The potential energy function (PEF) has been derived to perform the liquid simulations using the Monte Carlo method for three hydrogen-bonding systems, water, hydrogen fluoride, and ammonia. The PEF is a pair potential function of the overlap integrals between molecules and of the Coulomb interactions between atomic fractional charges. The parameters of the PEF are easily determined in order to reproduce the ab initio pair interaction energies. The lack of many-body interactions, however, prevents the reproduction of the liquid structures. The PEF consists of some physically meaningful terms, and using the characteristics of the function, it is found that the enhancement of a component in the PEF reasonably succeeds in producing the liquid structures. The general procedure for obtaining an effective pair potential function for the hydrogen-bonding systems is reported by a simple modification to the PEF.