Beyond Electrons: Correlation and Self‐Energy in Multicomponent Density Functional Theory

Post‐Kohn‐Sham methods are used to evaluate the ground‐state correlation energy and the orbital self‐energy of systems consisting of multiple flavors of different fermions. Starting from multicomponent density functional theory, suitable ways to arrive at the corresponding multicomponent random‐phase approximation and the multicomponent Green's function approximation, including relativistic effects, are outlined. Given the importance of both of this methods in the development of modern Kohn–Sham density functional approximations, this work will provide a foundation to design advanced multicomponent density functional approximations. Additionally, the quasiparticle energies are needed to study light‐matter interactions with the Bethe‐Salpeter equation.