  Lattice thermal conductivity of Cu$_2$O was studied using ab initio density
functional methods. The performance of generalized gradient approximation,
GGA-PBE, and PBE0 exchange-correlation functionals was compared for various
electronic and phonon-related properties. 3d transition metal oxides such as
Cu$_2$O are known to be a challenging case for pure GGA functionals and in
comparison to GGA-PBE the PBE0 hybrid functional clearly improves the
description of both electronic and phonon-related properties. The most striking
difference is found in the lattice thermal conductivity, where GGA
underestimates it as much as 40% in comparison to experiment, while the
difference between the experiment and the PBE0 hybrid functional is only a few
percent.
