  In this contribution we assess the performance of two different
exchange-correlation functionals in the first-principle prediction of the
lattice thermal conductivity of bulk semiconductors, namely the local density
approximation (LDA) and the Perdew-Burke-Ernzerhof implementation of the
generalized gradient approximation (GGA). Both functionals are shown to give
results in good agreement with experimental measurements. Such a consistency
between the two functionals may seem a bit surprising, as the LDA is known to
overbind and the GGA to soften the interatomic bonds. Such features ought to
greatly affect the value of the system interatomic force constants (IFCs) which
are necessary for the first-principle prediction of the lattice thermal
conductivity. In this study we show that the errors introduced by such
approximations tend to cancel themselves. In the case of LDA, the overbinding
generates larger absolute third-order IFCs, which tend to increase the
three-phonon scattering rates. On the other hand, larger absolute second-order
IFCs lead to a a larger acoustic-optical phonon band gap which in turns
decrease the available phase space for three-phonon scattering, compensating
the increase in the scattering rates due to stiffer IFCs.
