Applications of Wavelet-Based Density Functional Theory (Applications-Oriented Developments)

Laura E. Ratcli Department of Materials, Imperial College London

27.07.2018

Mohr, LER, Genovese et al., Phys. Chem. Chem. Phys. 17, 31360 (2015) [issue cover] Applications of Wavelet-Based Overview DFT Laura Ratcli MADNESS BigDFT Introduction core spectra using a Core Spectra in large (> 1000 atom) systems MADNESS multiresolution approach Motivation with Daubechies wavelets Pseudopotentials in 1.5 φ(x) MADNESS 1.0 ψ(x) Calculating Core 0.5 Spectra 0.0 Comparison with -0.5 PW-PAW -1.0 Core Hole Eects -1.5 Summary -6 -4 -2 0 2 4 6 8 x Applications of LS-BigDFT Motivation LS-BigDFT Focus on Applications – Points of Interest Molecular Fragment Approach Simulating OLEDs • what materials and properties do we want to simulate? Embedded Fragments Complexity Reduction • how do we adapt (or not) to a given application? Summary

Outlook • how do we define ‘accurate’ for an application? • how do we use a method in practice, i.e. could anyone else (easily) use the code? Applications of Wavelet-Based Outline DFT 1 Introduction Laura Ratcli 2 Core Spectra in MADNESS Introduction Motivation Core Spectra in MADNESS Pseudopotentials in MADNESS Motivation Pseudopotentials in Calculating Core Spectra MADNESS Calculating Core Spectra Comparison with PW-PAW Comparison with PW-PAW Core Hole Eects Core Hole Eects Summary Summary Applications of 3 Applications of LS-BigDFT LS-BigDFT Motivation Motivation LS-BigDFT Molecular Fragment LS-BigDFT Approach Simulating OLEDs Molecular Fragment Approach Embedded Fragments Complexity Reduction Simulating OLEDs Summary Embedded Fragments Outlook Complexity Reduction Summary 4 Outlook Applications of Wavelet-Based Motivation DFT Laura Ratcli Electron Energy Loss Spectroscopy

Introduction • can be used to extract information about: Core Spectra in • chemical bonding environment MADNESS Motivation • valence state Pseudopotentials in MADNESS Calculating Core • nearest neighbour distances Spectra Comparison with PW-PAW • but spectra can be complicated to interpret Core Hole Eects Summary → need simulation to shed light on experiments

Applications of LS-BigDFT Motivation LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary

Outlook

EELS of graphite/diamond: Hamon, Verbeeck, Schryvers, EELS of fullerenes: Tizei, Liu, Koshino, Iizumi, Okazaki Benedikt and Sanden, J. Mater. Chem. 14, 2030 (2004) and Suenaga, Phys. Rev. Le., 113, 185502 (2014) Applications of Wavelet-Based Motivation DFT Laura Ratcli Two Approches to Calculating EELS with DFT Introduction all electron: pseudopotential + PAW: Core Spectra in MADNESS • conceptually • more complex formalism Motivation Pseudopotentials in straightforward • lower (but still good!) MADNESS Calculating Core • high accuracy accuracy Spectra Comparison with PW-PAW • computationally expensive • cheaper → larger systems Core Hole Eects Summary Applications of Why a Multiresolution Approach? LS-BigDFT Motivation LS-BigDFT • EELS can be used to probe the local electronic structure Molecular Fragment Approach • oen only interested in a particular region of interest Simulating OLEDs Embedded Fragments • Complexity Reduction but region is nonetheless coupled to an environment Summary Outlook → use multiresolution to vary the accuracy according to needs, i.e. combine AE and PSP approaches Applications of Wavelet-Based Outline DFT 1 Introduction Laura Ratcli 2 Core Spectra in MADNESS Introduction Motivation Core Spectra in MADNESS Pseudopotentials in MADNESS Motivation Pseudopotentials in Calculating Core Spectra MADNESS Calculating Core Spectra Comparison with PW-PAW Comparison with PW-PAW Core Hole Eects Core Hole Eects Summary Summary Applications of 3 Applications of LS-BigDFT LS-BigDFT Motivation Motivation LS-BigDFT Molecular Fragment LS-BigDFT Approach Simulating OLEDs Molecular Fragment Approach Embedded Fragments Complexity Reduction Simulating OLEDs Summary Embedded Fragments Outlook Complexity Reduction Summary 4 Outlook Applications of Wavelet-Based Pseudopotentials in MADNESS DFT Laura Ratcli Pseudopotential Choice – HGH-GTH PSPs

Introduction • relativistic and non-linear core corrections to be implemented Core Spectra in • MADNESS high accuracy (Delta Test elements up to Ar) Motivation • Pseudopotentials in allows for comparison with BigDFT MADNESS Calculating Core • MRA/MADNESS → straightforward implementation Spectra Comparison with PW-PAW Core Hole Eects Summary

Applications of LS-BigDFT Motivation LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary

Outlook

Delta Test: https://molmod.ugent.be/deltacodesdft; Lejaeghere et al., Science 351, 6280 (2016) HGH-GTH: Hartwigsen, Goedecker and Huer, Phys. Rev. B 58, 3641 (1998); Krack, Theor. Chem. Acc. 114, 145 (2005) NLCC PSPs: Willand, Kvashnin, Genovese, Vázquez-Mayagoitia, Deb, Sadeghi, Deutsch and Goedecker, J. Chem. Phys. 138, 104109 (2013) Applications of Wavelet-Based PSP Example I DFT Laura Ratcli Benchmark: Cysteine Molecule

