  Based on the integral representation of the semiclassical propagator of
Herman and Kluk (HK), and in the limit of high temperatures, we formulate a
hybrid expression for the correlation function of infrared spectroscopy. This
is achieved by performing a partial linearization inside the integral over the
difference of phase space variables that occurs after a twofold application of
the HK propagator. A numerical case study for a coupled anharmonic oscillator
shows that already for a total number of only two degrees of freedom, one of
which is treated in the simplified manner, a substantial reduction of the
numerical effort is achieved.
