A theory for calculating rates of transitions in quantum systems is pr
esented and applied to desorption of H-2 from a Cu(110) surface. The q
uantum transition state is defined as a conical dividing surface in th
e space of closed Feynman paths and a 'reaction coordinate' in this ex
tended space is used to parametrize a reversible work evaluation of th
e free energy barrier. In a low temperature, harmonic limit the theory
reduces to instanton theory. Above the cross-over temperature for tun
neling, the theory reduces to the centroid density approximation and i
n the classical limit, variational classical transition state theory i
s recovered. (C) 1997 Elsevier Science B.V.