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We know that an Oxygen atom has two lone pairs. Why doesn't oxygen then form coordinate covalent bonds using those since it has nothing to lose?

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Oxygen very much does form bonds in which both electrons come from the oxygen atom. Examples include:

1. The $\ce{H3O^+}$ ion at the center of the solvated proton in aqueous acids, also available as salts of some of the strongest acids such as $\ce{(H3O)(ClO4)}$

2. Carbon monoxide, with its triple rather than double bond.

3. Ozone, in which the oxygen atoms form a bent chain and one of the three bonds must have both electrons coming from the middle atom. The resulting charge separation makes ozone one of the few one-element substances with a nonzero dipole moment.

Oscar Lanzi
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The number of complex compounds that are surrounded by water molecules is quite big , a few examples of water being a ligand include [Cu(H2O)4]2+ or [Co(H2O)6]2+. Anyway oxygen is indeed less eager to donate its electrons because its electronegativity is considerably high, nitrogen for example works better as a ligand (actually the first complex compounds to be observed and classified were with NH3 as ligands).But the examples where O donates his electrons can be found quite readily.