Acceleration of catalyst discovery with easy, fast, and reproducible computational alchemy
Charles D. Griego, John R. Kitchin and John A. Keith, “Acceleration of catalyst discovery with easy, fast, and reproducible computational alchemy”, International Journal of Quantum Chemistry 121(1), e26380 (2021; published online 2020). https://doi.org/10.1002/qua.26380
This summary was written by a language model from the paper and has not been checked line by line. Rely on the published paper for details.
Question
Screening hypothetical catalysts with density functional theory (DFT) is limited by cost. Each binding energy needs separate calculations of the bare site and the site with the adsorbate, and each activation energy needs a nudged elastic band (NEB) calculation with typically 10 to 20 images. The paper notes that binary pairs of 20 metals already give 190 alloys, each with a huge number of configurations. It asks whether a simple, first-principles perturbation scheme can turn a single set of DFT reference calculations into many predictions of binding energies and barrier heights on related alloys, accurately enough to decide which cases deserve full calculations, and it is written as a tutorial with reproducible code (Griego et al. 2020).
Approach
The method is alchemical perturbation density functional theory (APDFT), also called computational alchemy. A thermodynamic cycle links the binding energy on a reference surface (lambda = 0) to the binding energy on a “transmuted” surface (lambda = 1) in which some nuclear charges are changed. The change in binding energy equals the difference between the transmutation energies of the adsorbate-covered and bare slabs, and these are estimated from a first-order Taylor expansion in lambda. Two simplifications reduce the first-order derivative to a single term. Atomic positions are held fixed, assuming relaxation effects largely cancel between the two legs of the cycle, and the total electron count is conserved through “isoelectronic transmutations”: for example, raising one Pt to Au (Delta Z = +1) is balanced by lowering another Pt, far from the site, to Ir (Delta Z = -1). The binding energy change is then a dot product between an array of alchemical potentials (the change in each atom’s electrostatic potential between the bare and adsorbate-covered reference slabs, taken from VASP) and an array of nuclear charge changes. Once the reference calculations exist, each prediction is essentially free (Griego et al. 2020).
Two benchmarks were run against single-point DFT. The first was OH on a four-layer 2 x 2 Pt(111) slab, transmuting one of eight atoms in the top two layers by plus or minus one, compensated in the fourth layer. The second applied the same binding energy procedure image by image to an NEB path for CH4* dehydrogenation to CH3* + H* on Pt(111) at 1/4 coverage.
Key findings
For OH on Pt(111), the 32 hypothetical Pt-Au and Pt-Ir alloys had binding energy changes predicted with a mean absolute error of 0.045 eV. These data had been reported earlier; here they are replotted to show how far each transmuted atom sits from the adsorbate. Errors are largest for transmutations directly at the binding site, where alchemical derivatives are biggest, and grow further for larger changes such as Delta Z = plus or minus 2 (Griego et al. 2020).
For CH4 dehydrogenation, the single reference NEB produced 32 new reaction energy profiles. Turning a nearby atom into Au generally raised the barrier and turning it into Ir lowered it. The largest barrier errors were about 0.3 eV, for the alloys with the largest alchemical derivatives, while most predictions were considerably better. Most transmutations barely changed the profile because their alchemical derivatives were small (Griego et al. 2020).
The authors note that, unlike the d-band model, first-order APDFT appears to work whether or not binding is dominated by d-orbital contributions. Its known limitations are reduced accuracy for large derivatives or multiple and large transmutations, and failure for materials with a band gap. Adding metal dopants to collapse the gap appears to restore validity. Python modules and Binder-hosted Jupyter notebooks (the phystone repository) built on ASE and VASP outputs let readers compute alchemical potentials, map alchemical derivatives as a heatmap over the slab, enumerate isoelectronic transmutations and predict binding or activation energies (Griego et al. 2020).
Significance
The paper presents computational alchemy as a cheap, physically grounded alternative to empirical models and linear scaling relations for screening alloy sites and barriers: one DFT reference calculation yields roughly 30 extra estimates and also shows which nearby atoms most affect binding. It stresses reproducibility by shipping executable notebooks with the tutorial. Proposed improvements include second-order corrections and machine learning models trained to correct the first-order errors (Griego et al. 2020).