  The intersection of Quantum Chemistry and Quantum Computing has led to
significant advancements in understanding the potential of using quantum
devices for the efficient calculation of molecular energies. Simultaneously,
this intersection is enhancing the comprehension of quantum chemical properties
through the use of quantum computing and quantum information tools. This paper
tackles a key question in this relationship: Is the nature of the orbital-wise
electron correlations in wavefunctions of realistic prototypical cases
classical or quantum?
  We delve into this inquiry with a comprehensive examination of molecular
wavefunctions using Shannon and von Neumann entropies, alongside classical and
quantum information theory. Our analysis reveals a notable distinction between
classical and quantum mutual information in molecular systems when analyzed
with Hartree-Fock canonical orbitals. However, this difference decreases
dramatically, by approximately 100-fold, when Natural Orbitals are used as
reference. This finding suggests that wavefunction correlations, when viewed
through the appropriate orbital basis, are predominantly classical. This
insight indicates that computational tasks in quantum chemistry could be
significantly simplified by employing Natural Orbitals. Consequently, our study
underscores the importance of using Natural Orbitals to accurately assess
molecular wavefunction correlations and to avoid their overestimation. In
summary, our results suggest a promising path for computational simplification
in quantum chemistry, advocating for the wider adoption of Natural Orbitals and
raising questions about the actual computational complexity of the multi-body
problem in quantum chemistry.
