  Microcanonical instanton theory offers the promise of providing rate
constants for chemical reactions including quantum tunneling of atoms over the
whole temperature range. We discuss different rate expressions, which require
the calculation of stability parameters of the instantons. The traditional way
of obtaining these stability parameters is shown to be numerically unstable in
practical applications. We provide three alternative algorithms to obtain such
stability parameters for non-separable systems, i.e., systems in which the
vibrational modes perpendicular to the instanton path couple to movement along
the path. We show the applicability of our algorithms on two molecular systems:
H$_2$ + OH $\rightarrow$ H$_2$O + H using a fitted potential energy surface and
HNCO + H $\rightarrow$ NH$_2$CO using a potential obtained on-the-fly from
density functional calculations.
