  The molecular-crystal model, that describes a one-dimensional electron gas
interacting with quartic anharmonic lattice vibrations, offers great potentials
in the mapping of a relatively wide range of low-dimensional fermion systems
coupled to optical phonons onto quantum liquids with retarded interactions.
Following a non-perturbative approach involving non-Gaussian partial functional
integrations of lattice degrees of freedom, the exact expression of the
phonon-mediated two-electron action for this model is derived. With the help of
Hubbard-Stratonovich transformation the charge-density-wave instability is
examined in the sequel, with particular emphasis on the effect of the quartic
anharmonic phonons on the charge-density-wave transition temperature.
