Toward Quantum Chemical Free Energy Simulations of Platinum Nanoparticles on Titania Support

Platinum
nanoparticles (Pt-NPs) supported on titania surfaces are
costly but indispensable heterogeneous catalysts because of their
highly effective and selective catalytic properties. Therefore, it
is vital to understand their physicochemical processes during catalysis
to optimize their use and to further develop better catalysts. However,
simulating these dynamic processes is challenging due to the need
for a reliable quantum chemical method to describe chemical bond breaking
and bond formation during the processes but, at the same time, fast
enough to sample a large number of configurations required to compute
the corresponding free energy surfaces. Density functional theory
(DFT) is often used to explore Pt-NPs; nonetheless, it is usually
limited to some minimum-energy reaction pathways on static potential
energy surfaces because of its high computational cost. We report
here a combination of the density functional tight binding (DFTB)
method as a fast but reliable approximation to DFT, the steered molecular
dynamics (SMD) technique, and the Jarzynski equality to construct
free energy surfaces of the temperature-dependent diffusion and growth
of platinum particles on a titania surface. In particular, we present
the parametrization for Pt-X (X = Pt, Ti, or O) interactions in the
framework of the second-order DFTB method, using a previous parametrization
for titania as a basis. The optimized parameter set was used to simulate
the surface diffusion of a single platinum atom (Pt1) and
the growth of Pt6 from Pt5 and Pt1 on the rutile (110) surface at three different temperatures (T = 400, 600, 800 K). The free energy profile was constructed
by using over a hundred SMD trajectories for each process. We found
that increasing the temperature has a minimal effect on the formation
free energy; nevertheless, it significantly reduces the free energy
barrier of Pt atom migration on the TiO2 surface and the
transition state (TS) of its deposition. In a concluding remark, the
methodology opens the pathway to quantum chemical free energy simulations
of Pt-NPs’ temperature-dependent growth and other transformation
processes on the titania support.