Estimating Coulomb interaction strength U using constrained dynamical mean-field theory method

Accurate first-principles estimation of the screened Coulomb interaction (U), which is both material- and method-dependent, is crucial for understanding correlated materials. The screening arises from physical processes not inherently captured by the many-body method, making the U method-dependent. In the case of the embedded dynamical mean-field theory (eDMFT), which employs quasi-localized atomic basis functions for the interaction part of the Hamiltonian and the full Kohn-Sham basis for the kinetic energy part, conventional screening estimation approaches are inadequate. In this work, we compute U using constrained eDMFT, which incorporates essential vertex corrections that are often neglected in other methods, such as constrained-RPA or constrained-DFT methods. By calculating the total energy of a large supercell and the charging energies for a single impurity atom at the center, we estimate the screening of multiple layers of neighbors treated via the eDMFT method. Our computed U values span a range of material classes—including correlated metals, insulators, altermagnets, superconducting nickelates and pnictides. We observe that U for materials with open s, p, d, and f shells clusters around a few characteristic values, which are primarily determined by the correlated atom type, valence and bonding environment. Notably, the dependence of U on material specifics is less pronounced in eDMFT compared to DFT+U, where fine-tuning is often required.