Catalytic thermodynamic model for nanocluster adsorbates

We present an approach to study nanocatalysis using density functional theory (DFT), statistical mechanics, and thermodynamics. The analysis starts by using a coordination style approach, which is key to producing a mesoscale model free of arbitrary parameters for sizes of similar to 3 nm < D < 100 nm. We apply DFT in a coordination type calculation of the nanocrystal binding energy and the adatom adsorption energy to give us a Hamiltonian of the nanocluster-adatom system. This is followed by informational statistical mechanical principles and thermodynamics to complete the model. Carbon monoxide adsorbates are studied on gold clusters, hydrogen molecules on palladium clusters, and oxygen radicals on platinum clusters. The data exhibits size effects for the measured thermodynamic properties with cluster diameters between 3 and 9 nm. In spite of modeling three different systems, we find only small differences in the large-scale entropy (similar to-70 J/K-mol) and enthalpy (similar to-20 kJ/mol) of the nanoclusters. Shape effects are predicted to be greatest for nanoclusters of size-10 nm. For the Pd-H-2 system, we use a cubic model which has close agreement with experimental data for Pd cubes. The computationally efficient procedure we derive provides a theoretical scheme to determine the size and shape dependence of the entropy and enthalpy of nanocluster-adsorbate systems from sequential single molecule adsorption.