Subgroup‐chain symmetry‐adapted irreducible matrices and CG coefficients of point groups

The irreducible matrices and Clebsch–Gordan coefficients of any crystallographic point group adapted to all possible canonical subgroup chains are calculated ab initio for both single‐valued and double‐valued representations and tabulated with exact values in the form of or and with components labeled by the irrep labels of the group chain in Koster notation. The phases and ordering of the components of irreducible bases for the cubic point groups are properly chosen so that irreducible matrices for all subgroup chains of G=T_d, O, O_h obey the associated relations D(G)=D(G)D(G), i=4, 6, and the complex conjugation relation for the group T, D(T)=D(T)*. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 67–80, 1999