Impacts of polarizable continuum models on the SCF convergence and DFT delocalization error of large molecules

Advances in algorithm developments have enabled density functional theory (DFT) description of large molecules, including whole proteins, but the self-consistent field (SCF) convergence issues often hamper practical applications. The conductor-like polarizable continuum model (CPCM), although initially introduced as an implicit solvent model, was reported to improve SCF convergence in some large molecules. However, the underlying mechanisms and applicable use cases were unclear. We investigated the impacts of CPCM on the SCF convergence of 25 peptides and found that the CPCM only effectively reduced the SCF iterations for molecules with charge separations (e.g., the zwitterionic form of peptides) but had little effect on non-charge-separated molecules. We observed that CPCM increased the HOMO-LUMO gap of both the zwitterionic and non-charge-separated molecules, but only the charge-separated molecules suffered from the vanishing HOMO-LUMO gap problem in the gas phase, which is the origin of the convergence issue. We revealed CPCM's gap-opening mechanism as the selective stabilization/destabilization of molecular orbitals (MOs) based on their local electrostatic environment. Compared to level-shifting, a traditional SCF improvement technique, CPCM has superior performance because the stabilization/destabilization of MOs is consistent through SCF iterations. Finally, we examined CPCM's impacts on DFT density delocalization error (DDE) when used as an SCF accelerator. CPCM can mitigate the DDE and reproduce the density-derived properties (e.g., dipole moments) matching high-level methods when a very low dielectric constant is used but tends to over-localize the electron density at higher dielectric constants.