  The atomic third-order open-shell many-body perturbation theory is developed.
Special attention is paid to the generation and algebraic analysis of terms of
the wave operator and the effective Hamiltonian as well. Making use of
occupation-number representation and intermediate normalization, the
third-order deviations are worked out by employing a computational software
program that embodies the generalized Bloch equation. We prove that in the most
general case, the terms of effective interaction operator on the proposed
complete model space are generated by not more than eight types of the $n$-body
($n\geq2$) parts of the wave operator. To compose the effective Hamiltonian
matrix elements handily, the operators are written in irreducible tensor form.
We present the reduction scheme in a versatile disposition form, thus it is
suited for the coupled-cluster approach.
