  In this work, rate coefficients of four prototypical insertion reactions, X +
H2 -- H + XH (X=C(1D), N(2D), O(1D), S(1D)) and associated isotope reactions
are calculated based on ring polymer molecular dynamics (RPMD) with Cayley
propagator (Cayley-RPMD). The associated kinetic isotope effects (KIEs) are
systematically studied too. The Cayley propagator used in this work increases
the stability of numerical integration in RPMD calculations, and also supports
a larger evolution time interval, allowing us to reach both high accuracy and
efficiency. So, our results do not only provide chemical kinetic data for the
title reactions in an extended temperature range, but also consist of
experimental results, standard RPMD, and other theoretical methods. The results
in this work also reflect that Cayley-RPMD has strong consistency and high
reliability in the investigations of chemical dynamics for insertion reactions.
