For the purpose of getting insight into the reason for the anomalous vibrational frequency shifts observed in some usually used solvents for a mode that has a large dipole derivative, the role of atomic quadrupoles in intermolecular electrostatic interactions is studied for some halogen-containing molecules (CX4, HX, and X-2 with X=F, Cl, and Br), CH4, CO2, and CS2. From the fitting to the electrostatic potentials around the molecules, large atomic quadrupoles are obtained for the chlorine, bromine, and sulfur atoms, suggesting that the atomic quadrupolar effect is important for electrostatic interactions around covalently bonded atoms on the third and higher rows in the periodic table. Taking the case of the chlorine atoms as an example, the electron densities inside the atoms in CCl4, HCl, and Cl-2 are examined. It is found that these electron densities are highly anisotropic. This anisotropy in electron densities is reasonably explained by the forms of the occupied molecular orbitals, and is considered to be the electronic structural origin of the large atomic quadrupoles. (C) 2003 American Institute of Physics.