Alchemical Predictions for Computational Catalysis: Potential and Limitations
Karthikeyan Saravanan, John R. Kitchin, O. Anatole von Lilienfeld and John A. Keith, “Alchemical Predictions for Computational Catalysis: Potential and Limitations”, The Journal of Physical Chemistry Letters 8(20), 5002-5007 (2017). https://doi.org/10.1021/acs.jpclett.7b01974
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Question
Kohn-Sham density functional theory (DFT) is the standard tool for computing adsorbate binding energies, but it is far too expensive to sweep through the enormous space of hypothetical alloys and binding sites. Computational alchemy, a perturbation theory approach that estimates how an energy changes when nuclear charges are altered, had been used for biomolecules, materials properties, and binding on small nanoparticles and graphene. This letter asks whether it is accurate enough to predict binding energies on periodic transition metal alloy surfaces, where such energies serve as catalytic activity descriptors, and where it breaks down (Saravanan et al. 2017).
Approach
A binding energy on a hypothetical alloy is written as the reference binding energy plus a first-order Taylor correction in a coupling parameter lambda that transmutes the reference slab into the alloy. Two simplifications make the correction cheap: the alloy keeps the atomic coordinates of the reference slab, and the transmutations are isoelectronic, so the total nuclear charge of the slab is unchanged. The first-order term (the alchemical derivative) is then a sum over atoms of the change in nuclear charge times the difference in each atom’s electrostatic potential between the adsorbate-covered and bare reference slabs. These potentials are read directly from standard VASP output, so after the three reference calculations (slab, adsorbate on slab, gas molecule) any number of alloy predictions costs only arithmetic. The authors contrast this with scaling relations, which need many DFT points to fit, and with the d-band model, which correlates binding with projected d-state energies (Saravanan et al. 2017).
All calculations used PBE with PAW pseudopotentials in VASP (350 eV cutoff, 8 x 8 x 1 k-points), non-spin-polarized except for the Pt3Ni skin alloy family, on four-layer fcc(111) slabs. Alchemy was benchmarked against single-point DFT on the same geometries for the oxygen reduction reaction (ORR) intermediates O*, OH* and OOH*, which prefer fcc, bridge and fcc sites. Two alloy classes were built from Pt, Pd and Ni hosts: surface alloys, with top-layer atoms changed by plus or minus 1 in nuclear charge and compensated in the bottom layer (which is screened and barely affects the derivative), and M3Ni skin alloys (M = Pt or Pd, half the second-layer atoms Ni), in which the Ni atoms were changed by -6 to +2 to span the first d-block row (Saravanan et al. 2017).
Key findings
The main benchmark contains 360 data points, obtained from 15 full DFT optimizations plus 705 single-point calculations on the DFT side, while the alchemy values came from near-instantaneous Python post-processing. Mean absolute errors were 0.06 to 0.24 eV for surface alloys and 0.02 to 0.12 eV for skin alloys. Skin alloys do better because alchemical derivatives on subsurface atoms are much smaller than on surface atoms (Saravanan et al. 2017).
Errors grow systematically with the number of transmuted atom pairs, are larger for O* than for OH* or OOH* because O* produces larger alchemical derivatives, and depend strongly on which atom is changed. Transmuting the three atoms of the fcc hollow under O* gives errors of 0.1 eV or more, as does changing the subsurface atom directly beneath the hollow in skin alloys. For OH* on the Pt bridge, changing atoms with large gradients gives errors near 0.1 eV versus about 0.04 eV for other sites (Saravanan et al. 2017).
For large charge changes in M3X skin alloys, O* and OH* binding energies were mostly within 0.2 eV of DFT, but OOH* errors were generally above 0.2 eV, and M3Mn, M3Fe and M3Zn alloys failed. The authors attribute the Mn and Fe failures to spin polarization and the Zn failure to Zn not being a transition metal. They also note the cost advantage: a 2 x 2 cell with up to three unit transmutations gives 28 alloys for the price of one DFT binding energy, and in principle a 3 x 3 cell could give over 2.6 million alloys from three DFT optimizations (Saravanan et al. 2017).
The extracted text is complete. The parity plots and error bar charts were not readable, so this summary reports only numbers stated in the text. Errors are defined relative to PBE, not experiment.
Significance
This was an early test of first-order computational alchemy on periodic metal surfaces for catalysis. It shows that one reference DFT binding energy can often give alloy binding energies within about 0.1 eV, and it maps where the method fails: transmutations at the binding site, many simultaneous transmutations, large charge changes, magnetic solutes and non-transition-metal solutes. Those limits set the agenda for later work on improving and applying the approach, including the tutorial and barrier study of Griego et al. (2020).