  We discuss the approximate inclusion of three-nucleon interactions into ab
initio nuclear structure calculations using a multi-reference formulation of
normal ordering and Wick's theorem. Following the successful application of
single-reference normal ordering for the study of ground states of closed-shell
nuclei, e.g., in coupled-cluster theory, multi-reference normal ordering opens
a path to open-shell nuclei and excited states. Based on different
multi-determinantal reference states we benchmark the truncation of the
normal-ordered Hamiltonian at the two-body level in no-core shell-model
calculations for p-shell nuclei, including 6-Li, 12-C, and 10-B. We find that
this multi-reference normal-ordered two-body approximation is able to capture
the effects of the 3N interaction with sufficient accuracy, both, for
ground-state and excitation energies, at the computational cost of a two-body
Hamiltonian. It is robust with respect to the choice of reference states and
has a multitude of applications in ab initio nuclear structure calculations of
open-shell nuclei and their excitations as well as in nuclear reaction studies.
