will converge to a certain value since T A µp,µ p and T A νq,ν q → 0 when the distance between orbital ν and the embedding orbitals increase. An implication of this is that, for sufficiently large systems, the time cost to maintain a constant truncation error in the ERI transformation will scale linearly with the system size (although empirically speaking, the system should be very large for linear scaling to be achieved). However, if the system size is not large enough, the threshold t must be adjusted to control the truncation error. To address this, we provide a simple formula to determine t for controlling the truncation error: