Every covalent bond has some ionic character and every ionic bond some covalent character. I can understand why a completely ionic bond is an ideal situation. But completely covalent bonds can exist(?).
Take the case of $\ce{H_2}$ or any other diatomic molecule between identical atoms. How can these have any ionic character?
Answer
According to Pauling's famous The Nature of the Chemical Bond , 3rd edition, at page 73:
In the hydrogen molecule a quantum-mechanical treatment has shown that the two ionic structures $\ce{H+H-}$ and $\ce{H- H+}$ enter into resonance with the extreme covalent structure $\ce{H-H}$ only to a small extent, each ionic structure contributing only about 2 percent to the normal state of the molecule.
He goes on to state that other diatomics such as chlorine should have even less ionic character.
So all molecules, even homonuclear diatoms, have some ionic character.
For further information on diatomic hydrogen's ionic character see section 1.5 of the book and The Normal State of the Hydrogen Molecule Journal of Chemical Physics vol. 1, pages 593-596.
See also Overlaps of Trial Functions for the Hydrogen Molecule. II. Covalent and Ionic Character of H2 J. Chem. Phys. 23, 176
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