CHEMICAL APPLICATIONS OF TOPOLOGY AND GROUP-THEORY .31. ATOMIC ORBITAL GRAPHS AND THE SHAPES OF THE G-ORBITALS AND H-ORBITALS

Atomic orbitals, which are described by the quantum numbers n, l, and m, can be depicted by an orbital graph in which the vertices correspon d to the lobes of the atomic orbitals and the edges to nodes between a djacent lobes of opposite sign. The orbital graph for the unique orbit al with m = 0 for a given value of l consists of a linear graph with l + 1 vertices. The orbital graphs for the pair of orbitals with m = +/ -l consist of polygons with 2l vertices. The orbital graphs for the re maining 2(l - 1) orbitals with 0 < /m/ < l consist of a stack of l + 1 - /m/ polygons each with /2m/ vertices. For a given value of 1 the at omic orbitals with /m/ = k and /m'/ = l + 1 - k have the same numbers of lobes. Orbital graphs are useful for understanding not only the sha pes of atomic orbitals of high nodality but also the shapes of the mol ecular orbitals in molecules approximated by a sphere such as the C-60 fullerene.