Knowledge Bank

Recent interest in high resolution vibration-rotation spectra of octahedral $XY6$ molecules has motivated a study of $techniques1$ for computation of cubic harmonics, i.e., linear combinations of spherical harmonics which transform according to tetrahedral and octahedral symmetry. Choleski factorization is used explicitly to develop complete sets of orthonormal symmetry-adapted $functions2$ for very high values of J. Properties of $dJKK\prime (\pi$/2) are investigated as they relate to internal consistency of this application of the Choleski technique.