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F3- does not form a Lewis structure because F (Fluorine) has 7 valance electrons. F3 totals 21 valance electrons +1 for the - charge for a total of 22. However when you attempt to bond 3 F atoms together in a Lewis structure there is only space for 20 valance electrons. This is not a problem for atoms like Br or I because they can fit those extra electrons in the near by d orbital. Fluorine being a period 2 element does not have a d orbital and can not form a F3- Lewis structure.

-JCS

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