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The Lewis structure of nitrogen dioxide requires that the central atom nitrogen be bonded to one oxygen through a double covalent bond and to another oxygen through an unusual 'three electron bond'. Only in this way could all the atoms satisfy their octets. Out of these three electrons, any two get their spins paired up, leaving one electron unpaired. So the molecule should have been one electron paramagnetic.
Another less appreciated concept of bonding in NO2 is that nitrogen is involved in a dative covalent bonding with the other oxygen. This leaves nitrogen to be octet-deficient, and the odd electron is supposed to be placed above N.
But if two NO2 units dimerize through N-N bond formation, there is no necessity of such unusual conceptualisation. The odd electron on N couples with that of another molecule. This way, octet of each nitrogen atom is fulfilled. Pairing of odd electrons means that the molecule is no longer paramagnetic. It should be diamagnetic in nature.
That is the reason NO2 exists as dimers, i.e N2O4.
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