Class Structure and Character Tables of Permutation Groups for Weakly Bound Polymer Molecules and Some Applications.
Permutation and permutation-inversion groups for polymer molecules have been systematically studied. This encompasses review of the permutation and permutation-inversion groups for dimer molecules, followed by extension to trimers, tetramers and higher polymer molecules. Some formulae for determining the conjugacy classes of both the symmetric and non-symmetric polymers are presented. It has been shown that the character tables for the polymer molecules are easy to construct once the feasible operations of the appropriate monomer groups are determined. The Frobenius formula for characters of induced representations and Clifford’s theorem has been used to compute the characters of the irreducible representations of the various polymer groups. The permutation groups for (NH3)3, (C6H6)3 and (NH3)4 have been found to consist of 1296, 10368 and 31104 elements while their various permutation-inversion groups have 2592, 20736 and 62208 elements respectively. The character tables of non-symmetric polymer molecules are relatively much easier to construct. A method for determining the nuclear spin functions and hence the statistical weights is presented using (H20)3 and (NH3)2 as examples. The general theory of the nuclear hyperfine structure has been simplified and this has been used in predicting the possible number of spectral transitions for some molecules.