  In this paper we calculate the motivic Donaldson-Thomas invariants for
(-2)-curves arising from 3-fold flopping contractions in the minimal model
programme. We translate this geometric situation into the machinery developed
by Kontsevich and Soibelman, and using the results and framework developed
previously by the authors we describe the monodromy on these invariants. In
particular, in contrast to all existing known Donaldson-Thomas invariants for
small resolutions of Gorenstein singularities these monodromy actions are
nontrivial.
