The compound which does not exist is

We need to identify which compound does not exist among the given options.

Option A: NaO$$_2$$ (Sodium superoxide)

Alkali metals react with oxygen to form different products. Lithium forms Li$$_2$$O (oxide), sodium forms Na$$_2$$O$$_2$$ (peroxide), and potassium/rubidium/cesium form superoxides (KO$$_2$$, RbO$$_2$$, CsO$$_2$$). Sodium does not readily form a stable superoxide NaO$$_2$$ under normal conditions. This compound is considered non-existent or extremely unstable.

Option B: BeH$$_2$$ - Beryllium hydride exists as a polymeric solid.

Option C: PbEt$$_4$$ - Tetraethyl lead exists and was historically used as an anti-knock agent in gasoline.

Option D: NH$$_4$$BeF$$_4$$ - Ammonium tetrafluoroberyllate is a known compound.

The correct answer is Option A: NaO$$_2$$.