Molecular dynamics simulations are used to investigate typical coordination shells of molecules in the liquid water surface, for two potential energy surfaces. The major undercoordinated species found in the surface include three-coordinated H2O with either a dangling-H or a dangling-O atom and two-coordinated H2O with one hydrogen bond via H, and another via O. Vibrational signatures of the different coordinations are calculated. The 3400 cm(-1) band in the surface sum frequency generation (SFG) spectrum is assigned to four-coordinated molecules within the surface layer. The low-frequency wing of the OH-stretch band, near 3200 cm(-1) in the SFG spectrum, is proposed to be due to collective excitations of a relatively small number of intermolecularly coupled O-H bond vibrations.