  Peierls-type instabilities in quarter-filled ($\bar{n}=1/2$) and half-filled
($\bar{n}=1$) quantum double-well hydrogen-bonded chain are investigated
analytically in the framework of two-stage orientational-tunnelling model with
additional inclusion of the interactions of protons with two different optical
phonon branches. It is shown that when the energy of proton-phonon coupling
becomes large, the system undergoes a transition to a various types of
insulator states. The influence of two different transport amplitudes on ground
states properties is studied. The results are compared with the pressure effect
experimental investigations in superprotonic systems and hydrogen halides at
low temperatures.
