I particularly like the Figure below taken from a paper The radical character of the acenes: A density matrix renormalization group study by Johannes Hachmann, Jonathan Dorando, Michael Avilés, and Garnet Chan.
LUNO = lowest occupied natural orbital
Note how as the acene gets longer the spread in orbital occupation number increases.
In a nice review article Schmidt and Gordon state:
The presence of occupation numbers between 0.1 and 1.9 indicates considerable multireference character.(Multi-reference character means how many Slater determinants are required to describe the state.)
It seems to me that the spread in the above distribution gives a measure of the number orbitals M one needs to include in the active space of a Complete Active Space (CAS) calculation. In a Hartree-Fock calculation the occupations are all 2 or 0. The number of natural orbital occupations that deviate significantly from 2 or 0 is a good measure of M. It may be possible to relate this to various quantum entanglement measures.
Readers with backgrounds in solid state physics may note the similarity to the above picture to how in Fermi liquids one can quantify the strong electronic correlations in terms of the discontinuity in orbital occupation number at the Fermi surface (discussed in an earlier post).