The Heisenberg Hamiltonian has previously been used in conjunction with DFT calculations to correctly find the magnetic ground states of materials for complicated structures with large number of possible spin configurations.[1] The mapping of a few DFT calculations to reduced-order models allows for the exploration of a much larger subset of parameter space with much more computational efficiency than DFT alone. We expand this spin Hamiltonian with other energetic contributions including an occupation and nearest neighbor electronic interaction terms. The parameters of this model can be tuned to high fidelity and therefore can accurately extend to high throughput. This reduced order model can then be used with Monte Carlo simulations to generate relevant phase spaces with high resolution and less compute power than comparable collection of DFT only calculations.

A unique aspect of this work is the incorporation of error estimation through the use of the Bayesian Error Estimation Functional (BEEF)[2] and apply that to the prediction of magnetic ground states [3]. This allows us to predict c-values related to the reliability of the prediction of magnetic states identified through the DFT calculations. We use this approach to systematically understand the magnetic properties of various Li-ion cathodes. We then apply that method to predict precisely the Li-NMC (Ni-Mn-Co) phase-diagram and calculate their corresponding voltages. We will report on a robust approach to carry out high-throughput screening of cathode materials using the developed method for uncertainty estimation.

[1] D. Morgan, B. Wang, G. Ceder, and A. van de Walle, Phys. Rev. B 67, 134404 (2003).

[2] J. Wellendorff, K. T. Lundgaard, A. Møgelhøj, V. Petzold, D. D. Landis, J. K. Nørskov, T. Bligaard, and K. W. Jacobsen, Phys. Rev. B 85, 235149 (2012).