In chemical engineering often functional groups like OH, C=O, or NHx with an asymmetric charge distribution occur. Aside from polar interactions, such groups often show H-bonding interactions. The combination of both types is especially hard to describe with equations of state. This leads to the effect that including polar interactions for clearly polar pure compounds may lead to a worse description of mixtures containing this component. One possible reason for this behavior is that equations of state are usually based on perturbation theory that ignores the change in fluid structure due to interactions. This approximation is good for e.g. dispersive interactions, but is known to be bad for at least the gaseous phase of polar fluids up to moderate densities. The issue is addressed in this article by developing a perturbation theory around the target fluid rather than the reference fluid, as is usually the case. This makes it possible to include ordering effects into the equation of state and to calculate additional structural information in a fraction of the time used by typical methods like molecular simulation or integral equation theory. The perturbation theory is parameterized on the Stockmayer fluid's structure and vapor-liquid equilibria, calculated from molecular simulation, and agrees quantitatively with them. It is verified on a second simple fluid, the shifted Stockmayer fluid, where the dipole is shifted along its axis away from the Lennard-Jones center. For this fluid also molecular simulations are performed for both structure and vapor-liquid equilibria. Both properties are predicted by the new equation of state and again agree quantitatively with simulation. The new theory is then applied to hydrogen chloride and shows improvements over models for existing theories. Namely, liquid density description is improved over a literature model for PCP-SAFT, where the dipolar nature of hydrogen chloride is considered, and vapor pressure description is improved over a literature model for PC-SAFT, where the weak H-bonding nature is considered. The number of parameters can be kept at three, as for the PCP-SAFT model, by using quantum mechanics results from literature for the dipole shift. The model shows improvements for the predicted vapor density compared to both models from literature. Aside from improving thermodynamic property description and prediction, the new theory allows the fast calculation of a fluid's mutual orientation structure. This is useful e.g. for assessing availability of two reactant groups to each other, thereby allowing a better description of reaction kinetics. This has not been accomplished by any equation of state before. (C) 2017 Elsevier Ltd. All rights reserved.