Contraction algorithms for third-order reduced density matrices: Symmetric group approach

In this work, we present the mapping formulae for the contraction of the third-order reduced density matrices represented in the basis of the irreducible representations (IR) of the symmetric group S3 into the second-order ones which are represented in the basis of the IR of group S2. These algorithms, which can be useful in several fields, have been applied for the approximation of reduced density matrices within the spin-adapted reduced Hamiltonian theory. Some results obtained with this procedure are also presented.