The equation of the state of the hydrogen bonding fluid system of A a D d type is studied by the principle of statistical mechanics. The influences of hydrogen bonds on the equation of state of the system are obtained based on the change in volume due to hydrogen bonds. Moreover, the number density fluctuations of both molecules and hydrogen bonds as well as their spatial correlation property are investigated. Furthermore, an equation describing relation between the number density correlation function of "molecules-hydrogen bonds" and that of molecules and hydrogen bonds is derived. As application, taking the van der Waals hydrogen bonding fluid as an example, we considered the effect of hydrogen bonds on its relevant statistical properties.
hydrogen bonding fluid, equation of state, fluctuation, correlation effectFluid is often referred to as the gases or liquids, which can be classified into polar and non-polar fluids according to whether the molecules in fluid are polar or not. Hydrogen bonding (HB) fluids are polar fluids, for instance, water, acids, alkalis and their mixtures are all such kind of HB fluids. Besides the usual properties of fluids, there exist the molecular associations by hydrogen bonds in HB fluid systems. This results in the formation of HB clusters with various sizes, even the HB networks, and hence the HB fluid systems are very complicated in nature [1] .According to the statistical mechanics, the thermodynamic properties of a system can be determined if the free energy and the equation of state (EOS) are known [2,3] . The normal systems of gases can be well described by the outstanding EOS proposed by van der Waals because of its lower molecular number density. However, for most of liquids, the complexity arises due to its local ordered structures and disordered structures in long-distance. Usually, liquids can be studied by the methods of cluster expansions, radial distribution function, corresponding-states principle, perturbation theory, density functional theory and cell models as well as the approaches of Monte Carlo simulation, molecular dynamical simulation, and so forth [3] . For the associated systems, the theory based on the molecular thermodynamics is more convenient and efficient [4] . In this article, a simple HB fluid system of A a D d type is investigated on the basis of part of previous results [5] . In detail, the effects of hydrogen bonds on the EOS of the system, the fluctuations in both molecular and hydrogen bond number densities and their spatial correlations are discussed. Moreover, taking the van der Waals HB fluid as an example, we calculated the second virial coefficient and considered the influence of hydrogen bonds on which.