A density matrix evolution (DME) method (Berendsen, H. J. C.; Mavri, J. J. Phys. Chem. the preceding paper in this issue) in combination with classical molecular dynamics simulation was applied to calculate the rate of proton tunneling in the intramolecular double-well hydrogen bond of hydrogen malonate (HM) in aqueous solution. The one-dimensional time-dependent Schrodinger equation was solved for an ensemble of 50 000 configurations td:obtain a time course of the splitting and coupling matrix elements between the product and reactant states. The rate of tunneling is in agreement with the approximate analytical solutions given by Borgis and Hynes (J. Chem. Phys. 1991, 94, 3619). When the in vacuo contribution to the free energy difference between the symmetric and asymmetric form of HM is omitted, the free energy difference has the meaning of the reversible work necessary for such a solvent reorganization that zero energy splitting between product and reactant states is achieved. The method of biased sampling is used to enhance the sampling of such configurations where tunneling probability is large. After the correction for biased sampling, the DME method results in practically the same rate of tunneling as obtained by an unbiased calculation. The rates of tunneling are compared to the classical proton-transfer rate in the nonadiabatic limit.