which only the hydrogen motion is treated quantum mechanically and simulations in which both the hydrogen and the donor-acceptor vibrational motions are treated quantum mechanically. The analysis of these simulations elucidates the fundamental issues arising from a quantum mechanical treatment of the donor-acceptor vibrational motion as well as the hydrogen motion. This insight is relevant to future mixed quantum/classical molecular dynamics simulations of proton and hydride transfer reactions in solution and in enzymes. (C) 2003 American Institute of Physics.