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Reconciling spectroscopy with dynamics in global potential energy surfaces: the case of the astrophysically relevant SiC$_{2}$

SiC$_2$ is a fascinating molecule due to its unusual bonding and astrophysical importance. In this work, we report the first global potential energy surface (PES) for ground-state SiC$_2$ using the combined-hyperbolic-inverse-power-representation (CHIPR) method and accurate ab initio energies. The calibration grid data is obtained via a general dual-level protocol developed afresh herein that entails both coupled-cluster and multireference configuration interaction energies jointly extrapolated to the complete basis set limit. Such an approach is specially devised to recover much of the spectroscopy from the PES, while still permitting a proper fragmentation of the system to allow for reaction dynamics studies. Besides describing accurately the valence strongly-bound region that includes both the cyclic global minimum and isomerization barriers, the final analytic PES form is shown to properly reproduce dissociation energies, diatomic potentials, and long-range interactions at all asymptotic channels, in addition to naturally reflect the correct permutational symmetry of the potential. Bound vibrational state calculations have been carried out, unveiling an excellent match of the available experimental data on $c$-$\mathrm{SiC}_{2}(^{1}A_1)$. To further exploit the global nature of the PES, exploratory quasi-classical trajectory calculations for the endothermic $\mathrm{C_{2}\!+\!Si}\rightarrow\mathrm{SiC\!+\!C}$ reaction are also performed, yielding thermalized rate coefficients for temperatures up to $5000$ K. The results hint for the prominence of this reaction in the innermost layers of the circumstellar envelopes around carbon-rich stars, thence conceivably playing therein a key contribution to the gas-phase formation of SiC, and eventually, solid SiC dust.