A nine-dimensional potential energy surface (PES) for the ammonium cation has been constructed by fitting similar to 30 000 AE-CCSD(T)-F12a/cc-pCVTZ-F12 points up to 32 262 cm(-1) (4.0 eV) from the minimum. The fitting using the permutation invariant polynomial-neural network method has high fidelity, with a root-mean-square error of merely 2.34 cm(-1). The low-lying vibrational energy levels of NH4+ have been determined quantum mechanically using both Jacobi and normal coordinates, and the fundamental frequencies are in excellent agreement with available experimental data.