Self-consistent pressure-dependent on-site Coulomb correction for zero-temperature equations of state of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>f</mml:mi></mml:math>-electron metals

The $f$-electron materials display many anomalous properties under pressure, making them of great interest in high-pressure physics and related industrial fields. However, the $f$-electrons pose a substantial challenge to simulations since the electron correlation effects. In this work, we present a first-principles calculation scheme for the equations of state (EoS) of $f$-electron materials. The self-consistent pressure-dependent on-site Coulomb correction is performed based on our recently developed doubly screened Coulomb correction approach. We investigated pressure dependence of the on-site Coulomb interaction, zero-temperature EoS over a wide range of pressures and the phase stabilities of four prototypical lanthanide and actinide metals, Pr, Eu, Th, and U. The simulated compressive properties agree better with the experimental data than those obtained by conventional density functional theory (DFT) and fixed-parameter $\mathrm{DFT}+U$ approaches. The pressure-induced phase transitions can also be well described.