Density-Functional Errors in Alkanes: A Real-Space Perspective.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Density-functional theory (DFT) approximations often show systematic errors for isodesmic reaction energies in n-alkanes.
• Previous explanations have focused on the nature of exchange-correlation or the range of interactions (medium- to long-range).

Purpose of the Study:

• To define a new isodesmic reaction to pinpoint the origin of DFT errors in n-alkane reactions.
• To introduce a real-space interpretation of these errors using electron density changes.
• To investigate the role of localized interactions in DFT inaccuracies.

Main Methods:

• Definition of a novel isodesmic reaction for n-alkanes.
• Application of the Non-Covalent Interactions (NCI) method to analyze electron density.
• Real-space analysis of changes in electron density and reduced density gradients.
• Examination of exchange energy contributions within NCI regions.

Main Results:

• Reaction energy differences in n-alkanes are attributed to localized 1,3 interactions between contiguous CH2 units.
• The Non-Covalent Interactions (NCI) method reveals smaller reduced density gradients for 1,3 interactions in n-alkane reactants versus ethane products.
• A constant energy bias against propane units in n-alkanes is observed due to reduced exchange energy contributions.
• Errors in DFT calculations for Diels-Alder addition barrier heights using GGA-based hybrid functionals share a similar source.

Conclusions:

• Localized 1,3 interactions between CH2 units are the primary source of systematic DFT errors for n-alkane isodesmic reactions.
• The Non-Covalent Interactions (NCI) method provides a real-space explanation for these DFT errors, linking them to exchange energy differences.
• The findings offer insights into improving DFT accuracy for various chemical systems, including reaction barriers.