Quantum information reveals that orbital-wise correlation is essentially classical in natural orbitals

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 enhances 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 address this question with a detailed investigation of molecular wavefunctions in terms of Shannon and von Neumann entropies, common tools of 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 ∼100-fold, when natural orbitals are used as reference. This finding suggests that orbital correlations, when viewed through the appropriate basis, are predominantly classical. Consequently, our study underscores the importance of using natural orbitals to accurately assess molecular orbital correlations and to avoid their overestimation.