Introduction • PSP vs. BigDFT . 0.5 meV, PSP vs. AE ∼ 10 meV Core Spectra in • MADNESS ideal for benchmarking PSPs (eliminate basis set eects) Motivation Pseudopotentials in MADNESS madness BigDFT Calculating Core Spectra AE PSP PSP Comparison with PW-PAW HOMO − 3 -7.88670 -7.89152 7.89157 Core Hole Eects HOMO − 2 -6.90242 -6.90990 -6.90945 Summary HOMO − 1 -6.07081 -6.06520 -6.06520 Applications of LS-BigDFT HOMO -5.79053 -5.78121 -5.78125 Motivation LUMO -1.73653 -1.72627 -1.72633 LS-BigDFT Molecular Fragment Approach AE Simulating OLEDs PSP Embedded Fragments Complexity Reduction Summary

Outlook DOS (arb. units)

-10 -8 -6 -4 -2 0 2 4 6 Energy (eV) Applications of Wavelet-Based PSP Example II DFT Laura Ratcli Specifying a PSP Calculaiton Introduction Core Spectra in • advantage of MRA – no extra ‘thinking’ involved to run a MADNESS Motivation PSP calculation Pseudopotentials in MADNESS • same input file as usual, just add psp_calc flag Calculating Core Spectra Comparison with • need gth.xml file containing appropriate PSP parameters PW-PAW Core Hole Eects Summary

Applications of cysteine_psp.in LS-BigDFT Motivation dft LS-BigDFT xc lda_x 1.0 lda_c_vwn 1.0 Molecular Fragment ... Approach Simulating OLEDs psp_calc Embedded Fragments end Complexity Reduction Summary geometry Outlook units angstrom N 0.0000 0.0000 0.0000 ... end Applications of Wavelet-Based Mixed AE/PSP DFT Laura Ratcli Mixed Mode Calculations

Introduction • PSP is suiciently accurate for many applications Core Spectra in MADNESS • in some cases, want very high precision/access to core states Motivation Pseudopotentials in • but oen only need high precision for select atoms MADNESS Calculating Core Spectra Comparison with Implementation PW-PAW Core Hole Eects Summary • the user can choose which atoms should be AE/PSP Applications of LS-BigDFT • multiresolution approach → balance of accuracy and Motivation eiciency (more refinement for AE) LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments Potential Applications Complexity Reduction Summary • environmental eects (e.g. molecule on surface) Outlook • core spectra for select atoms (e.g. high symmetry materials, select species) • benchmarking individual PSPs in dierent materials Applications of Wavelet-Based Mixed AE/PSP Example I DFT Laura Ratcli Dierent Mixed Scenarios Introduction • one species – AE, others – PSP Core Spectra in MADNESS • high accuracy in each case Motivation Pseudopotentials in MADNESS Calculating Core Spectra Comparison with PW-PAW AE Core Hole Eects PSP Summary mixed (H) Applications of mixed (C) LS-BigDFT mixed (N) Motivation mixed (O) LS-BigDFT mixed (S) Molecular Fragment Approach Simulating OLEDs Embedded Fragments

Complexity Reduction DOS (arb. units) Summary

Outlook

-10 -8 -6 -4 -2 0 2 4 6 Energy (eV) Applications of Wavelet-Based Mixed AE/PSP Example II DFT Laura Ratcli cysteine_mixed_C.in Introduction dft Core Spectra in xc lda_x 1.0 lda_c_vwn 1.0 MADNESS ... Motivation Pseudopotentials in end MADNESS Calculating Core geometry Spectra Comparison with units angstrom PW-PAW psN 0.0000 0.0000 0.0000 Core Hole Eects Summary C -0.2000 -1.1400 -0.8800 C -1.5600 -1.1000 -1.5000 Applications of LS-BigDFT psO -2.5400 -0.9200 -0.8200 Motivation psO -1.5800 -1.2600 -2.8200 LS-BigDFT C 0.9200 -1.2000 -1.9200 Molecular Fragment Approach psS 1.4200 -2.9200 -2.2200 Easy to Use Simulating OLEDs psH -0.7358 0.0321 0.6764 Embedded Fragments psH 0.8792 -0.0903 0.4678 • Complexity Reduction as with PSP, no Summary psH -0.1534 -2.0427 -0.3075 complications for psH -2.4146 -1.2359 -3.2938 Outlook psH 1.7634 -0.6543 -1.5514 the user psH 0.5730 -0.7695 -2.8361 psH 2.4005 -2.9474 -3.1329 end Applications of Wavelet-Based Outline DFT 1 Introduction Laura Ratcli 2 Core Spectra in MADNESS Introduction Motivation Core Spectra in MADNESS Pseudopotentials in MADNESS Motivation Pseudopotentials in Calculating Core Spectra MADNESS Calculating Core Spectra Comparison with PW-PAW Comparison with PW-PAW Core Hole Eects Core Hole Eects Summary Summary Applications of 3 Applications of LS-BigDFT LS-BigDFT Motivation Motivation LS-BigDFT Molecular Fragment LS-BigDFT Approach Simulating OLEDs Molecular Fragment Approach Embedded Fragments Complexity Reduction Simulating OLEDs Summary Embedded Fragments Outlook Complexity Reduction Summary 4 Outlook Applications of Wavelet-Based EELS and Fermi’s Golden Rule DFT Laura Ratcli ELNES conduction Introduction • low EELS involves dierent processes Core Spectra in loss in dierent energy ranges MADNESS Motivation • we are interested in energy loss Pseudopotentials in valence MADNESS near edge spectra (ELNES) Calculating Core Spectra Comparison with • i.e. energy losses due to PW-PAW Core Hole Eects ELNES transitions between core and Summary core virtual states Applications of LS-BigDFT Motivation Fermi’s Golden Rule LS-BigDFT Molecular Fragment Approach • use Fermi’s golden rule to calculate energy loss: Simulating OLEDs 1 iq·r 2 Embedded Fragments ε2 (ω)= |hψf |e |ψii| δ Ef − Ei − ω Complexity Reduction Ω X Summary i,f Outlook • first (naive) approximation – assume virtual energies are unaected by loss of core electron

