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

Abstract

Geometry optimization is efficient using generalized Gaunt coefficients, which significantly limit the amount of cross differentiation for multi-center integrals of highangular-momentum solid-harmonic basis sets. The geometries of the most stable C 240 , C 540 , C 960 , C 1500 , and C 2160 icosahedral fullerenes are optimized using analytic densityfunctional theory (ADFT), which is parameterized to give the experimental geometry of C 60 . The calculations are all electron, the orbital basis set includes d functions and the exchange-correlation-potential basis set includes f functions. The largest calculation on C 2160 employed about 39000 basis functions.

Structural, electronic and energetic properties of giant icosahedral fullerenes up to C6000: insights from an ab initio hybrid DFT study

“…22,40 . In this study the values of 8,8,8,8,20 were chosen. The threshold on the SCF energy for geometry optimization was set to 10 −8 Ha.…”

“…Finally, only in recent cases the relative stability compared to the graphene sheet was investigated [19][20][21] at the ab initio level, the limiting factors being either the low level of adopted theory 19 or the small number of investigated members 20,21 .…”

Smooth Scaling of Valence Electronic Properties in Fullerenes: From One Carbon Atom, to C60, to Graphene

“…The neutralstate geometry of each structure C n was optimized and its average radius r n determined using a Gaussian 6-311G** basis and a functional [17] that gives an exact geometry for C 60 . The DFT calculations involved the reoptimization of previously determined [18] icosahedral geometries, as well as the optimization of a new geometry for C 320 .…”

Dipole Moments From Atomic-Number-Dependent Potentials in Analytic Density-Functional Theory

“…Therefore matrix elements and thus the total energy can be computed to machine precision. This approach enables calculations on the largest molecules that be treated using an all-electron TZP basis set [16]. Its functional form is restricted but its space of atomic parameters is rich.…”