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A non-bonding molecular orbital or NBMO is a molecular orbital which do not contribute to the stability of the molecule, whether it is occupied by electrons or not. That is because the energy of NBMO stays the same in the molecule as it would in an atom.
Take an example of a molecule where one atom has many more electrons than the other, say hydrogen fluoride, HF. The lone electron of hydrogen will enable it to form bonding and antibonding orbitals with 2`p_z` orbital of fluorine. Here, the NBMOs are `p_x` and `p_y` orbitals, as they do not have any other orbital to combine with. As already stated, the energy of these orbitals will be the same in the molecule, HF, as it is in the fluorine atom and hence occupation of these NBMOs by electrons will not lend stability to the molecule.
Hope this helps.
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