Since ionic solids are not molecular, can a single sodium chloride unit exist and if so, what is such a unit called? I am aware of the concept of "formula units", but as far as I can tell, this is a notional term and does not describe any physical structure. Is "unit cell" the correct term and can a single unit cell exist?
Just to be sure people understand the question: I am talking about solid sodium chloride and not an aqueous solution of it.
A “formula unit” would be closer to the answer than a “unit cell”. A unit cell is used in crystallography to define the smallest repeating unit of the crystal that has all the symmetries of the overall crystal structure. For NaCl, there are a variety of different ways to visualize the unit cell (2 interpenetrating FCC lattices, FCC with a 2-atom basis, etc. ), but regardless, there are four formula units of NaCl in the NaCl unit cell (4 Na and 4 Cl atoms).
