In the situation where gas phase calculation is not converged, we assume that 𝜖 T+'+ (gas) -𝜖 UV'+ (gas) = 0. If their SCF acceleration mechanisms are the same, they should give similar performance. The applied λ values range from 0.07 to 0.25 Hartree (1.9 to 6.8 eV) for the 25 tested peptides. For gas-phase calculations that cannot converge within 1000 steps, we assume that the gas phase HOMO-LUMO gap is zero.