• ψi (ψf ) are merely core (virtual) KS states Applications of Wavelet-Based Dipole Approximation DFT Laura Ratcli Dipole Approximation

Introduction 1 iq·r 2 ε2 (ω)= |hψf |e |ψii| δ Ef − Ei − ω Core Spectra in Ω X MADNESS i,f Motivation iq·r Pseudopotentials in • given small q can expand e as MADNESS Calculating Core iq·r Spectra hψf |e |ψii = hψf |ψii + ihψf |q · r|ψii + . . . Comparison with PW-PAW Core Hole Eects • hψf |ψii = 0, neglect higher order terms → dipole term only Summary • core spectra ∼ angular momentum projected DoS (pdos) Applications of LS-BigDFT Motivation LS-BigDFT conduction Two Key antities Molecular Fragment Approach low Simulating OLEDs • dipole matrix elements between Embedded Fragments loss Complexity Reduction core and virtual states Summary valence • transition energies – use KS Outlook eigenvalues εf and εi • ELNES use Gaussian or Lorentzian broadening core Applications of Wavelet-Based EELS Ingredients DFT Laura Ratcli Core States Introduction • core states for select atoms require all electron approach Core Spectra in MADNESS • remaining atoms treated using pseudopotentials Motivation Pseudopotentials in • have direct access to ψi and εi MADNESS Calculating Core Spectra • can have mixing between core states, but should ideally have Comparison with PW-PAW 1 AE atom per calculation (see later) Core Hole Eects Summary Applications of Unoccupied KS States LS-BigDFT Motivation LS-BigDFT empty states calculated in tandem with occupied states, some Molecular Fragment Approach issues/caveats with this approach: Simulating OLEDs Embedded Fragments • stability – cannot always reach convergence Complexity Reduction Summary • can only access low energy virtuals – limited energy window Outlook • need to use canonical orbitals – no localization • incorrect ordering of initial guess – low energy states can be missed Applications of Wavelet-Based Virtual States DFT Laura Ratcli

Introduction ONETEP Approach

Core Spectra in MADNESS State Initial 0Extra 4Extra Motivation Pseudopotentials in States States MADNESS Calculating Core LUMO+14 0.628 >0.368 -0.042 Spectra Comparison with LUMO+15 0.355 0.045 0.039 PW-PAW Core Hole Eects LUMO+16 0.259 0.082 0.061 Summary

Applications of LS-BigDFT Motivation LS-BigDFT Molecular Fragment Approach Solving the Initial Guess Problem Simulating OLEDs Embedded Fragments take inspiration from similar issue in ONETEP: Complexity Reduction Summary • request more eigenstates than needed Outlook • gradually reduce number of states to ensure correct ordering

Conduction States in ONETEP: LER, Hine and Haynes, Phys. Rev. B 84, 165131 (2011) Applications of Wavelet-Based EELS Example I DFT

Laura Ratcli EELS in Mixed Mode Introduction • mixed approach gives excellent results compared with AE Core Spectra in

MADNESS Motivation Pseudopotentials in MADNESS O 1s AE

Calculating Core mixed (O) Spectra Comparison with PW-PAW 503 504 505 506 507 508 509 Core Hole Eects N 1s AE Summary mixed (N) Applications of LS-BigDFT 374 375 376 377 378 379 380

Motivation C 1s AE LS-BigDFT mixed (C) Molecular Fragment Approach 265 266 267 268 269 270 271 Simulating OLEDs Intensity (arb. units) Embedded Fragments S 2p AE Complexity Reduction mixed (S) Summary 204 205 206 207 208 209 210 Outlook S 2s AE mixed (S)

151 152 153 154 155 156 157 Energy (eV) Applications of Wavelet-Based EELS Example II DFT Laura Ratcli EELS Input File Introduction • specify initial number of virtual states nvalpha and nvbeta Core Spectra in MADNESS • parameters for gradually decreasing virtual states Motivation Pseudopotentials in • add print_dipole_matels flag to generate matrix elements MADNESS Calculating Core Spectra Comparison with PW-PAW cysteine_ae.in Core Hole Eects Summary dft Applications of xc lda_x 1.0 lda_c_vwn 1.0 LS-BigDFT canon Motivation nvalpha 13 LS-BigDFT Molecular Fragment nvbeta 13 Approach nv_step 2 Simulating OLEDs nv_extra 8 Embedded Fragments Complexity Reduction maxiter_nv 3 Summary ... Outlook print_dipole_matels end

geometry ... end Applications of Wavelet-Based Outline DFT 1 Introduction Laura Ratcli 2 Core Spectra in MADNESS Introduction Motivation Core Spectra in MADNESS Pseudopotentials in MADNESS Motivation Pseudopotentials in Calculating Core Spectra MADNESS Calculating Core Spectra Comparison with PW-PAW Comparison with PW-PAW Core Hole Eects Core Hole Eects Summary Summary Applications of 3 Applications of LS-BigDFT LS-BigDFT Motivation Motivation LS-BigDFT Molecular Fragment LS-BigDFT Approach Simulating OLEDs Molecular Fragment Approach Embedded Fragments Complexity Reduction Simulating OLEDs Summary Embedded Fragments Outlook Complexity Reduction Summary 4 Outlook Applications of Wavelet-Based Carbon Nanotube I DFT Laura Ratcli Mixed Setup

Introduction • 3 (symmetry unrelated) C atom types : A, B and C Core Spectra in • MADNESS one of each type treated as AE, others (including H) as PSP Motivation Pseudopotentials in MADNESS Calculating Core Spectra AE Comparison with mixed PW-PAW PW Core Hole Eects Summary

