To understand the mechanism behind this, we investigated the HOMO-LUMO of these peptides as a function of e values (Figure and Supplementary Material Table ). The gas phase calculations of 21 out of 25 zwitterionic peptides have small HOMO-LUMO gaps that less than 0.5 eV, agreeing with the vanishing HOMO-LUMO gap problem reported in previous studies of DFT convergence issues in proteins. The HOMO-LUMO gap increases as e increases, with an approximately linear relationship to (e-1)/e, consistent with our analysis in Section 2. The gap opening usually results in faster convergence than the gas-phase SCF. However, the DIIS iteration does not decrease monotonically as the gap (or e) increases, remaining almost unchanged for ε values from 2 to 80. The increased gap is also observed for the non-charge separated peptides, but the increment is much smaller than that observed in zwitterions.