Isotopic substitution of a hydrogen atom by deuterium turns a non-pola
r ion such as CH3+ into a non-centrosymmetric system, CH2D+, suitable
for rotational spectra detection in space. The vibrational contributio
n to the dipole moment of the ion is investigated in this paper. The e
lectronic potential surface has been obtained in a first-order CI, sta
rting from a full valence active space built by using projected locali
zed orbitals, to which core valence correlation effects have been adde
d to account for rehybridization. The vibrational functions are obtain
ed in a basis of harmonic oscillators. Three levels of vibrational tre
atment are presented, i.e, harmonic, non-coupled and coupled modes. Th
e final result for the transition moment in the lowest vibrational lev
el, mu(v) = 0.327 Debye, shows that CH2D+ should be observed and may b
e a useful tracer of CH3+ in interstellar chemistry.