The nonlocal resonance model developed previously for the description of low-energy electron collisions with hydrogen halides is generalized to include the
dependence of the dipole-modified threshold exponent on the internuclear distance. An efficient computational scheme has been developed to deal with the resulting
nonseparability of the nonlocal complex potential for the nuclear motion within the Schwinger-Lanczos approach. The results reveal that the R-dependence of the
threshold exponent has a significant effect on the threshold peaks in the vibrational excitation cross sections of HCl. The shape and intensity of the calculated
threshold peak in the 0 --> 1 vibrational excitation channel, in particular, are in much better agreement with experimental data than previous results. For the
electron-HBr and electron-HI collision systems the effects of the R-dependence of the threshold exponent are not significant.