Fullerenes Pose a Strain on Hybrid Density Functional Theory

Area of Science:

• Computational Chemistry
• Materials Science
• Nanotechnology

Background:

• Accurate computational modeling of fullerenes is crucial for designing novel carbon nanostructures.
• Previous studies have not comprehensively analyzed the relative energies of larger fullerenes (beyond C24) using high-accuracy ab initio methods like CCSD(T).

Purpose of the Study:

• To investigate the relative energies of 29 diverse C40 fullerene isomers using the G4(MP2) composite ab initio method.
• To examine the performance of various hybrid density functional theory (DFT) methods in predicting fullerene energies, particularly concerning pentagon-pentagon strain.
• To establish a relationship between the percentage of exact Hartree-Fock (HF) exchange in DFT functionals and their accuracy for strained fullerene isomers.

Main Methods:

• Calculation of C40 fullerene energies using the G4(MP2) composite ab initio method, approximating CCSD(T)/TZ.
• Analysis of isomerization energies and their correlation with fullerene pentagon signatures (P1 index).
• Evaluation of hybrid DFT method performance against CCSD(T)/TZ reference energies, focusing on the impact of HF exchange percentage on accuracy for varying strain levels.

Main Results:

• A linear correlation (R2 = 0.96) was found between CCSD(T)/TZ isomerization energies and the fullerene pentagon signatures (P1 index).
• The accuracy of hybrid DFT methods in predicting fullerene energies deteriorates with increasing pentagon-pentagon strain.
• This performance degradation is exacerbated by higher percentages of HF exchange in DFT functionals, with notable deviations observed for functionals like B3LYP and BH&HLYP.

Conclusions:

• Pentagon-pentagon strain in fullerenes presents a significant challenge for hybrid DFT methods, especially those with high HF exchange content.
• An inverse relationship exists between the optimal percentage of HF exchange and the pentagon-pentagon strain energy, indicating lower HF exchange is preferable for highly strained isomers.
• The findings provide critical insights for selecting appropriate computational methods for accurate modeling and design of low-dimension carbon nanostructures.