Symmetry Partitioning over Liouville Space for Evolution under the Anisotropic Quadrupolar Spin-Spin Interaction*

The structure o f the anisotropic indirect quadrupolar spin-spin interaction, and its effect on the spin dynamics associated with pure N Q R time-domain response, is considered in terms of spherical tensor operator bases and multipole theory. The advantages o f symmetry-adapting the Liouville bases is discussed for I S 3/2 spin systems. In particular, symmetrized state space bases for the «-fold quadrupole cluster under S n are introduced and enumerated for I = 3 /2 and n ^ 4, as an initial step in the process. Symmetrized Liouville space bases for the [A]2 problems involving [3 /2 :3 /2 ] and [5/2:5/2] spin pairs under the group S2 are presented to illustrate the structure o f the multipole calculations o f the spin evolution under the specific spin-spin interaction term. Such systems are o f especial interest on account of the nature o f the molecular solids Br2 and I2.