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

The structure of the anisotropic indirect quadrupolar spin-spin interaction, and its effect on the spin dynamics associated with pure NQR time-domain response, is considered in terms of spherical tensor operator bases and multipole theory. The advantages of symmetry-adapting the Liouville bases is discussed for I ≧ 3/2 spin systems. In particular, symmetrized state space bases for the n-fold quadrupole cluster under Sn 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 of the multipole calculations of the spin evolution under the specific spin-spin interaction term. Such systems are of especial interest on account of the nature of the molecular solids Br2 and I2.