For k = n, the coefficient in eq. 4 is unity regardless of N . For k < n, the signs alternate with n for fixed k and increase in magnitude with n (see Table ). Because the SIE inherent in E (k) α is consistently stabilizing, the alternating signs of the lower order terms will overwhelm the always-positive n = k terms, leading to the pattern of errors that is observed in the PBE-MBE(n) calculations. Note that these errors need not result in a divergent MBE(n), as demonstrated by the HF/aug-cc-pVDZ data, where BSSE is strictly stabilizing for larger subsystems, yet the errors grow smaller as n increases. This suggests that there exists some expansion-depended error threshold, related to the combinatorial coefficients in eq. 4, beyond which MBE(n) calculations will diverge.