A combination of first-principles density functional theory calculations and a search over structures is used to predict the stability of a proton-transfer modification of ammonia monohydrate with space group P4∕nmm. The phase diagram is calculated with the Perdew-Burke-Ernzerhof (PBE) density functional, and the effects of a semi-empirical dispersion correction, zero point motion, and finite temperature are investigated. Comparison with MP2 and coupled cluster calculations shows that the PBE functional over-stabilizes proton transfer phases because too much electronic charge moves with the proton. This over-binding is partially corrected by using the PBE0 hybrid exchange-correlation functional, which increases the enthalpy of P4∕nmm by about 0.6 eV per formula unit relative to phase I of ammonia monohydrate and shifts the transition to the proton transfer phase from the PBE pressure of 2.8 GPa to about 10 GPa. This is consistent with experiment as proton transfer phases have not been observed at pressures up to ∼9 GPa, while higher pressures have not yet been explored experimentally.