Ion pairing of lithium and fluoride in water is described quantitatively using ab initio molecular dynamics simulations. We design a reliable computational protocol for evaluating the ion-ion potential of mean force using density functional based simulation methods. By comparison to classical molecular dynamics with empirical force fields we establish the statistical error of the procedure. We also check the accuracy of the electronic structure description by comparison to experimental structural data and to higher level calculations for model systems. The present approach not only points to deficiencies in force field calculations of potentials of mean force for difficult cases of high charge density ions like the aqueous lithium fluoride pair, but also allows extracting electronic information, such as the amount of charge transfer to solvent and its dependence on the ion-ion distance.