Quantum mechanical tunneling and relaxation are multidisciplinary phenomena omnipresent in various fields of physics, chemistry and biology. Unfortunately for many practically interesting cases the exact quantum calculations are still prohibitively difficult. In such situations the semiclassical approximation is probably the most promising way to attack the problems.

We (the ILL theory group) use this strategy applying the so-called instanton version of the semiclassical theory (see e.g., references 1. and  2.) to a number of problems of chemical physics and chemical dynamics (radiationless transitions, conversion of electronic states, isomerization reactions and so on).

Few links below to illustrate this point:

Coherent versus incoherent vibrational relaxation in strongly asymmetric double - well systems (ref. 3.).

Tunneling spectroscopy of non-rigid multi-stable molecules (ref. 4.).

Landau Zener mechanism for ultrafast photoisomerization reactions (ref. 5.).

Stochastic like vibrational quantum dynamics in nano systems (ref. 6.)

References:

1. V.A.Benderskii, E.V.Vetoshkin, E.I.Kats, Instanton versus traditional
   WKB approach to the Landau-Zener problem, JETP, 97, 232 (2003).
2. V.A.Benderskii, E.V.Vetoshkin, E.I.Kats, Semiclassical quantization of
   bound and quasistationary states beyond the adiabatic approximation, Phys. Rev. A, 69, 062508 (2004).
3. V.A.Benderskii, E.I.Kats, Coherent oscillations and incoherent tunneling
   in a one-dimensional asymmetric double-well potential, Phys. Rev. E,  65, 036217 (2002).
4. V.A.Benderskii, E.V.Vetoshkin, E.I.Kats, H.P.Trommsdorff, Competing
   tunneling trajectories in a two-dimensional potential with variable topology as a model for quantum bifurcations, Phys. Rev.
   E, 67, 026102 (2003).
5. V.A.Benderskii, E.V.Vetoshkin, E.I.Kats, H.P.Trommsdorff, A semiclassical 1D model of ultrafast photoisomerization reactions, Chem. Phys. Lett., 409, 240 (2005).
6. V.A.Benderskii, L.A.Falkovsky, E.I.Kats, Loschmidt echo and stochastic-like quantum dynamics of nano particles, JETP Lett., 86, 221 (2007).