A simple model for ultrafast and efficient photoisomerization reactions is presented. In this model, the relevant region of the potential results from double crossing of two harmonic 1D diabatic potentials with opposite curvature. The eigenvalue problem is solved within a semiclassical approximation using the method of connection matrices, and the propagation of wave packets, expanded over these semiclassical eigenfunctions, is calculated. Within this model, fast double non-adiabatic transitions through both crossing points circumvent slow tunneling through the potential barrier. The extension to real systems makes this model relevant for the design of bi-stable photochromic materials. (c) 2005 Elsevier B.V. All rights reserved.