The bounds allow us to neglect pairs of localized basis functions in different regions of the QM part, whose densities overlap very little. In this case, all polarization integrals for that pair of basis functions are screened, no matter where the polarizable atom is placed. As a result, it should be noted that the bounds are not especially tight since they do not take advantage of the decay of the polarization integral with the distance between the polarizable site and the basis functions. However, the CS bounds serve their purpose as a simple and efficient means to prescreen polarization integrals with knowledge of only the atomic orbitals' centers, contraction coefficients, and exponents.