Simulating Temperature Programmed Desorption of Oxygen on Pt(111) Using DFT Derived Coverage Dependent Desorption Barriers
Spencer D. Miller, Vladimir V. Pushkarev, Andrew J. Gellman and John R. Kitchin, “Simulating Temperature Programmed Desorption of Oxygen on Pt(111) Using DFT Derived Coverage Dependent Desorption Barriers”, Topics in Catalysis 57(1-4), 106-117 (2014). https://doi.org/10.1007/s11244-013-0166-3
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Question
Temperature programmed desorption (TPD) is the usual way to estimate desorption barriers and adsorption energies, and the most common analysis (Redhead) assumes the barrier does not depend on coverage. For oxygen on Pt(111) the adsorption energy is known to weaken with coverage, so that assumption can bias the result. A linear coverage dependence is the common fix, but nothing justifies that form, and methods that extract the coverage dependence directly from the data (leading edge, complete analysis) need large amounts of low-noise data. The paper asks whether DFT can supply the functional form of the coverage-dependent barrier, so that a whole family of TPD spectra can be fit with a single, physically motivated function (Miller et al. 2013).
Approach
The authors measured O2 TPD spectra from a Pt(111) single crystal in ultrahigh vacuum at a heating rate of 2 K/s for exposures up to roughly 500 L, normalizing peak areas to an assumed saturation coverage of 0.25 ML. Spectra were simulated by numerically integrating a second-order desorption rate equation with a pre-exponential factor of 3 x 1012 1/(ML s), obtained by leading edge analysis. The coverage dependence of the oxygen adsorption energy came from earlier DACAPO/PW91 calculations and a two-dimensional cluster expansion of O on Pt(111). Only configurations within a coverage-scaled energy window of the convex hull (up to 50 meV at 1 ML, about kT at 500 K) were kept as thermodynamically relevant. A fourth-order polynomial constrained to zero slope at zero coverage was fit to the average adsorption energy, converted to the differential adsorption energy, and mapped onto the desorption barrier with a Brønsted-Evans-Polanyi (BEP) relation containing two empirical parameters (a proportionality constant and an offset) that were fit to all spectra at once. The manuscript was itself written as an org-mode document containing the raw data, Python analysis and text, which also served as the supporting information (Miller et al. 2013).
Key findings
The experimental spectra become increasingly asymmetric on the leading edge, and their peak temperatures shift down, as initial coverage rises, which a constant second-order barrier cannot reproduce. Fitting a linear coverage-dependent barrier to one low-coverage spectrum gave a summed squared error (SSE) over all spectra of 2.08 x 10-5 and fit high coverages poorly; fitting a high-coverage spectrum gave SSE = 6.13 x 10-6 but overestimated low-coverage peak temperatures. Fitting each spectrum separately produced a spread of linear barriers (roughly 1.7 to 2.0 eV) whose intercepts rose with initial coverage, even though only one true function should exist (Miller et al. 2013).
The cluster expansion and DFT polynomial fits nearly coincide except at high coverages beyond those reached in TPD, and agree well even in the dilute limit where no DFT points exist. The single DFT-based barrier function, with fitted BEP parameters a = -0.47 and offset 0.01, reproduced all spectra with SSE = 6.17 x 10-6, comparable to the best linear fit but better at the low-temperature peaks. The DFT-derived barrier is roughly linear between about 0.1 and 0.2 ML but clearly nonlinear below about 0.1 ML. Remaining mismatch at leading and trailing edges suggests a coverage-dependent pre-exponential factor, which was not modeled (Miller et al. 2013).
Applying the same two parameters to low-coverage DFT adsorption energies on Au, Ag, Pd, Rh and Ir gave low-coverage desorption barriers whose 95% confidence intervals overlapped those estimated from literature TPD data for every metal except Au. The authors argue that the offset lumps together the BEP intercept and systematic differences between DFT and experiment, so the corrections are systematic rather than arbitrary (Miller et al. 2013).
Significance
The work offers a middle path between Redhead analysis and data-hungry complete analysis: DFT fixes the shape of the coverage dependence, and only two physically interpretable constants are fit to experiment. It connects the group’s cluster-expansion studies of coverage-dependent oxygen adsorption to a measurable observable, and it is an early example of a paper published together with its full data and analysis as a single literate-programming document (Miller et al. 2013).