  The effect of the exchange interaction on the vibrational properties and on
the electron-phonon coupling were investigated in several recent works. In most
of the case, exchange tends to enhance the electron-phonon interaction,
although the motivations for such behaviour are not completely understood. Here
we consider the class of weakly doped two-dimensional multivalley
semiconductors and we demonstrate that a more global picture emerges. In
particular we show that in these systems, at low enough doping, even a moderate
electron-electron interaction enhances the response to any perturbation
inducing a valley polarization. If the valley polarization is due to the
electron-phonon coupling, the electron-electron interaction results in an
enhancement of the superconducting critical temperature. We demonstrate the
applicability of the theory by performing random phase approximation and first
principles calculations in transition metal chloronitrides. We find that
exchange is responsible for the enhancement of the superconducting critical
temperature in Li$_x$ZrNCl and that much larger T$_c$s could be obtained in
intercalated HfNCl if the synthesis of cleaner samples could remove the
Anderson insulating state competing with superconductivity.
