Møller-Plesset and Density-Fixed Adiabatic Connections for a Model Diatomic System at Different Correlation Regimes

In recent years, adiabatic connection (AC) interpolations developed within density functional theory (DFT) have been found to provide good performances in the calculation of interaction energies when used with Hartree-Fock (HF) ingredients. The physical and mathematical reasons for such unanticipated performance have been clarified, to some extent, by studying the strong-interaction limit of the Møller-Plesset (MP) AC. In this work, we calculate both the MP and the DFT AC integrand for the asymmetric Hubbard dimer, which allows for a systematic investigation of different correlation regimes by varying two simple parameters in the Hamiltonian: the external potential, Δv, and the interaction strength, U. Notably, we find that, while the DFT AC integrand appears to be convex in the full parameter space, the MP integrand may change curvature twice. Furthermore, we discuss different aspects of the second-order expansion of the correlation energy in each AC, and we demonstrate why the derivative of the λ-dependent density in the MP AC at λ = 0 (i.e., at the HF density) is zero in the model. Concerning the strong-interaction limit of both ACs in the Hubbard dimer setting, we show that the asymptotic value of the MP AC, W_∞^HF, is lower than (or equal to) its DFT analogue, W_∞^KS, if the two are compared at a given density, just like in real space. However, we also show that this is not always the case if the two quantities are compared at a given external potential.