  The notion of a d-critical locus is an ingredient in the definition of
motivic Donaldson-Thomas invariants by [BJM19]. In this paper we show that
there is a d-critical locus structure on the Hilbert scheme of dimension zero
subschemes on some local toric Calabi-Yau 3-folds. We also show that using this
d-critical locus structure and a choice of orientation data, the resulting
motivic invariants agree with the definition given by the previous work of
[BBS13].
