Calculations on surface-supported clusters were performed using plane-wave DFT in VASP, using the PBE exchange-correlation functional and PAW pseudopotentials. Dispersion effects were described by the DFT-D3 method. Unit cells were constructed from a 5-layer 3x3 supercell of Al2O3 with a vacuum gap of 1 nm or more, and the lower layers of the slab were kept fixed during global optimization and subsequent adsorbate binding calculations. The plane-wave cut-off was 400 eV for structural optimizations, and Gaussian smearing with a width of 0.1 eV was used. Gamma-point sampling was used for all calculations due to the large supercell used in the study. Structural sampling was performed with our in-house code PGOPT and GOCIA (available with documentation on GitHub) to generate 500 chemically reasonable initial structures per cluster, which we later refined with DFT. The convergence criteria for electronic minimization and ionic optimization were 10 -6 eV and 0.02 eV/Å, respectively. QTAIM analysis was performed using the Bader program. Unique, rough binding modes of C2H4 and CO (20 binding modes per adsorbate for each Pt7 isomer, 30 for Pt7Ge2, and 40 for Pt7Ge2C2) for the thermally accessible structures were generated using PGOPT with a bond-length distribution algorithm, which we later refined at the same DFT level as the structural optimizations to obtain the final binding modes. Transition states were calculated using the climbing-image nudged elastic band (CI-NEB) method implemented in VTST until the forces on all images were less than 0.03 eV/Å. Local-basis projections for bonding analysis were performed using LOBSTER. The PBEvaspfit basis set was used, with basis functions 5p5d6s for Pt, 4s4p for Ge, 2s2p for C and O, and 3s3p for Al.