  In this work, we present a systematic first-principles density-functional
theory based study of geometry, electronic structure, and optical properties of
armchair phosphorene nanoribbons (APNRs), with the aim of understanding the
influence of edge passivation. Ribbons of width ranging from 0.33 nm to 3.8 nm
were considered, with their edges functionalized with the groups H, OH, F, Cl,
S, and Se. The geometries of various APNRs were optimized, and the stability
was checked by calculating their formation energies. Using the relaxed
geometries, calculations of their band structure and optical properties were
performed. Pristine APNRs, as expected, exhibit significant edge
reconstruction, rendering them indirect band gap semiconductors, except for one
width {\normalsize{}($N=5$, where $N$ is the width parameter)} for which a
direct band gap is observed. The edge passivated APNRs are found to be direct
band gap semiconductors, with the band gap at the $\Gamma$-point, for all the
functional groups considered in this work. To obtain accurate estimates of band
gaps, calculations were also performed using HSE06 hybrid functional for
several APNRs. Our calculations reveal that functional groups have significant
influence on the band gaps and optical properties of narrower APNRs. For wider
passivated ribbons, with the increasing ribbon widths, the gaps converge to
almost the same value, irrespective of the group. We also performed
calculations including the spin-orbit coupling (SOC) for hydrogen passivated
APNRs with $N=5$ and 11. We found that SOC has no significant influence on the
band structure of the studied APNRs. However, for the broader APNR, a lowering
of peak intensities was observed in the optical absorption spectrum beyond 5
eV.
