Prof. Aron Walsh Department of Chemistry University of Bath, UK From 1st October 2016: Imperial College London wmd-group.github.io @lonepair AIP – Future of Chemical Physics

Chemistry à Physics à Materials Trinity College Dublin, Ireland B.A. and Ph.D. in Computational Chemistry National Renewable Energy Laboratory, USA Department of Energy, Solar Energy Research Centre University College London, UK Marie Curie Intra-European Fellow University of Bath, UK Royal Society University Research Fellow

Talk Outline 1. First-Principles Materials Modelling 2. Beyond Perfect Crystals 3. Application: Solar Energy Conversion 4. Challenges and Outlook

(1929) Equations Too Difficult to Solve

(2016) Massively Parallel Computing UK’s Archer is #50 – we need sustained investment! Top500.org (Supercomputer Ranking)

First-Principles Materials Modelling Structure Properties William Hamilton (Dublin, 1805) Hamiltonian (ions and electrons) William Bragg (Wigton, 1862) X-ray Diffraction (unit cells) Physical Chemistry (stimuli) Neville Mott (Leeds, 1905) Input: Output:

Rephrase the Many-Body Question Multi-component solids may have 100s of atoms and 1000s of electrons in a single unit cell Source: F. Bechstedt – Many-body Approach to Electronic Excitations (2015)

Density Functional Theory (DFT) Core Electrons all-electron pseudopotential frozen-core Hamiltonian non-relativistic scalar-relativistic spin-orbit coupling Periodicity 0D (molecules) 1D (wires) 2D (surfaces) 3D (crystals) Electron Spin restricted unrestricted non-collinear Basis Set plane waves numerical orbitals analytical functions Functional beyond…….. hybrid-GGA meta-GGA GGA LDA QMC GW RPA TD-DFT Kohn-Sham DFT (Physical Review, 1965)

Talk Outline 1. First-Principles Materials Modelling 2. Beyond Perfect Crystals 3. Application: Solar Energy Conversion 4. Challenges and Outlook

The Perfect Crystal

Defects and Disorder in the Solid State The entropy of a perfect crystal at 0 K is equal to zero Third Law of Thermodynamics – Nerst 1912 At finite temperatures, entropy becomes important: G = U + PV – TS *Even for a perfect crystal consider: isotopes / nuclear spin / degenerate electronic states. According to R. H. Fowler: “There is no hope for a logical definition of absolute entropy”!

Imperfect Crystals (Entropy Driven)

Average Structure ≠ Local Structure X-rays exaggerate the perfection of crystals, and imperfections are in general difficult to detect, and even more difficult to measure. A. Guiner, 1963

Disorder in Crystalline Solids Without long-range order this mathematical edifice falls in ruins Models of Disorder, J. M. Ziman (1979) Thermal Disorder Lattice vibrations, rotations, and structural instabilities Crystal Disorder Point and extended defects, dopants, alloys, interfaces, domains (e.g. ferroelectric)

Thermal Disorder N atoms in crystal vibrate as 3N phonons with set wavelength and momentum Essential for: • Free energy • Vibrational spectra • Thermal expansion • Phase transformations • Heat flow • Electrical conductivity Animations with: https://github.com/ajjackson/ascii-phonons

Crystal Potential Static DFT model Anharmonicity Higher order terms Harmonic Phonons Phonons in 30 Seconds Expansion of potential energy in a crystal with respect to ion displacements (r) Ionic Forces 0 at equilibrium Open source Phonopy package: http://atztogo.github.io/phonopy

Thermal Properties of Crystals Influence of T on structure and properties Phonon lifetimes for accurate spectra and heat transport Phys. Rev. B 89, 205203 (2014); Phys. Rev. Lett. 117, 075502 (2016) PbTe thermal expansion Phonon softening Thermal conductivity

Modelling Dilute Defects in Crystals Supercells Repeat a larger piece of the crystal in 3D Embedded Clusters A finite piece of the crystal embedded in the crystal potential

Mathematical Procedure for Defects “A method, based on Born's lattice theory, is developed for calculating the polarisation round any lattice point in a polar crystal which contains an excess charge.” [Marjorie Littleton (a librarian) used a mechanical calculator]

Embedded Crystals: QM/MM Mott-Littleton (1938) Harwell Labs, UK A. B. Lidiard, JCSFT 85, 341 (1989) Daresbury Labs, UK S. Metz et al, CMS 4, 101 (2014) Electrostatic, electronic, elastic embedding scheme Current Implementation: ChemShell (QM/MM driver) Quantum / Molecular Mechanics (QM/MM) Nobel Prize in Chemistry 2013 http://www.chemshell.org

Point Defect Spectroscopy Ionisation of isolated defects Application: p-type GaN for LEDs Nobel Prize in Physics 2014

Electron Addition / Removal Energies Polymorph Dependence of Ionisation Potentials Important for photocatalysisand photoelectrochemistry

#OpenData Computational community: Make raw I/O files available in addition to custom tools. Valuable for the community and now mandated by the UK research councils. https://github.com/WMD-group Our Approach: GitHub Software developments (and writing papers) Mendeley Extended reading lists (free Endnote replacement) NoMaD EU materials data initiative (complement Materials Project) Aim for reproducible science: share raw data!