Applications of AE ÷8 LS-BigDFT Motivation DOS (arb. units) LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments −267 −262 −20 −15 −10 −5 0 5 Complexity Reduction Energy (eV) Summary Outlook Density of States • AE, mixed and PW-PSP DoS in agreement

EELS in CASTEP: Gao, Pickard, Perlov and Milman, J. Phys. Condens Maer 21 104203 (2009) Applications of Wavelet-Based Carbon Nanotube II DFT Laura Ratcli EELS

Introduction • can reconstruct total spectra from mixed calculations Core Spectra in • A, B and C spectra are similar between approaches MADNESS Motivation • dierence with PAW due to lack of core energies Pseudopotentials in MADNESS Calculating Core mixed tot. Spectra mixed A Comparison with PW A PW-PAW Core Hole Eects Summary mixed tot. Applications of mixed B LS-BigDFT PW B Motivation LS-BigDFT Molecular Fragment mixed tot. Approach mixed C Simulating OLEDs PW C Embedded Fragments Intensity (arb. units) Complexity Reduction Summary AE tot. mixed tot. Outlook PW tot. EELS and PSPs in MADNESS: LER et al. in preparation (2018)

266 267 268 269 270 271 Energy (eV) Applications of Wavelet-Based Outline DFT 1 Introduction Laura Ratcli 2 Core Spectra in MADNESS Introduction Motivation Core Spectra in MADNESS Pseudopotentials in MADNESS Motivation Pseudopotentials in Calculating Core Spectra MADNESS Calculating Core Spectra Comparison with PW-PAW Comparison with PW-PAW Core Hole Eects Core Hole Eects Summary Summary Applications of 3 Applications of LS-BigDFT LS-BigDFT Motivation Motivation LS-BigDFT Molecular Fragment LS-BigDFT Approach Simulating OLEDs Molecular Fragment Approach Embedded Fragments Complexity Reduction Simulating OLEDs Summary Embedded Fragments Outlook Complexity Reduction Summary 4 Outlook Applications of Wavelet-Based Core Hole Eects I DFT

Laura Ratcli conduction Introduction low Core Spectra in loss MADNESS Motivation valence Pseudopotentials in MADNESS Calculating Core Spectra Comparison with PW-PAW ELNES Core Hole Eects Summary core Applications of LS-BigDFT Motivation LS-BigDFT A More Realistic Approach Molecular Fragment Approach Simulating OLEDs • above approach assumes virtuals are unaected by the excited Embedded Fragments Complexity Reduction core electron Summary • i.e. we have neglected the interaction between the excited Outlook electron-hole pair → need to include core hole eects Applications of Wavelet-Based Core Hole Eects II DFT Laura Ratcli Core Hole Eects

Introduction • need to explicitly remove a core electron: Core Spectra in • simple approximation – Z + 1 MADNESS Motivation • PSP approach – generate PSP with a missing core electron Pseudopotentials in MADNESS • Calculating Core AE approach – constrain calculation to maintain core hole Spectra Comparison with • one calculation needed for each excited (AE) atom PW-PAW Core Hole Eects • can significantly improve agreement with experiment Summary

Applications of LS-BigDFT Motivation LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary

Outlook

EELS in ONETEP: Tait, LER, Payne, Haynes and Hine, J. Phys. Condens. Maer 28, 195202 (2016) Applications of Wavelet-Based Calculating Energy Osets DFT Laura Ratcli Absolute Energy Oset

Introduction • first approximation – manual alignment Core Spectra in MADNESS • beer approach – eigenvalue dierence (need core states) Motivation Pseudopotentials in • with core holes – calculate as a total energy dierence MADNESS Calculating Core (Eexcited − Einitial) Spectra Comparison with PW-PAW • oset can be estimated for PAW approach relative to AE Core Hole Eects calculations Summary

Applications of • but more direct with AE approach LS-BigDFT Motivation LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary

Outlook

EELS in ONETEP: Tait, LER, Payne, Haynes and Hine, J. Phys. Condens. Maer 28, 195202 (2016) Applications of Wavelet-Based Outline DFT 1 Introduction Laura Ratcli 2 Core Spectra in MADNESS Introduction Motivation Core Spectra in MADNESS Pseudopotentials in MADNESS Motivation Pseudopotentials in Calculating Core Spectra MADNESS Calculating Core Spectra Comparison with PW-PAW Comparison with PW-PAW Core Hole Eects Core Hole Eects Summary Summary Applications of 3 Applications of LS-BigDFT LS-BigDFT Motivation Motivation LS-BigDFT Molecular Fragment LS-BigDFT Approach Simulating OLEDs Molecular Fragment Approach Embedded Fragments Complexity Reduction Simulating OLEDs Summary Embedded Fragments Outlook Complexity Reduction Summary 4 Outlook Applications of Wavelet-Based Outlook DFT Laura Ratcli PSPs and Mixed AE/PSP in MADNESS

Introduction • MRA → ease of implementation and use Core Spectra in • high accuracy for regions of interest MADNESS Motivation • useful for benchmarking PSPs Pseudopotentials in MADNESS mixed tot. Calculating Core mixed A Spectra PW A Comparison with PW-PAW mixed tot. mixed B

Core Hole Eects Core Spectra PW B Summary

mixed tot. Applications of mixed C LS-BigDFT • first approximation of ELNES PW C Intensity (arb. units) Motivation • AE only where core states needed AE tot. LS-BigDFT mixed tot. Molecular Fragment PW tot. Approach Simulating OLEDs

