Does the DFT Self-Interaction Error Affect Energies Calculated in Proteins with Large QM Systems?

Abstract

We have examined how the self-interaction error in density-functional theory (DFT) calculations affects energies calculated on large systems (600-1000 atoms) involving several charged groups. We employ 18 different quantum mechanical (QM) methods, including Hartree-Fock, as well as pure, hybrid, and range-separated DFT methods. They are used to calculate reaction and activation energies for three different protein models in vacuum, in a point-charge surrounding, or with a continuum-solvent model. We show that pure DFT functionals give rise to a significant delocalization of the charges in charged groups in the protein, typically by ∼0.1 e, as evidenced from the Mulliken charges. This has a clear effect on how the surroundings affect calculated reaction and activation energies, indicating that these methods should be avoided for DFT calculations on large systems. Fortunately, methods such as CAM-B3LYP, BHLYP, and M06-2X give results that agree within a few kilojoules per mole, especially when the calculations are performed in a point-charge surrounding. Therefore, we recommend these methods to estimate the effect of the surroundings with large QM systems (but other QM methods may be used to study the intrinsic reaction and activation energies).

Multiscale modeling of enzymes: QM‐cluster, QM/MM, and QM/MM/MD: A tutorial review

“…However, it has been pointed out that as larger models are employed the choice of dielectric constant becomes increasingly less important . Conversely, finding the correct dielectric constant proves to be still quite problematic, for example, in the proximity of polar and negatively charged active sites in molybdenum enzymes …”

“…In addition to the effects noted above in section 2.1.2 from the Ryde group, the self‐interaction error (SIE) should be considered in the calculation of activation and reaction energies. Recently, SIE was investigated by Fouda and Ryde for three large enzymes ([NiFe] hydrogenase, glyoxalase I, and sulfite oxidase) with more than 600 atoms. They calculated both activation and reaction energies by DFT and HF methods using protein models of various sizes in three different schemes: (i) in a vacuum, (ii) in a point‐charge surroundings, and (iii) with a continuum solvent model.…”

“…Their results revealed that pure DFT functionals cause severe charge delocalization; therefore, the effect of the surroundings near charged functional groups should be considered. Fouda and Ryde recommended to use CAM‐B3LYP, BHLYP with 50% HF exchange, and M06‐2X with 54% HF exchange in a point‐charge surroundings of protein atoms and a sphere of water molecules of at least 30 Å …”

QM/MM Study of the Nitrogenase MoFe Protein Resting State: Broken-Symmetry States, Protonation States, and QM Region Convergence in the FeMoco Active Site

“…D. QM region size dependence: structures, vertical redox reactions and deprotonations Large QM regions have been used in the geometric analysis of FeMoco in this study. The sometimes slow convergence of QM/MM properties with respect to QM region size is an issue that has been discussed in recent articles 87,88,89,90,91 . It has been suggested that QM/MM properties such as chemical reaction barriers in proteins do not converge until the QM region is several hundred atoms in size.…”

Reassessment of the Mechanisms of Thermal C−H Bond Activation of Methane by Cationic Magnesium Oxides: A Critical Evaluation of the Suitability of Different Density Functionals

“…As mentioned above, the generally large deviations both in terms of geometries and bond energies provided by pure DFT functionals as compared to the CCSD‐method are due to the self‐interaction error; this is considered to be the largest deficiency in the DFT‐methods . As suggested by Lundberg and Siegbahn, this shortcoming can be reduced to a certain extent by using hybrid or double‐hybrid functional methods instead of pure DFT‐functionals . Yet, deficiencies remain to exist.…”