Integral-equation theories of fluid phase equilibria in simple fluids

We briefly review the application of integral equation theories (IETs) of the fluid state in order to predict fluid phase equilibria of simple fluids. In spite of the relatively simple picture emerging from an isotropic pair potential, IETs have been instrumental in the last few decades to show a quite complex phase behaviour, where multiple critical points are observed in the phase diagram. The application of thermodynamic self-consistency within the theory is shown to dramatically improve the reliability of IETs, allowing them to become a valid and computationally cheap tool, in comparison to computer simulation, to investigate the limits of stability of the fluid phase.