of chemical properties or for the simulation of molecular/materials behaviour. It also includes, e.g. synthesis planning, database searching, combinatorial library manipulation” IUPAC (2014) IBM 5MB hard drive (1956) IBM quantum computer (2020)

energy (10-7 J) J. E. Jones, Proc. Roy. Soc. A 106, 463 (1923) = !" − # Repulsive Attractive Molecular mechanics (MM): application of classical mechanics to model chemical systems. Often analytic functions (bond stretching, bending, etc.) John Lennard-Jones (1894–1954)

atoms now possible (e.g. protein folding, radiation damage, crystallisation, correlated diffusion) Y. Shibuta et al, Nat. Comm. 8, 10 (2017) Solidification of Fe with Finnis - Sinclair potential using molecular dynamics

the Schrödinger, or relativistic Dirac, equation to describe electron distributions (chemical bonds) The master equations appear simple, but for >1 electron these partial differential equations cannot be solved exactly and require approximations Many-body wavefunction

many-body N-dimensional electronic wavefunction by the 3-dimensional electron density Quantum mechanics (QM): numerical solutions of the Schrödinger, or relativistic Dirac, equation to describe electron distributions (chemical bonds) Walter Kohn (1923–2016)

e.g. 10⨉ atoms cost 1000⨉ more processing time Density functional theory scaling data in FHI-AIMS courtesy of Volker Blum https://aimsclub.fhi-berlin.mpg.de Using ELPA massively parallel eigensolvers https://gitlab.mpcdf.mpg.de/elpa

concepts can be difficult to extract from QM Five (of the many) ways to assign electron density to atomic centres in crystals “Oxidation states and ionicity” A. Walsh et al, Nature Mater. 17, 958 (2018)

electronic structure and properties of crystals Code Features Link ABINIT Plane wave basis set – many property calculators https://www.abinit.org CP2K Mixed basis set – fast for large and complex systems https://www.cp2k.org GPAW Flexible basis set – modern python interface https://wiki.fysik.dtu.dk/gpaw Quantum Espresso Plane wave basis set – many property calculators http://www.quantum- espresso.org Starting point: Atomic Simulation Environment https://wiki.fysik.dtu.dk/ase/

used in materials science Class Property Measurement Structural Ground-state crystal structure X-ray/neutron/electron diffraction Vibrational Phonon frequencies and lifetimes X-ray/neutron scattering IR/Raman spectroscopy Thermodynamic Internal and free energy changes Stability and chemical reactivity Point Defects Concentrations, barriers, diffusion rates Impedance spectroscopy; isotope tracers, etc. Extended Defects Changes at surfaces and grain boundaries Tomography; microscopy; spatially resolved probes

data and build a model to make predictions Quick-start machine learning guide: K. T. Butler et al, Nature 559, 547 (2018) Applications include: • Faster (or better) computational tools • New knowledge from existing data • “Self-driving” research workflows

e.g. decision trees to predict reaction outcome Predict a value, e.g. regression to extract a reaction rate Group by similarity, e.g. high-throughput crystallography Maximize reward, e.g. reaction conditions to optimize yield

beyond static tables and figures, e.g. raw spectra • Reuse – facilitate meta-studies comparing results from multiple samples, e.g. variation in UV-vis features / band gap assignments • Statistical Models – power of machine learning depends on the quantity, quality, and diversity of training data For data-management guidance: https://www.go-fair.org/fair-principles/

many exciting developments in materials modelling and design. The transition from analytical to numerical methods is now being augmented by statistical approaches – limited by available data! Thanks to research group, collaboration network, and the EFL team!