The polarizable valence-state-atoms-in-molecules (pVSAM) model describes the electron-pair bond in A-B molecules by superposing core-polarized A(+)B(-), A(-)B(+), and A:B structures, whose weights are determined by electronegativity equalization. The polarizable valence state potential energy curve (pVS-PEC) is derived through the systematic improvement of the valence state potential energy curve (VS-PEC) [Gardner, D. O. N.: von Szentpaly, L. J. Phys. Chem. A 1999, 103, 9313] and is given as U(R) = -[(K-1/R) + (K-2/R-4) + (K-3/R-7)] + (T/R) exp(-lambdaR). The first bracketed term contains the Coulomb, charge-induced dipole, and induced dipole-induced dipole terms, derived from weighted ionic and covalent bond-charge contributions. The potential is tested on a broad variety of homonuclear diatoms and heteronuclear halides and hydrides (a total of 52 molecules). The accuracies of the dimensionless vibration-rotation coupling constant (F) and the anharmonicity constant (G) for the halides of the alkali and coinage metals are significantly better than those of the Morse, Rydberg, simple bond-charge, and Rittner potentials. Adding core polarization to the VS-PEC reduces the average unsigned errors in the spectroscopic constants of 47 diatomic molecules from 17.1% to 7.5% in F and 18.9% to 7.8% in G, whereas those of the Morse potential amount to 32.6% and 31.4%, respectively.