The recently suggested method of recovering the Landau exponent of the quasiclassical matrix elements from the attributes of classical motion is illustrated by way of an example of dissociating anharmonic oscillators. For a Morse oscillator, in which case the exact analytical results are available, the so-called improved semiclassical approximation that incorporates the Landau exponential yields quite accurate matrix elements for classically strongly forbidden events. This provides a firm support for the method of estimation of quasiclassical matrix elements between distant States from the information on the motion of system in the classically allowed region.