We report the results of the first pseudopotential plane-wave simulations of the static properties of ammonia monohydrate phase I (AMH I) and ammonium hydroxide. Our calculated fourth-order logarithmic equation of state, at zero pressure and temperature, has molar volume, V-0=36.38(3) cm(3) mol(-1), bulk modulus, K-0=9.59(9) GPa, and the first derivative of the bulk modulus with respect to pressure, K-0(')=5.73(21). Both this and the lattice parameters are in very good agreement with experimental values. The monohydrate transforms, via a solid-state proton transfer reaction, to ammonium hydroxide (NH4OH) at 5.0(4) GPa. The equation of state of ammonium hydroxide is, V-0=31.82(5) cm(3) mol(-1), K-0=14.78(62) GPa, K-0(')=2.69(48). We calculate the reaction enthalpy, DeltaH(NH4OH,s --> NH3.H2O,s)=-14.8(5) kJ mol(-1) at absolute zero, and thus estimate the enthalpy of formation, Delta H-f(circle minus)(NH4OH,s)=-356 kJ mol(-1) at 298 K. This result places an upper limit of 84 kJ mol(-1) on the barrier to rotation of the ammonium cation, and yields an average hydrogen bond enthalpy of similar to 23 kJ mol(-1).