How is an Orbital Defined?

Undergraduate chemistry textbooks are not in full agreement over the question of whether an orbital should be defined as a wavefunction or as the square of a wavefunction. I argue here that the wavefunction definition is preferable both because it is Pauling’s original definition and because it is consistent with the terminology that molecular orbitals and hybrid orbitals are formed as linear combinations of atomic orbitals. Additionally, I discuss the fact that only single-electron spatial wavefunctions can be considered equivalent to orbitals.