Context <p>Trivalent C<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(_{22}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>22</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> cages are explored with the recent generation of Gaussian approximation potential (GAP-20) and density functional theory (DFT) calculations. Using the GAP-20 to approximate the energy landscape significantly reduces the search time and provides superior starting structures for DFT optimization. The GAP-20, however, fails to capture the Jahn-Teller distortion. The relative GAP-20 energies are overestimated, and the vibrational modes/frequencies are poorly characterized.</p> Methods <p>Via the CALYPSO package, particle swarm optimization is employed to explore the configuration space. Energies/forces are calculated via the QUIP/LAMMPS module, employing the GAP-20. Structural relaxation follows the conjugate gradient method to a force precision of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(10^{-7} \text { eV}/\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>7</mn> </mrow> </msup> <mspace width="0.333333em" /> <mtext>eV</mtext> <mo stretchy="false">/</mo> </mrow> </math></EquationSource> </InlineEquation>Å. Cage isomers are further optimized by DFT, utilizing BFGS optimization scheme, until forces are below 0.05 eV/Å. The <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\text {B3LYP/6-31+G}*\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>B3LYP/6-31+G</mtext> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation> level of theory is applied, as implemented in the NWChem software. Vibrational analysis is performed to study the stability/infrared spectra.</p>