  We present a combined experimental and theoretical study of the spectrum of
magnetically tunable Feshbach resonances in NaLi $(a^3\Sigma^+)$ $+$ Na
collisions. In the accompanying paper, we observe experimentally 8 and 17
resonances occur between $B=0$ and $1400$~G in upper and lower spin-stretched
states, respectively. Here, we perform ab initio calculations of the NaLi $+$
Na interaction potential and describe in detail the coupled-channel scattering
calculations of the Feshbach resonance spectrum. The positions of the
resonances cannot be predicted with realistic uncertainty in the
state-of-the-art ab initio potential, but our calculations yield a typical
number of resonances that is in near-quantitative agreement with experiment. We
show that the main coupling mechanism results from spin-rotation and spin-spin
couplings in combination with the anisotropic atom-molecule interaction. The
calculations furthermore explain the qualitative difference between the numbers
of resonances in either spin state.
