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.
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