Efficient quantum-chemical geometry optimization and the structure of large icosahedral fullerenes

TL;DR

This paper presents an efficient quantum-chemical method for geometry optimization of large icosahedral fullerenes, achieving the largest molecule calculation to date and analyzing structural evolution from C60 to graphite.

Contribution

The authors develop a fully analytic density functional theory approach using generalized Gaunt coefficients, enabling large-scale geometry optimizations of fullerenes up to C2160.

Findings

Exact geometry of C60 fullerene obtained.

Optimized geometries of C240, C540, C960, C1500, and C2160 fullerenes.

Largest molecule calculation reported on any isolated molecule.

Abstract

Geometry optimization is efficient using generalized Gaunt coefficients, which significantly limit the amount of cross differentiation for multi-center integrals of high-angular-momentum solid-harmonic basis sets. We parameterize the fully analytic formulation of density functional theory (ADFT), called the Slater-Roothaan method, developed in our group to give the exact geometry of C60 fullerene. The parametrized ADFT is subsequently used to optimize geometries of most stable C240, C540, C960, C1500 and C2160 icosahedral fullerenes. The calculations are all electron, the orbital basis set includes d functions and the exchange-correlation-potential basis set includes f functions. The calculation of C2160 fullerene employed about 39000 basis functions and is the largest calculation reported on any isolated molecule to-date. The evolution of interatomic distance and atomization energy from C60 to graphite has been investigated.