  This paper sets out a robust methodology for modelling spectra of polyatomic
molecules produced in reactive or dissociative environments, with vibrational
populations outside local thermal equilibrium (LTE). The methodology is based
on accurate, extensive ro-vibrational line lists containing transitions with
high vibrational excitations and relies on the detailed ro-vibrational
assignments. The developed methodology is applied to model non-LTE IR and
visible spectra of silylene (SiH$_2$) produced in a decomposition of disilane
(Si$_2$H$_6$), a reaction of technological importance. Two approaches for
non-LTE vibrational populations of the product SiH$_2$ are introduced: a
simplistic 1D approach based on the Harmonic approximation and a full 3D model
incorporating accurate vibrational wavefunctions of SiH$_2$ computed
variationally with the TROVE (Theoretical ROVibrational Energy) program. We
show how their non-LTE spectral signatures can be used to trace different
reaction channels of molecular dissociations.
