The F₂ molecule is obtained by the linear combination of two F atomic orbitals. When two electrons are supplemented to the antibonding orbitals of the molecule F₂⁻⁻ molecule will be produced. It is identical to Ne. The molecular orbital energy level diagram is given in the attachment.
Bond order = 1/2 (Bonding electrons - Antibonding electrons)
= 1/2 (8 - 8)
= 0, thus, the molecule does not exist.