Alchemical Perturbation DFT
Alchemical perturbation density functional theory (APDFT), often called computational alchemy, predicts how an energy changes when nuclear charges in a reference system are changed (atoms “transmuted” into neighboring elements) by expanding the energy in a Taylor series in a coupling parameter lambda. The first-order term is built from quantities available in the reference calculation, such as atom-centered electrostatic potentials, so many hypothetical compositions can be evaluated at almost no added cost after one quantum chemistry calculation.
First benchmark of alchemy for binding on alloy surfaces (2017)
Saravanan, Kitchin, von Lilienfeld and Keith tested first-order, fixed-geometry, isoelectronic computational alchemy for O*, OH* and OOH* binding energies on hypothetical alloys built from Pt(111), Pd(111) and Ni(111) slabs, using electrostatic potentials from VASP output. Against 360 single-point PBE benchmarks, mean absolute errors were 0.06 to 0.24 eV for surface alloys and 0.02 to 0.12 eV for skin alloys. Errors grew with the number of transmuted atoms, were largest when atoms at the binding site were changed (where alchemical derivatives are largest) and for O*, and became large for M3Mn, M3Fe and M3Zn skin alloys, which the authors linked to spin polarization (Mn, Fe) and Zn not being a transition metal (Saravanan et al. 2017). Summary: saravanan2017.
First-order APDFT tutorial for binding energies and barriers (2021)
Griego, Kitchin and Keith wrote a tutorial on first-order APDFT for computational catalysis. With fixed geometries and isoelectronic transmutations (a +1 change at the site balanced by a -1 change far away), the change in binding energy reduces to a dot product of alchemical potentials (differences in atomic electrostatic potentials between adsorbate-covered and bare slabs from VASP) with nuclear charge changes. For OH on Pt(111), 32 Pt-Au/Pt-Ir variants were predicted with a mean absolute error of 0.045 eV versus single-point DFT, and applying the scheme to every image of one CH4 dehydrogenation NEB gave 32 new barriers with errors up to about 0.3 eV. Accuracy degrades for large alchemical derivatives (transmutations at the binding site, or Delta Z larger than 1) and the simple scheme fails for band-gap materials. Open-source notebooks accompany the paper (Griego et al. 2020). Summary: griego2021.