[Jekel0000]

NH₄ is called Ammonium
NH₄⁺ is called the Ammonium ion...

Lewis structures say the valence on a
NH4 has 9 valence electrons and Nitrogen needs a electron count of 5 for no formal charge, the number of bonds with the hydrogen count on the molecule make 8 used electrons for 9 - 8 = 1 therefore NH4 would have no formal charge if the was a free radical circling around the Nitrogen in the molecule...

is it possible for NH4 to have a free radical on the molecule around the Nitrogen to have no formal charge?

[Hunter2]

It is not existing. Maybe in short time in space. Ammonium has positive charge.

[Borek]

NH₄ is called Ammonium

Is it? I don't think I have seen it used this way. Each time I see "ammonium" I feel like it is really referring to the NH₄⁺ cation.

[Corribus]

A search for "neutral ammonium radical" turned up these results:

http://www.rsc.org/chemistryworld/News/2011/September/23091104.asp
http://pubs.acs.org/doi/abs/10.1021/ed045p40?journalCode=jceda8