We investigate computationally the vibronic coupling constant in a large group of simple uncharged ABA(.) systems (A, B = H, Li, Na, K, Rb, Cs, F, Cl, Br, I), which may be formally mixed-valence or intermediate-valence ones. These open-shell species belong to three chemically quite distinct groups: intermetallic, interhalogen, and salt-like triatomics. Constraining these systems to a linear symmetric geometry, we optimize the A-B bond length at a certain level of theory and determine the electronic and vibrational structure of such species. At this common geometry we calculate a vibronic stability parameter for the antisymmetry mode (G), defined as the ratio of force constants for the antisymmetric to the symmetric stretching mode. G is a sensitive indicator of the magnitude of vibronic coupling. Values of G smaller than 1 (asymmetric mode softening) indicate large values of the off-diagonal vibronic coupling constant. Negative G indicate very large values of that constant, leading to vibronic instability. The smallest values of G are obtained for interhalogen species (most of them are vibronically unstable). Salt-like ABA and BAB molecules, as well as intermetallic species are vibronically stable. Two further interesting correlations evolve: the calculated force constants for the symmetric stretching mode correlate well with f, a parameter defined as the sum of the electronegativities of the A and B elements divided by the AB bond length. Large values off also indicate strong vibronic coupling.