Equivalent spherical harmonics

Abstract

AbstractsIt is known that the 21 + 1 spherical harmonics Yr, can be transformed into cyclically equivalent orbitals, of which only a few examples have so far been given explicitly. In this article the 'totality of such cyclic sets is derived.

Angular dependence of Gaussian‐Lobe orbitals. II. Set of axial Gaussian‐Lobe orbitals

“…Their method is founded theoretically on the work of Powell [ 5 ] , who showed that two sets of five cyclically equivalent real d-orbitals can be constructed. Recently, Schmelzer [6] has generalized this result for any Yl-subspace in the case of finite rotation groups. Unfortunately the above equivalent d-functions are far from cylindrically symmetrical about their own axis, as demonstrated by Pauling and McClure [7] and, therefore, the statement of SR cannot be rigorously supported in this way.…”