  We explore the impact of optimizations of the single-particle basis on the
convergence behavior and robustness of ab initio no-core shell model
calculations. Our focus is on novel basis sets defined by the natural orbitals
of a correlated one-body density matrix that is obtained in second-order
many-body perturbation theory. Using a perturbatively improved density matrix
as starting point informs the single-particle basis about the dominant
correlation effects on the global structure of the many-body state, while
keeping the computational cost for the basis optimization at a minimum. Already
the comparison of the radial single-particle wavefunctions reveals the
superiority of the natural-orbital basis compared to a Hartree-Fock or harmonic
oscillator basis, and it highlights pathologies of the Hartree-Fock basis. We
compare the model-space convergence of energies, root-mean-square radii, and
selected electromagnetic observables with all three basis sets for selected
p-shell nuclei using chiral interactions with explicit three-nucleon terms. In
all cases the natural-orbital basis provides the fastest and most robust
convergence, making it the most efficient basis for no-core shell model
calculations. As an application we present no-core shell model calculations for
the ground-state energies of all oxygen isotopes and assess the accuracy of the
normal-ordered two-body approximation of the three-nucleon interaction in the
natural-orbital basis.
