Computation of character tables for the permutation groups of weakly bound polymer molecules

Abstract

Permutation and permutation-inversion (PI) groups for dimer molecules have been extended to account for the trimers and higher polymers. It is shown that once the operations in the monomer groups are certified feasible, the character table for the polymer groups can easily be constructed. We give some formulae for obtaining the conjugacy classes of the symmetric and non-symmetric polymers. Using the Frobenius formula for characters of induced representations as well as Clifford's theorem simplified expressions have been given for obtaining the characters of the irreducible representations for various polymer groups. From this formulae, the permutation groups for ammonia trimer and tetramer as well as benzene trimer have been shown to consist of 1296, 31 104 and 10 368 symmetry operations, respectively. Character tables of non-symmetric trimer molecules of the type MM'N and MNL are relatively much easier to construct.