Theoretical ¹³C NMR Spectra of IPR Isomers of Fullerenes C₆₀, C₇₀, C₇₂, C₇₄, C₇₆, and C₇₈ Studied by Density Functional Theory

Optimized geometries and 13C NMR chemical shifts of all the isolated-pentagon-rule (IPR) isomers of fullerenes C60, C70, C72, C74, C76, and C78, except C76:2, have been calculated by density functional theory (B3LYP/6-31G*). C60 has the highest value of total energy per atom. The total energy per atom of other fullerenes decreases when the size of fullerene increases. The unobserved C72 is found to have higher total energy per atom while the also unobserved fullerenes C74, C78:4, and C78:5 have similar values of total energy per atom compared to those already observed. The general patterns of the calculated 13C NMR spectra give good agreement with the experimental patterns. Peaks above 140 ppm agree better with experiment while chemical shifts below 140 ppm are generally overestimated by 1−2 ppm. Local geometry is shown to be determined largely by the connectivity and have some effect on chemical shifts although no direct relationship between the π-orbital axis vector (POAV) angles and chemical shifts is apparent.