## 4 Materials and Methods
### Catalyst-Characterization Methods  
HPS-based catalysts were characterized by te liquid nitrogen physisorption, X-ray Fluorescence Analysis (_XFA_), X-ray photoelectron spectroscopy (_XPS_), and Scanning Transmission Electron Microscopy (_S/TEM_).  
_Liquid nitrogen physisorption_ was carried out to determine SSA and porosity, according to the procedure described above (Section 4.2).  
_XFA_ was carried out to determine the Pd content. It was performed with a VRA-30 spectrometer (Carl Zeiss, Jena, Germany) equipped with an Mo anode, LiF crystal analyzer, and SZ detector. Analyses were based on the Co K\(\alpha\) line, and a series of standards prepared by mixing 1 g of catalyst with 10-20 mg of standard compounds. The time of data acquisition was constant at 10 s.  
_XPS_ data were obtained using Mg K\(\alpha\) (hv = 1253.6 eV) radiation with an ES-2403 spectrometer (Institute for Analytic Instrumentation of RAS, Saint Petersburg, Russia) equipped with an energy analyzer, PHOIBOS 100-MCD5 (SPECS, Berlin, Germany) and X-ray source XR-50 (SPECS, Berlin, Germany). All the data were acquired at an X-ray power of 250 W. Survey spectra were recorded at an energy step of 0.5 eV with an analyzer pass energy of 40 eV. High-resolution spectra were recorded at an energy step of 0.05 eV with an analyzer pass energy of 7 eV. Samples were outgassed for 180 min before analysis and were stable during the examination. The data analysis was performed via CasaXPS. Binding energies (BEs) were determined with the error \(\pm 0.1\) eV.  
_S/TEM_ characterization was carried out using an FEI TecnaiOsiris instrument(Thermo Fisher Scientific, Madison, WI, USA) operating at an accelerating voltage of 200 kV, equipped with a high-angle annular dark field (_HAADF_) detector (Fischione, Export, PA, USA) and an energy-dispersive X-ray (_EDX_) microanalysis spectrometer (EDAX, Mahwah, NJ, USA). Samples were prepared by embedding the catalyst in epoxy resin with following microtomming (_ca_. 50 nm thick) at ambient temperature. For the image processing Digital Micrograph (Gatan, Warrendale, PA, USA) software and a TIA (Thermo Fisher Scientific, Madison, WI, USA) were used. Holey carbon/Cu grid was used as a sample support.  
Supplementary Materials: The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/molecules27123842/s1](https://www.mdpi.com/article/10.3390/molecules27123842/s1)]([https://www.mdpi.com/article/10.3390/molecules27123842/s1](https://www.mdpi.com/article/10.3390/molecules27123842/s1)). Figure S1: DFT calculation for MBY; Figure S2: DFT calculation for MNY; Figure S3: DFT calculation for DHIP; Table S1: Summary data on the physicochemical and catalytic properties of Pd/HPS.  
Conceptualization, L.Z.N.; methodology, L.Z.N. and A.Y.P.; data curation, L.Z.N.; validation, L.Z.N. and L.K.-M.; investigation, L.Z.N., A.Y.P., A.V.B. and A.I.S.; formal analysis, L.Z.N.; resources, L.K.-M.; writing--original draft preparation, L.Z.N.; writing--review and editing, L.K.-M.; visualization, L.Z.N.; supervision, L.K.-M.; project administration, L.K.-M. and L.Z.N.; funding acquisition, L.K.-M. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Russian Science Foundation, grant number 20-19-00386.  
Not applicable.  
The authors thank [PERSON] (National Research Centre \"Kurchatov Institute\", Moscow, Russia) for help with the STEM studies of the catalysts.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.  
Samples of the HPS-based catalysts are available from the authors.