Method development

Our predictions about materials are only as reliable as the methods behind them. First-principles calculations, chiefly density functional theory, rest on approximations that fail for some materials, and they can follow only a few hundred atoms for tens of picoseconds, while many properties of real materials, such as ion transport, phase behavior and degradation, emerge over far larger systems and longer times. Alongside our work on specific materials, we therefore develop and test methods that make first-principles simulations more accurate, build realistic models of surfaces and interfaces, and bridge length and time scales by combining first-principles data with cluster expansions, Monte Carlo and kinetic Monte Carlo simulations, and machine-learned interatomic potentials. We test them against experiments, often together with our collaborators, and, where we can, release them as open-source codes, such as kMCpy and SALAMI, listed on our Software page.

Errors in computed oxidation energies of transition-metal oxides for a range of density functionals — **Figure 1:** Errors in the oxidation energies of transition-metal oxides, in eV per O₂, computed with a range of density functionals, from LSDA-PW92 and PBE to r²SCAN, r²SCAN+U and r²SCANY@r²SCANX combinations such as r²SCAN10@r²SCAN50.¹

More accurate density functionals. Density functional theory struggles with transition-metal oxides, whose partly filled d shells make the self-interaction error of common functionals severe, which in turn degrades band gaps, magnetic moments and oxidation energies, all of which matter for battery cathodes. With r²SCANY@r²SCANX, we use one fraction of exact exchange to compute the electron density and another for the energy, correcting both sources of error at once. With only one or two parameters, it improves on r²SCAN for 20 strongly correlated oxides (see Figure 1) and outperforms the widely used r²SCAN+U.¹

Realistic surface models. Cutting a crystal of a multinary compound along a conventional plane often slices through its strongly bonded polyhedra and gives unphysical surface energies. Our code SALAMI builds symmetric, charge-neutral and dipole-free slab models whose surface atoms keep their preferred coordination. For the solid electrolyte Li₃PS₄ and the transparent conducting oxide ZnSb₂O₆, these models lower the surface energies markedly and shrink the predicted Wulff shape by about 20%.²

Ion transport over long times. Kinetic Monte Carlo can follow ion migration for far longer than molecular dynamics, but building a model of the migration rates has been laborious. Our Python package kMCpy enumerates all possible migration events in a crystal, derives their rates at first-principles accuracy through cluster-expansion Hamiltonians, and solves the kinetics, for materials of any dimensionality.³

Larger systems with machine learning. Machine-learning interatomic potentials, trained on first-principles calculations, reproduce their accuracy at a small fraction of the cost and make simulations of thousands of atoms over nanoseconds routine. With colleagues across the field, we have reviewed what these potentials can and cannot yet do for battery research, and what the next generation will need.⁴

Relevant references

All our papers on method development (21) →