We further compared CPCM and level-shifting by tracking the frontier orbital energy changes over SCF iterations. The gas phase SCF of zwitterionic 3ftr without level-shifting demonstrates a typical feature of SCF with convergence issues: the HOMO and LUMO energies are constantly oscillating and very close to each other, with less than 0.03 eV difference in most iterations (Figure ). Because of the small HOMO-LUMO gap, the LUMO switch between the MO localized on the N-terminal and the MO localized on the C-terminal. This near degeneracy of HOMO and LUMO also occasionally causes a vigorous mixture of the virtual and occupied spaces, leading to drastic character change for multiple frontier orbitals (e.g., iteration 51 of Figure ), requiring many more iterations to reconverge. Level-shifting leads to more stable orbital energies in the short term but still suffers from occasional vigorous oscillations that cause the SCF to continue for many iterations. The reason is that the energetic order of frontier MOs in the first few iterations may significantly deviate from the converged result, but level-shifting reinforces this wrong order by separating the virtual and occupied space, which delays the convergence. For example, the converged LUMO (localized on the N-terminal) used to be HOMO-2 in iterations 27-38, and the level-shifting keeps it in the occupied space for a long time (Figure ). In contrast, CPCM (ε=80) has the HOMO and LUMO well separated throughout all iterations and converges within 14 steps.