Recently there has been considerable interest in the subject of molecules, which are weakly bound states of hadron pairs. The question of the existence of molecules is closely related to the more general problem of the determination of low energy hadron-hadron scattering amplitudes, which is widely believed to require nonperturbative methods. In this contribution we report on quark model calculations using a simple perturbative scattering mechanism, one gluon exchange followed by constituent interchange. We refer to the associated diagrams as ``quark Born diagrams". For the cases chosen to isolate this mechanism, I=2 $����$, I=3/2 K$��$ and KN the results are usually in good agreement with experimental S-wave scattering amplitudes given standard potential model parameters, and for NN we find perturbative results very similar to the nonperturbative hard cores of Oka and Yazaki. We also discuss our findings for other less familiar channels; these include predictions of vector-vector bound states, one of which may be the $��(1710)$.

(Expanded version of results presented at Few Body XIV, Williamsburg, Virginia, 26-31 May 1994), LATEX using epsfig and wrapfig. postscript file incorporating figures available by anonymous ftp to COMPSCI.CAS.VANDERBILT.EDU, subdirectory QSM, file fbpp.ps