  The lack of computationally inexpensive and accurate ab-initio based
methodologies to predict lattice thermal conductivity, without computing the
anharmonic force constants or time-consuming ab-initio molecular dynamics, is
one of the obstacles preventing the accelerated discovery of new high or low
thermal conductivity materials. The Slack equation is the best alternative to
other more expensive methodologies but is highly dependent on two variables:
the acoustic Debye temperature, $\theta_a$, and the Gr\"{u}neisen parameter,
$\gamma$. Furthermore, different definitions can be used for these two
quantities depending on the model or approximation. In this article, we present
a combinatorial approach to elucidate which definitions of both variables
produce the best predictions of the lattice thermal conductivity, $\kappa_l$. A
set of 42 compounds was used to test accuracy and robustness of all possible
combinations. This approach is ideal for obtaining more accurate values than
fast screening models based on the Debye model, while being significantly less
expensive than methodologies that solve the Boltzmann transport equation.
