  Ab initio no-core configuration interaction (NCCI) calculations for the
nuclear many-body problem have traditionally relied upon an antisymmetrized
product (Slater determinant) basis built from harmonic oscillator orbitals. The
accuracy of such calculations is limited by the finite dimensions which are
computationally feasible for the truncated many-body space. We therefore seek
to improve the accuracy obtained for a given basis size by optimizing the
choice of single-particle orbitals. Natural orbitals, which diagonalize the
one-body density matrix, provide a basis which maximizes the occupation of
low-lying orbitals, thus accelerating convergence in a
configuration-interaction basis, while also possibly providing physical insight
into the single-particle structure of the many-body wave function. We describe
the implementation of natural orbitals in the NCCI framework, and examine the
nature of the natural orbitals thus obtained, the properties of the resulting
many-body wave functions, and the convergence of observables. After taking
$^3\mathrm{He}$ as an illustrative testbed, we explore aspects of NCCI
calculations with natural orbitals for the ground state of the $p$-shell
neutron halo nucleus $^6\mathrm{He}$.
