A hydrogen bond itself does not contain electrons in the same way a covalent bond does. Instead, it's an attractive force. While electrons participate in creating the partial charges that allow hydrogen bonds to form, the bond itself isn't a shared electron pair. There are no electrons in a hydrogen bond in the same sense that there are electrons shared in a covalent bond.
Here's a breakdown to clarify:
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What is a hydrogen bond? A hydrogen bond is an electrostatic attraction between a hydrogen atom that is covalently bonded to a highly electronegative atom (such as oxygen, nitrogen, or fluorine) and another electronegative atom in a different molecule or part of the same molecule.
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The role of electronegativity: The electronegative atom pulls electron density away from the hydrogen atom, giving the hydrogen a partial positive charge (δ+). The electronegative atom involved in the interaction has a partial negative charge (δ-).
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The attraction: The partial positive charge on the hydrogen atom is attracted to the partial negative charge on the electronegative atom in the other molecule or part of the molecule. This attraction is the hydrogen bond.
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Why no electrons "in" the bond: The hydrogen bond is fundamentally an intermolecular force. It's not a sharing of electrons (like a covalent bond) but an attraction of opposite partial charges. The electrons involved are already engaged in covalent bonds within the molecules participating in the hydrogen bond.
Think of it this way: A magnet attracts metal. The magnet doesn't contain the metal, it just exerts an attractive force on it. Similarly, the hydrogen bond is an attractive force, not a shared collection of electrons. The electrons are part of the underlying molecules exhibiting the partial charges that make the attraction possible.