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As far as I know, an electric dipole exists between any two atoms in a polar covalent bond. And since a dipole moment is just how the size of an electric dipole is reported, any atoms with bonds in between ionic and covalent would have some kind of dipole moment. Enough electronegativity to cause a polar covalent bond should be sufficient for a dipole moment to occur.
Also, there is a dipole moment if a molecule is on some way unsymetric. For example, if the central atom has a lone pair or if the atoms attached to the central atom are different, the moleule will be polar and have a dipole moment.
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