Embedded Fragments 266 267 268 269 270 271 Complexity Reduction Energy (eV) Summary Future Work Outlook • implement core hole eects • compare energy osets calculated with dierent approaches • improve stability/energy range of virtual states Applications of Wavelet-Based Outline DFT 1 Introduction Laura Ratcli 2 Core Spectra in MADNESS Introduction Motivation Core Spectra in MADNESS Pseudopotentials in MADNESS Motivation Pseudopotentials in Calculating Core Spectra MADNESS Calculating Core Spectra Comparison with PW-PAW Comparison with PW-PAW Core Hole Eects Core Hole Eects Summary Summary Applications of 3 Applications of LS-BigDFT LS-BigDFT Motivation Motivation LS-BigDFT Molecular Fragment LS-BigDFT Approach Simulating OLEDs Molecular Fragment Approach Embedded Fragments Complexity Reduction Simulating OLEDs Summary Embedded Fragments Outlook Complexity Reduction Summary 4 Outlook Applications of Wavelet-Based Outline DFT Laura Ratcli Motivation Linear Scaling DFT Introduction why large/disordered systems? Core Spectra in QM of large systems MADNESS Motivation 50

Pseudopotentials in 40 MADNESS Calculating Core 30 Spectra 20 Comparison with PW-PAW Walltime (min.) 10 Core Hole Eects 0 Summary 5000 10000 15000 20000 25000 Number of atoms Applications of LS-BigDFT Motivation Fragment Approach LS-BigDFT Application Areas Molecular Fragment Approach exploiting repetition Simulating OLEDs treating complex systems Embedded Fragments Complexity Reduction Summary

support function Outlook reformatting support function optimization Applications of Wavelet-Based Bridging the Lengthscale Gap DFT Laura Ratcli What is a ‘Large’ System? Introduction ∼ 1000 atoms up to & 10000 atoms Core Spectra in MADNESS Motivation Pseudopotentials in MADNESS Calculating Core Spectra Comparison with PW-PAW Core Hole Eects Summary

Applications of LS-BigDFT Motivation LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary

Outlook Applications of Wavelet-Based Why Large Scale QM? DFT Laura Ratcli Why do we Need QM for Large Systems?

Introduction • bridge lengthscale gap between QM and MM (validate Core Spectra in empirical models) MADNESS Motivation • new possibilities for simulating complex materials Pseudopotentials in MADNESS Calculating Core • intrinsically QM quantities, e.g. electronic excitations Spectra Comparison with • access error bars and statistics PW-PAW Core Hole Eects Summary Why Numerical Methods? Applications of LS-BigDFT • for large systems we have to make some approximations Motivation LS-BigDFT • aim is to maintain systematically controllable accuracy Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary

Outlook Applications of Wavelet-Based Outline DFT 1 Introduction Laura Ratcli 2 Core Spectra in MADNESS Introduction Motivation Core Spectra in MADNESS Pseudopotentials in MADNESS Motivation Pseudopotentials in Calculating Core Spectra MADNESS Calculating Core Spectra Comparison with PW-PAW Comparison with PW-PAW Core Hole Eects Core Hole Eects Summary Summary Applications of 3 Applications of LS-BigDFT LS-BigDFT Motivation Motivation LS-BigDFT Molecular Fragment LS-BigDFT Approach Simulating OLEDs Molecular Fragment Approach Embedded Fragments Complexity Reduction Simulating OLEDs Summary Embedded Fragments Outlook Complexity Reduction Summary 4 Outlook Applications of Wavelet-Based The Cubic Scaling Limit DFT Laura Ratcli Scaling with System Size Size Limitations Introduction Core Spectra in the operations scale dierently: • up to ∼ 1000 atoms thanks to MADNESS wavelet properties and Motivation • O(N log N ): Poisson solver Pseudopotentials in 2 eicient parallelization MADNESS • O(N ): convolutions Calculating Core 3 Spectra 3 • for bigger systems O(N ) Comparison with • O(N ): linear algebra PW-PAW dominates Core Hole Eects and have dierent prefactors: Summary • also reach memory limits • cO N 3 ≪ cO N 2 ≪ Applications of ( ) ( ) LS-BigDFT cO(N log N ) −→ need a new approach Motivation LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary

Outlook Applications of Wavelet-Based Nearsightedness and Locality DFT Laura Ratcli

Introduction Nearsightedness

Core Spectra in MADNESS • the behaviour of large systems is short-ranged (nearsighted) Motivation ′ Pseudopotentials in • the density matrix, ρ(r, r ), decays exponentially in systems MADNESS Calculating Core Spectra with a gap Comparison with PW-PAW Core Hole Eects → how can we exploit nearsightedness to treat large systems? Summary

Applications of LS-BigDFT Support Functions (SFs) Motivation LS-BigDFT Molecular Fragment write extended KS orbitals Approach Simulating OLEDs in terms of localized SFs Embedded Fragments Complexity Reduction ({φα(r)}): Summary Outlook Ψ (r)= cαφ (r) KS orbitals i X i α α Applications of Wavelet-Based Density Matrix Formulation DFT Laura Ratcli Avoiding Diagonalization ′ Introduction • express ρ(r, r ) in terms of density kernel Kαβ and SFs: Core Spectra in MADNESS ′ ′ Motivation ρ(r, r ) = fi Ψi(r)ihΨi(r ) Pseudopotentials in X MADNESS i Calculating Core Spectra αβ ′ = φα(r)iK hφβ(r ) Comparison with X PW-PAW α,β Core Hole Eects Summary • no explicit reference to KS orbitals – avoid diagonalization Applications of LS-BigDFT • orthogonality requirement translates to idempotency: Motivation LS-BigDFT Molecular Fragment hΨi|Ψji = δij → K = KSK Approach Simulating OLEDs • the density is found via n(r)= ρ(r, r) Embedded Fragments Complexity Reduction Summary Matrix Expressions Outlook

Hαβ = hφα|Hˆ |φβi; Sαβ = hφα|φβi E = Tr (KH) ; N = Tr (KS) Applications of Wavelet-Based Support Functions DFT Laura Ratcli SF Properties Introduction

