Electronic structures of fullerenes Cn with Ih symmetry and n=20k2.

Abstract

There are two classes of fullerenes with {ital I}{sub {ital h}} symmetry, one with {ital n}=60{ital k}{sup 2} and the other with {ital n}=20{ital k}{sup 2}, where {ital n} is the number of carbon atoms and {ital k} is any positive integer. Actually, the second class {ital n}=20{ital k}{sup 2} can be further divided into three types: {ital n}=20(3{ital m}+1){sup 2}, {ital n}=20(3{ital m}+2){sup 2}, and {ital n}=20(3{ital m}+3){sup 2}, where {ital m} is any non-negative integer. We have proposed a method for H{umlt u}ckel theory calculations that is based on combining the topology of fullerenes and the irreducible representation matrices as the elements of the secular equations. The method has been used to calculate the electronic structures of fullerenes C{sub {ital n}} ({ital I}{sub {ital h}}, {ital n}=60{ital k}{sup 2}) with the values of {ital k} from 1, 2, up to 25 in our previous papers. In this article this method has been further extended with some computational alterations to calculate the {pi} electronic energy levels of fullerenes C{sub {ital n}} [{ital I}{sub {ital h}}, {ital n}=20(3{ital m}+1){sup 2}, {ital n}=20(3{ital m}+2){sup 2}, and {ital n}=20(3{ital m}+3){sup 2}] with the values of {ital m} from 0, 1 up tomore » 12. From the calculated results of the 39 fullerene molecules certain general rules on the stability and chemical reactivity have been drawn for the three types of fullerenes. {copyright} {ital 1996 The American Physical Society.}« less