Talk Outline 1. First-Principles Materials Modelling 2. Beyond Perfect Crystals 3. Application: Solar Energy Conversion 4. Challenges and Outlook

Harvesting Solar Energy Electricity Solar Cells Chemical Energy Solar Fuels High efficiency (10 – 50%) Low efficiency (< 5%) Physics (electron – hole separation) is easier than chemistry (oxidation and reduction reactions) Our Fusion Reactor 89,000 Terawatts reaches the Earth’s surface

CH 3 NH 3 PbI 3 – Hybrid Perovskite APL Mater. 1, 042111 (2013); Nano Letters 14, 2484 (2014) A B X3 a (Å) Eg (eV) CH3 NH3 + Pb I 6.36 1.61 CH(NH2 )2 + Pb I 6.32 1.48 CH(NH2 )2 + /CH3 NH3 + Pb I /Br - - (2009) 4% à (2016) 22% light-to-electricity conversion > 2500 Publications. Mendeley Group: “Hybrid Perovskite Solar Cells” Inorganic Hybrid

What is Moving in Hybrid Perovskites? Faster (fs) Slower (ps) Electrons and Holes Drift and diffusion of carriers Lattice Vibrations Phonons: organic and inorganic units Molecular Rotations Reorientation of MA+ or FA+ Ions and Defects Transport of charged species

Lattice Dynamics: Phonons Pseudo-cubic phase = 12 atoms = 36 modes (3N) F. Brivio et al, Phys. Rev. B 92, 144308 (2015) TO TO TO LO LO LO cm-1 Simulated IR and Raman spectra have accelerated materials characterisation: wide distribution from 0 – 3200 cm-1

[PBEsol/DFT] https://www.youtube.com/watch?v=PPwSIYLnONY First Principles Dynamics (300 K) “MAPI is as soft as jelly” Jarvist 11.2013

Timescales of Molecular Motion Librations Rotations Validated by quasi-elastic neutron scattering (N. Comm 2015) and 2D IR spectra (JPCL 2015) Antiferroelectric < 165 K; paraelectric at 300 K with short-range order Flips between equivalent <100> basins

Monte Carlo: Large Scale Disorder Polar networks in CH 3 NH 3 PbI 3 separate e- / h+ Regions of high (red) and low (blue) electrostatic potential APL Materials 2, 081506 (2014); Nature Photonics 7, 695 (2015) e- h+

Relativistic Electronic Structure: QSGW Symmetry breaking by CH 3 NH 3 + / tilting Relativistic Rashba splitting of band edges also separates electrons / holes Reduced recombination: Momentum selection rule Recombination modeling by Pooya Azarhoosh (KCL) optically excite thermalise recombine Energy vs k Physical Review B 89, 155204 (2014); APL Materials 4, 091501 (2016)

Electron-Hole Recombination Changes in radiative recombination rate Hybrid perovskites behave differently to conventional semiconductors APL Materials 4, 091501 (2016) First-principles description of radiative e-h recombination from QSGW band structures

Talk Outline 1. First-Principles Materials Modelling 2. Beyond Perfect Crystals 3. Application: Solar Energy Conversion 4. Challenges and Outlook

Challenges for Materials Modelling 1. Transport: ions; electrons; phonons 2. Excited states: electron-hole interaction 3. Polarons: electron-lattice interaction 4. Thermodynamics: metastable phases 5. Kinetics: phase growth, separation and lifetimes 6. Interfaces: emergent properties 7. Multidisciplinarity: bridging hard and soft matter 8. Multiscale: bridging materials and devices 9. Big data: sharing, collecting and learning 10. Design: structure-property relationships Materials for energy storage and conversion

Accuracy: “Total” Crystal Hamiltonian Source: D. C. Wallace – Statistical Physics of Crystals and Liquids (2002) Crystals are not frozen in space and time. Let’s describe the full picture! Crystal Potential Static DFT model Electronic Excitations Harmonic Phonons Anharmonicity Phonon interactions Electron-Phonon Coupling

Application: Materials Design Combinatorial Explosion > 10100 materials Type & ratio of elements, and their arrangement in space Nature Chemistry 7, 274 (2015); https://github.com/WMD-group/SMACT approach, but origin-of-life chemists still 52, 5845–5847 (2013). or new functionality hemical bond, advances in synthetic chemistry, and large-scale computation, ality. From a pool of 400 unknown compositions, 15 new compounds have structures and properties. Structural prediction Property simulation Targeted synthesis Chemical input Figure 1 | A modular materials design procedure, where an initial selection of chemical elements is subject to a series of optimization and screening steps. Each step may involve prediction of the crystal

Outlook First-principles modelling of crystalline materials has rapidly advanced over the past decade. Its predictive power is increasing, which can be exploited for pushing the boundaries of chemical physics. Group Members: PV – Lucy, Federico, Suzy, Keith, Youngkwang, Dan, Jarvist; MOFs – Jess, Katrine; Metastability – Jonathan, Lora, Ruoxi Collaborators: Mark van Schilfgaarde (KCL); Saiful Islam (Bath); Piers Barnes and Brian O’Regan (ICL); Alexey Sokol and David Scanlon (UCL); Atsushi Togo (Kyoto) Slides: https://speakerdeck.com/aronwalsh