Core Spectra in • strictly localized (∼ 6 − 8 a0 radius) MADNESS Motivation • minimal (1 SF per H, 4 per C/N/O...) Pseudopotentials in MADNESS Calculating Core • atom-centred Spectra Comparison with PW-PAW • quasi-orthogonal Core Hole Eects Summary • numerical functions expanded in wavelets → 2 levels of basis

Applications of LS-BigDFT Motivation LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary

Outlook Applications of Wavelet-Based Support Function Optimization DFT Laura Ratcli SF Optimization

Introduction • start with atomic orbitals as a guess for the SFs Core Spectra in • use a gradually decreasing confining potential: MADNESS Motivation 4 Pseudopotentials in Hˆ = Hˆ + c (r − R ) MADNESS α α α Calculating Core Spectra • optimize SFs in situ by minimizing Ω subject to constraints: Comparison with PW-PAW αα αβ Core Hole Eects Ω= K hφα|Hˆ |φαi + K hφα|Hˆ |φβi Summary X X α β=6 α Applications of LS-BigDFT Motivation → minimal, localized basis with accuracy of wavelets LS-BigDFT Molecular Fragment Approach DFT potential Simulating OLEDs confining potential Embedded Fragments effective potential Complexity Reduction Summary

Outlook Applications of Wavelet-Based Density Kernel Optimization DFT Laura Ratcli Three Methods for Obtaining K:

Introduction • Diagonalization Core Spectra in • good for small systems and benchmarking/debugging MADNESS Motivation Pseudopotentials in • Direct Minimization MADNESS Calculating Core Spectra • work directly with the KS coeicients Comparison with PW-PAW • can include a few unoccupied states Core Hole Eects Summary • Fermi Operator Expansion (FOE) Applications of LS-BigDFT • density matrix is expressed in terms of H, i.e. K = f (H) Motivation LS-BigDFT • use a Chebyshev polynomial expansion Molecular Fragment Approach Simulating OLEDs • uses a (small) finite temperature – works for metals Embedded Fragments Complexity Reduction • implemented in CheSS (Chebyshev Sparse Solvers) library Summary Outlook Kernel Truncation

• simple distance criterion Kαβ = 0 if |Rα − Rβ| > Kcut

LS-BigDFT Metals: Mohr, Eixarch, Amsler, Mantsinen and Genovese, J. Nucl. Mater. Energy 15, 64 (2018) CheSS: Mohr, Dawson, Wagner, Caliste, Nakajima and Genovese, J. Chem. Theory Comput. 13, 4684 (2017) Applications of Wavelet-Based The Algorithm atomic DFT orbitals Laura Ratcli Calculation Steps Introduction • Core Spectra in energy is minimized with respect optimize SFs MADNESS to both SFs and K Motivation Pseudopotentials in MADNESS • accurate forces without Pulay Calculating Core Spectra terms Comparison with optimize K PW-PAW Core Hole Eects • can diagonalize H at the end to Summary obtain KS energies Applications of LS-BigDFT • Γ-point only – real SFs energy Motivation & forces LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary

Outlook Applications of Wavelet-Based Support Function Convergence DFT Laura Ratcli

Introduction

Core Spectra in Controlling the Accuracy MADNESS Motivation • SF radii are the key parameters Pseudopotentials in MADNESS Calculating Core • can choose dierent values for dierent atomic species Spectra Comparison with • energies and forces converge to cubic scaling values PW-PAW Core Hole Eects Summary 1e+00 1e+00 Applications of Energy LS-BigDFT 1e−01 Forces Motivation 1e−01

LS-BigDFT 1e−02 ) (eV / Å) Molecular Fragment −

) / atom (eV) 1e 02 Approach cubic

1e−03 F Simulating OLEDs − cubic

E 1e−03 Embedded Fragments 1e−04 Complexity Reduction − (E Summary 1e−05 1e−04 Av. (F 2 3 4 5 6 7 Outlook Localization radius (Å) Applications of Wavelet-Based Sparse Matrices DFT Laura Ratcli Sparse Matrices Introduction • strict localization leads to sparse matrices Core Spectra in MADNESS • sparsity depends on size, dimensionality, and SF radii Motivation Pseudopotentials in MADNESS Calculating Core Spectra Comparison with PW-PAW Core Hole Eects Summary

Applications of LS-BigDFT Motivation LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary

Outlook Applications of Wavelet-Based Time Scaling DFT Laura Ratcli Sparse Matrices

Introduction • use of sparse matrix algebra → linear scaling Core Spectra in MADNESS • sparsity aects crossover point Motivation Pseudopotentials in MADNESS Calculating Core Spectra Comparison with PW-PAW Core Hole Eects Summary

Applications of LS-BigDFT Motivation LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary

Outlook Applications of Wavelet-Based Memory Scaling DFT Laura Ratcli Sparse Matrices Introduction • even bigger savings in memory Core Spectra in MADNESS Motivation Pseudopotentials in MADNESS Calculating Core Spectra Comparison with PW-PAW Core Hole Eects Summary

Applications of LS-BigDFT Motivation LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary

Outlook Applications of Wavelet-Based Densities of States DFT Laura Ratcli Controllable Accuracy Introduction • accurate total energies, (occupied) densities of states... Core Spectra in MADNESS Motivation Pseudopotentials in MADNESS Calculating Core Spectra Comparison with PW-PAW Core Hole Eects Summary

Applications of LS-BigDFT Motivation LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary

Outlook Applications of Wavelet-Based Parallel Scaling DFT Laura Ratcli

Introduction

Core Spectra in Parallelization MADNESS Motivation • MPI and OpenMP parallelism Pseudopotentials in MADNESS • excellent parallel scaling – upper limit of 1 SF per MPI Calculating Core Spectra Comparison with PW-PAW Core Hole Eects Summary

