Impacts of Polarizable Continuum Models on the SCF Convergence and DFT Delocalization Error of Large Molecules

24 August 2022, Version 2
This content is a preprint and has not undergone peer review at the time of posting.

Abstract

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 (MO) 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.

Keywords

Self-Consistent Field
Polarizable Continuum Model
Electronic Structure

Supplementary materials

Title
Description
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Title
Supplementary Materials for Impacts of Polarizable Continuum Model on DFT Delocalization Error and SCF convergence
Description
This file includes the proof of Eq. (4) in the continuous form of CPCM, the characteristics of the 25 tested proteins, Bader charge convergence tests, the SCF iteration number, HOMO-LUMO gap, and dipole moment for all the 25 peptides, the criteria for selecting comparable 1s orbitals, energy variation of 1s orbitals for the other three peptides, the partial charge and dipole moment for the 4 small zwitterions calculated by BLYP, and the comparison of charge calculation methods using the BLYP and B3LYP result for the 4 zwitterions
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The structure of the molecules studied in this work
Description
This file includes structures of all tested 25 zwitterionic proteins and their non-charge-separated counterparts, and the structure of the 4 zwitterions
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