Interactions between polar atoms are challenging to model because at very short ranges they form hydrogen bonds (H-bonds) that are partially covalent in character and exhibit strong orientation preferences; at longer ranges the orientation preferences are lost, but significant electrostatic interactions between charged and partially charged atoms remain. To simultaneously model these two types of behavior, we refined an orientation dependent model of hydrogen bonds [Kortemme et al. J. Mol. Biol. 2003, 326, 1239] used by the molecular modeling program Rosetta and then combined it with a distance-dependent Coulomb model of electrostatics. The functional form of the H-bond potential is physically motivated and parameters are fit so that H-bond geometries that Rosetta generates closely resemble H-bond geometries in high-resolution crystal structures. The combined potentials improve performance in a variety of scientific benchmarks including decoy discrimination, side chain prediction, and native sequence recovery in protein design simulations and establishes a new standard energy function for Rosetta.