The tensor J8 contribution to the rotational energy of a tetrahedral molecule

Two methods are outlined for calculating the tensor distortion energy of a tetrahedral molecule to the eighth degree in the rotational angular momentum. In the first, the entire distortion Hamiltonian including the eighth-rank distortion tensor $\text{Ω}{}_8$ is diagonalized. In the second, the basis which diagonalizes only the fourth rank tensor $\text{Ω}{}_4$ is used to generate tables which allow the direct determination of the octic energy terms. For J ≤ 20, numerical values are given of the diagonal matrix elements of $\text{Ω}{}_8$ and of the second-order perturbation correction due to offdiagonal matrix elements of the sixth-rank tensor $\text{Ω}{}_6$. Explicit expressions in terms of angular momentum operators are given for $\text{Ω}{}_8$ and a selection of the operator equivalents T_8,m.