Machine Learning‐Assisted Second‐Order Perturbation Theory for Chemical Potential Correction Toward Hubbard <i>U</i> Determination

Determining the Hubbard U parameter is critical for characterizing the electronic structures of novel materials, especially atomic catalysts (ACs), where conventional linear response (CLR) and two‐way crossover linear response methods under density functional theory (DFT) often yield distinct results. This study integrates machine learning (ML) with second‐order perturbation theory to systematically derive the chemical potential in the Hubbard model, focusing on electron–electron interaction‐induced energy corrections. The framework establishes explicit relationships between perturbation energy, chemical potential, bandwidth ( W ), and particle number ( N ), with exponential decay terms quantifying bandwidth‐driven screening. It clarifies nonlinear U‐perturbation relationships and particle‐dependent corrections, which are critical for ACs with unique coordination environments. Validations in ACs and metal systems demonstrate that ML‐improved derivations resolve ambiguities in Hubbard U determination, enhancing the chemical potential prediction accuracy and linking U determinations to catalytic activity.