Davies et al., Computational screening of all stoichiometric inorganic materials, Chem, 2016 First 100 elements in their known charge states, stoichiometry limit of 8 How many compositions could there be for… • Ay Bz • Ax By Cz • Aw Bx Cy Dz … ensuring charge neutrality and a few other rules about electron distribution?
- Estimating properties of solar energy materials - Estimating conductivity in energy storage materials PART 2: What is worth making - Calculating stability from first principles
prediction of fermi energies and photoelectric threshold based on electronegativity concepts, Phys. Rev. Lett 1974 W. A. Harrison, Electronic structure and the properties of solids, 1980 B. D. Pelatt et al., Atomic solid state energy scale, JACS, 2011 • Solid state energy (SSE) scale derived from IP and EA of various binary semiconductors “The solid state energy (SSE) scale is obtained by assessing an average EA (for a cation) or an average IP (for an anion) for each atom by using data from compounds having that specific atom as a constituent. For example, the SSE for Al (-2.1 eV) is the average EA for AlN, AlAs, and AlSb.”
prediction of fermi energies and photoelectric threshold based on electronegativity concepts, Phys. Rev. Lett 1974 W. A. Harrison, Electronic structure and the properties of solids, 1980 B. D. Pelatt et al., Atomic solid state energy scale, JACS, 2011 • Solid state energy (SSE) scale derived from IP and EA of various binary semiconductors • Used to screen a space of 160k chalcohalide compositions for water splitting materials D. W. Davies et al., Computer-aided design of metal chalcohalide semiconductors: from chemical composition to crystal structure, Chem. Sci., 2018
oxides are not good “training data” (e.g. BaO: -5.0 eV, SiO2 : -9.9 eV, Al2 O3 : -12.4 eV…) Input data from Castelli et al., New Light-Harvesting Materials Using Accurate and Efficient Bandgap Calculations, Adv. Energy. Mat., 2015 How to improve on this? Better representation of materials? More sophisticated model? µ(𝝌) Max(𝝌) Min(𝝌) µ(rion ) … y 2.2 3.4 0.9 4.3 … 3.6 3.5 5.3 0.3 3.3 … 5.6 85 compositional features + + Number of trees Error Gradient boosting regression algorithm
0.95 eV D. W. Davies et al., Data-Driven Discovery of Photoactive Quaternary Oxides Using First-Principles Machine Learning, Chem. Mater., 2019 IPs of oxides are not good “training data” (e.g. BaO: -5.0 eV, SiO2 : -9.9 eV, Al2 O3 : -12.4 eV…) RMSE = 0.95 eV is approaching the limit of accuracy without structural information
polarons P. A. Cox, Electronic Structure and Chemistry of Solids, 1987 Quasiparticles describing a charge carrier plus surrounding polarization of the lattice But polarons are currently impossible to model from first principles fully: • Large supercells required even for simple systems • DFT is a mean field theory • DFT relies on the Born- Oppenheimer approximation For latest efforts see: W. H. Sio, et al., Polarons from first principles, without supercells, PRL, 2019 W. H. Sio, et al., Ab initio theory of polarons: Formalism and applications, PRB 2019
dielectric tensor S. Pekar, Local quantum states of electrons in an ideal ion crystal, J. Exp. Theor. Phys., 1946 H. Fröhlich, Electrons in lattice fields, Adv. Phys., 1954
ion crystal, J. Exp. Theor. Phys., 1946 H. Fröhlich, Electrons in lattice fields, Adv. Phys., 1954 We can estimate polaron binding energy from effective mass and dielectric tensor
dielectric tensor 214 metal oxides Type I Type II Type III D. W. Davies et al., Descriptors for electron ahd nhole charge carriers in metal oxides, J. Phys. Chem. Lett., 2019
screening • ML models • Automated first- principles calculations Q 1: What is worth calculating from first principles? Q 2: What is worth making? What is worth trying to make?
B2 O5 ]2+ Cu 3d – Ch 2p mixing in VBM à favourable band dispersion and delocalized holes. Large band gap due to perovskite- like layer. A2+ B3+ O Ch Cu A-B-O-Cu-Ch
Cu A-B-O-Cu-Ch A = Sr, Ca, Ba, Mg, Na, K, Rb, Cs, Zn, Al, Ga, In, Sc, Y, La, Ti, Zr, Hf, Ge, Sn, Pb O Cu 24 materials à 1200 materials ?? 🤔 B = Sr, Ca, Ba, Mg, Na, K, Rb, Cs, Zn, Al, Ga, In, Sc, Y, La, Ti, Zr, Hf, Ge, Sn, Pb S, Se
1. A and B chosen to be electropositive and closed shell 2. qA ≤ qB for perovskite-like framework 3. Goldschmidt tolerance factor for perovskite-like framework (0.7 – 1.0) 4. Charge neutrality t > 1 A too big t < 0.7 A and B similar in size 1200 704 496 154
DFT total energy == enthalpy Key parameter of interest: Energy above convex hull of composition phase diagram Materials Project Find competing phases 154 charge neutral PBEsol relaxations Thermodynamic stability Multiple magnetic orderings possible? Generate different spin- ordered supercells Y N 154 candidates 784 competing phases
Thermodynamic stability Multiple magnetic orderings possible? Generate different spin- ordered supercells Y N 154 candidates 784 competing phases Key parameter of interest: Energy above convex hull of composition phase diagram First-principles calculations (using e.g. the VASP code), give access to DFT total energy == enthalpy
Ag-Se Sc 0 0 2 0 In 0 0 8 0 Y 46 0 46 0 La 132 76 120 107 Ehull (meV/atom) Would a stricter (than < 90 meV/atom) Ehull threshold be more useful for this class of materials?
first principles calculations can be used to predict the “synthesizability” of a compound accurately • A closer look at what is stable and what is unstable according to DFT is probably needed.
quickly and roughly predict properties of hypothetical energy materials • Predicting the stability of hypothetical compounds remains a challenge. We can do it for some well-known crystal structures but lack the tools to do it for much else. • Even with first-principles methods, thermodynamically stable =/= dynamically stable =/= synthesizable. The chemistry and structure type has a huge impact and this still needs unravelling. • Data-driven techniques have an important role to play in the prediction of the stability of new compounds.
chemistry and materials science Targeting discovery of new compounds Enhancing theoretical chemistry Assisting characterization Mining existing literature K. T. Butler et al., Machine learning for molecular and materials science, Nature, 2018