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 a full version of density functional theory. Nearest neighbor distributions at the surface indicate mostly fivefold coordination, though there are noticeable fractions of fourfold and sixfold coordinated atoms. Bond angle distributions suggest a movement toward the angles corresponding to a sixfold coordinated hexagonal arrangement of the atoms as the temperature is decreased towards the solidification point. We rationalize these results with a distorted hexagonal model at the surface, showing a mixture of regions of five- and sixfold 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. (c) 2007 American Institute of Physics.