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Why do Ionic compounds not combine as single molecules?
The smallest particles of ionic compounds are not molecules, but a collection of ions arranged in a regular pattern(crystals).
For example, each unit of a NaCl crystal consists of a Na+cation surrounded by 6 Cl-anions.
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Because the term 'molecule' signifies that atoms are joined together and that their orbitals are mixed. It means a covalent bond.
But in ionic bond, the atoms are not 'joined' together, rather they are held together by electrostatic forces of attraction between them.
So a molecule more or less represents a new identity where as an ionic bond is just two ions being attracted toward one another?
Yes. More or less. But an ionic bond also has its own unique identity, which is given by the structure of its crystal lattice. Refer to the topic The Solid State.
Also, how do the orbitals 'mix'? The chemistry books I use use the space filling model, but when two atoms combine to form a molecule, how do the orbitals change?