Structure and thermodynamics of fluids made of particles that interact via a central force model potential are studied by means of Monte Carlo simulations and integral equation theories. The Hamiltonian has two terms, an intramolecular component represented by a harmonic oscillatorlike potential and an intermolecular interaction of the Lennard-Jones type. The potential does not fulfill the steric saturation condition so it leads to a polydisperse system. First, we investigate the association (clustering) and thermodynamic properties as a function of the potential parameters, such as the intramolecular potential depth, force constant, and bond length. It is shown that the atomic hypernetted chain (HNC) integral equation provides a correct description of the model as compared with simulation results. The calculation of the HNC pseudospinodal curve indicates that the stability boundaries between the vapor and liquid phases are strongly dependent on the bond length and suggests that there might be a direct gas-solid transition for certain elongations. On the other hand, we have assessed the ability of the model to describe the thermodynamics and structure of diatomic liquids such as N-2 and halogens. To this end we have devised a procedure to model the intramolecular potential depth to reproduce the complete association limit (i.e., an average number of bonds per particle equal to one). This constraint is imposed on the Ornstein-Zernike integral equation in a straightforward numerical way. The structure of the resulting fluid is compared with results from molecular theories. An excellent agreement between the HNC results for the associating fluid and the reference interaction site model (RISM)-HNC computations for the atom-atom model of the same fluid is obtained. There is also a remarkable coincidence between the simulation results for the molecular and the associating liquids, despite the polydisperse character of the latter. The stability boundaries in the complete association limit as predicted by the HNC integral equation have been computed for different bond lengths corresponding to real corresponding to real molecular liquids. These boundaries appear close to experimental liquid branch of the vapor-liquid coexistence line of the molecular systems under consideration.