The accurate ground‐state potential energy function of aluminum monohydride (AlH) has been determined from ab initio calculations using the multireference averaged coupled‐pair functional (MR‐ACPF) method in conjunction with the correlation‐consistent core‐valence basis sets up to septuple‐zeta quality. The vibration‐rotation energy levels of the two isotopologues, AlH and AlD, were predicted to near the “spectroscopic” accuracy. The importance of electron correlation beyond the MR‐ACPF level of approximation, the scalar relativistic, spin‐orbit, adiabatic, and nonadiabatic effects was discussed. © 2019 Wiley Periodicals, Inc.