The electronic structures of the As/Si(001) 2\ifmmode\times\else\texttimes\fi{}1 and Sb/Si(001) 2\ifmmode\times\else\texttimes\fi{}1 surfaces with symmetric dimers are calculated self-consistently with the use of planar basis functions made of two-dimensional plane waves and one-dimensional Gaussian functions, based on local-density-approximation and norm-conserving pseudopotentials. The calculations show that both the As/Si(001) 2\ifmmode\times\else\texttimes\fi{}1 and Sb/Si(001) 2\ifmmode\times\else\texttimes\fi{}1 surfaces are semiconductors with energy gaps of about 1.0 eV. Both As and Sb surface bands have similar dispersion and are very different from that of the Si(001)2\ifmmode\times\else\texttimes\fi{}1 surface. The calculated dispersion of surface states for As/Si(001) is in good agreement with the angle-resolved photoemission measurements. The calculated work functions are 5.56 and 4.03 eV for As/Si(001) and Sb/Si(001) surfaces, respectively. We find substantial charge transfer for the As/Si(001) surface, indicating a strong ionic character in the As-Si bonds and small charge transfer for the Sb/Si(001) surface, indicating covalent character in the Sb-Si bonds. The strong polar covalent bonding between surface As atoms and underlying Si atoms may be responsible for the stability of the As/Si(001) surface.