Applications of LS-BigDFT Motivation LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary

Outlook Applications of Wavelet-Based Accurate DFT for 1000s of atoms DFT Laura Ratcli Linear Scaling DFT with Wavelets Introduction • range of materials, including metals Core Spectra in MADNESS • forces → geometry optimizations, MD Motivation Pseudopotentials in MADNESS • > 10000 atoms possible Calculating Core Spectra -1994.6 Comparison with PW-PAW 50 -1994.8

Core Hole Eects -1995 Summary 40 -1995.2 Applications of 30 -1995.4 LS-BigDFT -1995.6 Motivation 20 -1995.8 LS-BigDFT total energy (Ha)

Walltime (min.) Walltime -1996 Molecular Fragment 10 Approach -1996.2 Simulating OLEDs 0 linear -1996.4 cubic Embedded Fragments 5000 10000 15000 20000 25000 linear minus offset -1996.6 Complexity Reduction Number of atoms 0 50 100 150 200 Summary time (fs) Outlook LS-BigDFT: Mohr, LER, Boulanger, Genovese, Caliste, Goedecker and Deutsch, J. Chem. Phys. 140, 204110 (2014) Mohr, LER, Genovese, Caliste, Boulanger, Deutsch and Goedecker, Phys. Chem. Chem. Phys. 17, 31360 (2015) Goedecker, Rev. Mod. Phys. 71, 1085 (1999) LS-DFT Reviews: Bowler and Miyazaki, Rep. Prog. Phys. 75, 036503 (2012) Applications of Wavelet-Based How to Run a Calculation I DFT Laura Ratcli Input File 1: Atomic Coordinates

Introduction • filename: default is posinp.xyz, can have any name.xyz Core Spectra in MADNESS • units: angstroem, atomic or reduced (atomic) Motivation Pseudopotentials in • boundary conditions: free, surface or periodic MADNESS Calculating Core Spectra Comparison with h2o.xyz PW-PAW Core Hole Eects 3 atomic Summary free O 6.299701 1.514214 7.255132 Applications of H 5.367750 2.527720 8.481293 LS-BigDFT H 7.370068 0.372820 8.278471 Motivation LS-BigDFT Molecular Fragment Approach graphene.xyz Simulating OLEDs Embedded Fragments 8 atomic Complexity Reduction surface 9.22776 0.00000 7.99146 Summary C 0.00000 0.00000 0.00000 C 0.00000 0.00000 2.66382 Outlook C 2.30694 0.00000 3.99573 C 2.30694 0.00000 6.65955 C 4.61388 0.00000 0.00000 C 4.61388 0.00000 2.66382 C 6.92082 0.00000 3.99573 C 6.92082 0.00000 6.65955 Applications of Wavelet-Based How to Run a Calculation II DFT Input File 2: Everything Else Laura Ratcli

Introduction • filename: default is input.yaml, can have any name.yaml Core Spectra in • as few parameters as possible – sensible defaults and profiles MADNESS Motivation Pseudopotentials in Input/Output File Format MADNESS Calculating Core Spectra • use of a human readable markup language (YAML) Comparison with PW-PAW Core Hole Eects • towards workflows (Jupyter notebooks) Summary Applications of h2o.yaml LS-BigDFT Motivation import: linear_accurate LS-BigDFT dft: Molecular Fragment Approach ixc: LDA # from ABINIT or LibXC Simulating OLEDs hgrids: 0.35 # wavelet grid spacing Embedded Fragments Complexity Reduction rmult: [6, 8] # extent of grids Summary lin_basis_params:

Outlook O: nbasis: 4 # number of SFs rloc: 7.0 # SF radii H: nbasis: 1 # number of SFs rloc: 6.0 # SF radii Applications of Wavelet-Based Jupyter Notebook: Calculation Setup DFT Laura Ratcli

Introduction

Core Spectra in MADNESS Motivation Pseudopotentials in MADNESS Calculating Core Spectra Comparison with PW-PAW Core Hole Eects Summary

Applications of LS-BigDFT Motivation LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary

Outlook Applications of Wavelet-Based Jupyter Notebook: Post-Processing DFT Laura Ratcli

Introduction

Core Spectra in MADNESS Motivation Pseudopotentials in MADNESS Calculating Core Spectra Comparison with PW-PAW Core Hole Eects Summary

Applications of LS-BigDFT Motivation LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary

Introduction Calculation Boleneck Core Spectra in • SF optimization takes the majority of compute time MADNESS Motivation • what happens in similar chemical environments? Pseudopotentials in MADNESS Calculating Core Spectra Comparison with PW-PAW Core Hole Eects Water Droplet Summary

Applications of LS-BigDFT • internal molecular Motivation environment dominates LS-BigDFT Molecular Fragment Approach • dierences between water Simulating OLEDs Embedded Fragments molecules are small Complexity Reduction Summary • can we use the same SFs Outlook for each molecule? Applications of Wavelet-Based Fragment Approach DFT Laura Ratcli

Introduction

Core Spectra in MADNESS Motivation Pseudopotentials in MADNESS Calculating Core Spectra Comparison with PW-PAW Core Hole Eects Summary

Applications of LS-BigDFT Motivation LS-BigDFT Molecular Fragment Approach Calculation Steps Simulating OLEDs Embedded Fragments Complexity Reduction (1) template calculation: optimize SFs for isolated fragment Summary (2) reformaing: replicate and rototranslate template SFs for Outlook each fragment instance (3) full calculation: use fragment SFs as a fixed basis, optimizing density kernel only Applications of Wavelet-Based Detecting Rototranslations DFT Laura Ratcli Rototranslations

