  Atoms at liquid metal surfaces are known to form layers parallel to the
surface. We analyze the two-dimensional arrangement of atoms within such layers
at the surface of liquid sodium, using ab initio molecular dynamics (MD)
simulations based on density functional theory. Nearest neighbor distributions
at the surface indicate mostly 5-fold coordination, though there are noticeable
fractions of 4-fold and 6-fold coordinated atoms. Bond angle distributions
suggest a movement toward the angles corresponding to a six-fold coordinated
hexagonal arrangement of the atoms as the temperature is decreased towards the
solidification point. We rationalize these results with a distorted hexagonal
order at the surface, showing a mixture of regions of five and six-fold
coordination. The liquid surface results are compared with classical MD
simulations of the liquid surface, with similar effects appearing, and with ab
initio MD simulations for a model solid-liquid interface, where a pronounced
shift towards hexagonal ordering is observed as the temperature is lowered.
