The theory for calculating the energies and relative intensities of the photodetachment transitions of the weakly bound diatomic anions is implemented for simulations of the zero electron kinetic energy spectra of the ArCl- and KrCl-anions using high-quality ab initio potentials. Its key features are the reduction of the molecular electronic photodetachment transition dipole moment matrix elements to the combination of atomic ones within the atoms-in-molecule model and estimation of the latter by well-developed approaches to the atomic photodetachment processes. The difference in the electronic photodetachment transition dipole moments for distinct electronic states of the neutral, importance of vibrational-rotational coupling, and rotational structure of vibronic bands are analyzed. It is shown that ab initio simulations provide almost the same level of agreement with measured spectra as did the empirical potentials adjusted to reproduce the experimental data. The predictive power of the theory is demonstrated by the discovery of the hidden transitions to the I3/2 state of KrCl which strongy overlap with those to X1/2 state.