Ammonium does not have a permanent electric dipole moment, just as the isoelectronic methane. The asymetrically deuterated isotopologs have comparatively large dipole moments because the center of charge differs considerably from the center of mass.
The predictions are mainly based on improved IR data of the ν₄ band from
(1) J. L. Doménech, M. Cueto, V. J. Herrero, I. Tanarro, B. Tercero, A. Fuente, and J. Cernicharo, 2013, Astrophys. J. 771, L11.
The molecule was subsequently detected in space and an accurate rest frequency for the J = 1 – 0 transition was derived by
(2) J. Cernicharo, B. Tercero, A. Fuente, J. L. Doménech, M. Cueto, E. Carrasco, V. J. Herrero, I. Tanarro, N. Marcelino, E. Roueff, M. Gerin, and J. C. Pearson, 2013, Astrophys. J. 771, L10.
At low temperatures, it may be necessary to discern between A-NH₃D⁺ and E-NH₃D⁺. The A state levels are described by K = 3n, those of E state by K = 3n ± 1. The nuclear spin-weight ratio is 2 : 1 for A-NH₃D⁺ with K > 0 and all other states, respectively. The J_K = 1₁ level is the lowest E state level. It is about 10.2349 cm^–1 above ground.
Separate E and A predictions are available along with separate E and A partition function values. It appears unlikely that many additional transitions of NH₃D⁺ are observable in space beyond J = 1 – 0. Therefore, we assume to predictions to be of sufficient accuracy if the astronomically determined rest frequency is correct within the quoted uncertainties.
The dipole moment was derived from the structure by
(3) T. Nakanaga and T. Amano, 1986, Can. J. Phys. 64, 1356.