In this paper we present the so far most extended investigation of the calculation of the coupling constant polarizability of a molecule. The components of the coupling constant polarizability are derivatives of the NMR indirect nuclear spin-spin coupling constant with respect to an external electric ¿eld and play an important role for both chiral discrimination and solvation e¿ects on NMR coupling constants. In this study we illustrate the e¿ects of one-electron basis sets and electron correlation both at the level of density functional theory as well as second order polarization propagator approximation for the small molecule hydrogen peroxide, which allowed us to carry out calculations with the largest available basis sets optimized for the calculation of NMR coupling constants. We ¿nd a systematic but rather slow convergence with the one-electron basis set and that augmentation functions are required. We observe also large and non-systematic correlation e¿ects with signi¿cant di¿erences between the density functional and wave function theory methods.