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Computing thermal transport from first-principles in UO$_2$ is complicateddue to the challenges associated with Mott physics. Here we use irreduciblederivative approaches to compute the cubic and quartic phonon interactions inUO$_2$ from first-principles, and we perform enhanced thermal transportcomputations by evaluating the phonon Green's function via self-consistentdiagrammatic perturbation theory. Our predicted phonon lifetimes at $T=600$ Kagree well with our inelastic neutron scattering measurements across the entireBrillouin zone, and our thermal conductivity predictions agree well withprevious measurements. Both the changes due to thermal expansion andself-consistent contributions are nontrivial at high temperatures, though theeffects tend to cancel, and interband transitions yield a substantialcontribution.

Phonon thermal transport in UO$_2$ via self-consistent perturbation theory