Now, we consider how decaying behavior can be introduced to reduce the asymptotic scaling further to linear. The first is to realize that the orbital transformation matrix, T A µp decays with the distance between the EOs and the AO µ. That is, not all of the orbitals in the AO basis contribute significantly to the orbitals in the EO basis. From this, one can set up a threshold ϵ such that an AO contributes to the EO basis significantly if and only if all of the absolute values of the elements in T A µp is larger than ϵ.