  Starting from a set of different two- and three-nucleon interactions from
chiral effective field theory, we use the importance-truncated no-core shell
model for ab initio calculations of excitation energies as well as electric
quadrupole (E2) and magnetic dipole (M1) moments and transition strengths for
selected p-shell nuclei. We explore the sensitivity of the excitation energies
to the chiral interactions as a first step towards and systematic uncertainty
propagation from chiral inputs to nuclear structure observables. The
uncertainty band spanned by the different chiral interactions is typically in
agreement with experimental excitation energies, but we also identify
observables with notable discrepancies beyond the theoretical uncertainty that
reveal insufficiencies in the chiral interactions. For electromagnetic
observables we identify correlations among pairs of E2 or M1 observables based
on the ab initio calculations for the different interactions. We find extremely
robust correlations for E2 observables and illustrate how these correlations
can be used to predict one observable based on an experimental datum for the
second observable. In this way we circumvent convergence issues and arrive at
far more accurate results than any direct ab initio calculation. A prime
example for this approach is the quadrupole moment of the first 2^+ state in
C-12, which is predicted with an drastically improved accuracy.
