Exact Møller-Plesset Adiabatic Connection Correlation Energy Densities

The Møller–Plesset adiabatic connection (MPAC) provides a powerful tool for developing density functional theory (DFT)-like approximations that map Hartree–Fock densities to the wavefunction-based correlation energy, thereby leveraging both wavefunction and DFT concepts for electronic structure approximations. A key object in this context is the correlation energy density, which represents the local (pointwise) contribution to the total correlation energy. While well-studied in DFT, it remains largely unexplored in the wavefunction framework. Here, we introduce a rigorous formulation of the wavefunction-based correlation energy density within MPAC, implement it via full configuration interaction calculations, and analyze its behavior and physically meaningful contributions for representative small (di)atomic systems. We define this quantity by employing a general gauge strategy, from which the conventional DFT correlation energy density gauge also arises. We then discuss the resulting commonalities and differences between correlation energy densities in the DFT and wavefunction frameworks and derive the small-interaction (MP2) limit of the latter in terms of Hartree–Fock orbitals. Finally, we show how these newly introduced energy densities can serve as new approximation targets in both machine-learning-assisted and traditional electronic structure methods for mapping HF-density-based features to correlation energy within the wavefunction framework.