  In this paper, we apply Lagrangian descriptors to study the invariant
manifolds that emerge from the top of two barriers existing in the LiCN<->LiNC
isomerization reaction. We demonstrate that the integration times must be large
enough compared with the characteristic stability exponents of the periodic
orbit under study. The invariant manifolds manifest as singularities in the
Lagrangian descriptors. Furthermore, we develop an equivalent potential energy
surface with 2 degrees of freedom, which reproduces with a great accuracy
previous results [Phys. Rev. E 99, 032221 (2019)]. This surface allows the use
of an adiabatic approximation to develop a more simplified potential energy
with solely 1 degree of freedom. The reduced dimensional model is still able to
qualitatively describe the results observed with the original
2-degrees-of-freedom potential energy landscape. Likewise, it is also used to
study in a more simple manner the influence on the Lagrangian descriptors of a
bifurcation, where some of the previous invariant manifolds emerge, even before
it takes place.
