Using semi-empirical density functional theory and the quasi-classical trajectory (QCT) method, a specific reaction parameter (SRP) density functional is developed for the dissociation of dihydrogen on Pt(111). The validity of the QCT method was established by showing that QCT calculations on reaction of D-2 with Pt(111) closely reproduce quantum dynamics results for reaction of D2 in its rovibrational ground state. With the SRP functional, QCT calculations reproduce experimental data on D2 sticking to Pt(111) at normal and off-normal incidence with chemical accuracy. The dissociation of dihydrogen on Pt(111) is non-activated, exhibiting a minimum barrier height of -8 meV. (C) 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).