One of the earliest attempts at virtual space localization was through projected atomic orbitals (PAOs). Since the span of the atomic orbital (AO) space is the same as the molecular orbital (MO) space, a set of linearly dependent functions that span the virtual space can be formed by subtracting out the span of the occupied space from the complete AO space. These are known as projected atomic orbitals (PAOs). PAOs have a more local character compared to canonical virtual molecular orbitals.