  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.
