An Investigation into Transition States of Cyclic Tetra-Atomic Silicon and Germanium Interstellar Dust Compounds: Si(x)C(4−x), Ge(x)C(4−x), and Ge(x)Si(4−x) (x ∈ {1, 2, 3})

Presented in this work is a thorough determination of the transition states between the different isomers of cyclic tetra-atomic silicon-carbide, germanium-carbide, and germanium-silicide clusters. Through use of density functional theory (B3LYP-D3BJ, M06-2X, ωB97X-D4, and B2GP-PLYP) in conjunction with the aug-cc-pVTZ basis set, transition state structures and their barrier heights are determined for the interconversions between the various isomers for the family of tetra-atomic SiC, GeC, and GeSi compounds. SiC dust grains are known to be prevalent in interstellar dust, and among this group, so far only diamond-shaped (d-)SiC(3) has been detected in the interstellar medium (ISM). Determining which other structures might be detectable not only depends on their intrinsic spectroscopic features, but whether or not they are likely to exist as isomers in interstellar environments. By examining the energy barrier heights for transitions between isomers, we determined that many of these structures are unlikely to exhibit interconversion in the ISM, outside of hotter circumstellar environments. Although Boltzmann population ratios at approximate circumstellar temperatures suggest the presence of higher energy minima, it is likely that once interconversion happens, as molecules travel away from a star and cool, they will get kinetically trapped in the potential energy well they inhabit, making how the ratios freeze out dependent on the time and pathways the molecules take to cool down. As such, many of these higher energy minima may still be good candidates for detection including (rhomboidal) r-SiC(3), r-GeC(3), r-GeSi(3), (trapezoidal) t-Si(2)C(2), r-Ge(2)C(2), and d-Si(3)C.