Electron Correlation in Chemical Bonding: From Dispersion to Covalent Stabilization in Prototype Diatomic Systems

The interplay between electron correlation and chemical bonding remains a central issue in quantum chemistry. While covalent bonds arise from electron sharing and long-range interactions from weak correlation, the quantitative connection between these regimes is not fully understood. In this work, we combine ab initio Quantum Monte Carlo (QMC) and Hartree-Fock (HF) calculations to examine how correlation contributes to bonding in the prototypical diatomic systems H2, LiH, and Li2. By mapping correlation energies and reaction forces along the full dissociation coordinate, we show that correlation gives rise to the asymptotic long-range dispersion attraction between separated neutral fragments, while also modifying the interaction at shorter bond distances. Near equilibrium, HF interactions dominate in H2 and LiH, although correlation contributes significantly to the binding energy, reaching about 41% in LiH. In H2, the correlation contribution to the interatomic force becomes repulsive near equilibrium, giving a force-level interpretation of the well-known shift of the correlated equilibrium bond length relative to the HF result. In contrast, in Li2, correlation accounts for nearly 80% of the binding energy, indicating that stabilization can arise primarily from correlation when HF attraction is weak. These results provide a quantitative and physically transparent characterization of how electron correlation contributes across different bonding regimes in representative diatomic systems. The present analysis offers a consistent interpretation of the evolution from long-range dispersion to short-range covalent stabilization within computationally reliable prototype molecules.