Introduction • need to account for varying orientations and positions

Core Spectra in • scheme to detect rototranslations with respect to reference MADNESS Motivation (“template”) coordinates Pseudopotentials in MADNESS • need to account for non-rigid fragments (i.e. distortions) Calculating Core Spectra Comparison with PW-PAW Finding the Rotation Matrix Core Hole Eects Summary • want to find the rotation matrix R between the template Applications of T S LS-BigDFT ({Ra }) and system ({Ra}) atomic positions Motivation LS-BigDFT • minimize the cost function: Molecular Fragment N N Approach 1 S T 2 Simulating OLEDs J (R)= ||Ra − RabRa || Embedded Fragments 2 X X Complexity Reduction a=1 b=1 Summary • J = 0 → rigid fragments Outlook • R can be found using the Kabsch algorithm (Wahba’s problem) via a SVD of a 3 × 3 matrix

Finding R: Kabsch, Acta Crystallogr 34, 827 (1978); Wahba, SIAM Rev. 7, 409 (1965) Markley, J. Astronaut. Sci. 36, 245 (1988) Applications of Wavelet-Based Reformaing DFT Laura Ratcli How to Rototranslate?

Introduction • accurate and eicient interpolating scaling function approach

Core Spectra in (decompose 3D rotation into 1D rotations) MADNESS Motivation 10 Pseudopotentials in cubic eggbox MADNESS linear eggbox Calculating Core template Spectra Comparison with PW-PAW 1 Core Hole Eects Summary

Applications of 0.1

LS-BigDFT (meV / atom) Motivation ref

LS-BigDFT E − Molecular Fragment Approach E 0.01 Simulating OLEDs Embedded Fragments Complexity Reduction Summary 0.001 Outlook 0 180 0 180 0 180 0 180 0 180 0 180 0 180 (0,0,1) (0,1,0) (0,1,1) (1,0,0) (1,0,1) (1,1,0) (1,1,1) θ (°), u Applications of Wavelet-Based Interacting Fragments I DFT Laura Ratcli H2O Dimer Introduction

Core Spectra in • errors decrease with increasing R MADNESS Motivation Pseudopotentials in Fragments vs. Optimized SFs MADNESS Calculating Core Spectra R (Å) E (Ha) ∆E (Ha) Comparison with PW-PAW 1.50 -34.357 0.015 Core Hole Eects 1.75 -34.368 0.008 Summary 2.00 -34.370 0.005 Applications of LS-BigDFT 2.25 -34.368 0.005 Motivation LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary

Outlook Applications of Wavelet-Based Interacting Fragments II DFT 1e+00

Laura Ratcli (eV) 1e−01 1e−02 Introduction cubic E 1e−03 −

Core Spectra in E 1e−04 MADNESS 0.5 Motivation 2.00 cubic Pseudopotentials in 0.4 linear MADNESS 0.3 1.95 fragment 1,4 Calculating Core

(Å) 1.90 fragment 2,5 Spectra 0.2 fragment 5,8 eq

(eV) 1.85 Comparison with 0.1 R PW-PAW ref 1.80

E 0.0 Core Hole Eects 1.75 − Summary −0.1 E − Applications of 0.2 R (Å) LS-BigDFT −0.3 Motivation −0.4 LS-BigDFT 1 1.5 2 2.5 3 3.5 4 4.5 5 Molecular Fragment Approach R (Å) Simulating OLEDs Embedded Fragments H2O Dimer Complexity Reduction Summary • basis set superposition error Outlook • smaller signal → bigger impact of errors • can increase basis to improve accuracy → approach is suited to weakly interacting fragments Applications of Wavelet-Based Simple Fragment Calculation I DFT Laura Ratcli

Introduction Specifying Atomic Coordinates Core Spectra in MADNESS • fragments must be listed contiguously in the position file Motivation Pseudopotentials in MADNESS Calculating Core Spectra h2o_oh_h2o.xyz Comparison with PW-PAW Core Hole Eects 8 angstroem Summary free Applications of LS-BigDFT O 0.5165 4.0131 1.5072 Motivation H 0.2906 4.0409 2.4113 LS-BigDFT Molecular Fragment H 1.4305 4.0050 1.7893 Approach Simulating OLEDs O 1.9769 1.4997 0.5021 Embedded Fragments H 2.9130 1.2542 0.7026 Complexity Reduction Summary O 3.8892 1.9854 2.2068 Outlook H 4.3592 2.8221 1.8443 H 4.3356 1.1931 1.7625 Applications of Wavelet-Based Simple Fragment Calculation II DFT Laura Ratcli Defining the Fragments Introduction Core Spectra in • each fragment type must have its own position file MADNESS Motivation Pseudopotentials in MADNESS Calculating Core h2o.xyz Spectra Comparison with PW-PAW 3 angstroem Core Hole Eects free Summary O 0.5165 4.0131 1.5072 Applications of LS-BigDFT H 0.2906 4.0409 2.4113 Motivation LS-BigDFT H 1.4305 4.0050 1.7893 Molecular Fragment Approach Simulating OLEDs Embedded Fragments oh.xyz Complexity Reduction Summary 2 angstroem Outlook free O 1.9769 1.4997 0.5021 H 2.9130 1.2542 0.7026 Applications of Wavelet-Based Simple Fragment Calculation III DFT Laura Ratcli Specifying the Fragments Introduction • each atom must be associated with a fragment Core Spectra in MADNESS • some variables need to be changed/added Motivation Pseudopotentials in MADNESS Calculating Core h2o.yaml and oh.yaml Spectra Comparison with PW-PAW lin_general: Core Hole Eects _ Summary output wf: 1 # or other values _ Applications of output mat: 21 # or other values LS-BigDFT Motivation LS-BigDFT h2o_oh_h2o.yaml Molecular Fragment Approach Simulating OLEDs dft: {inputpsiid: linear_restart} Embedded Fragments _ Complexity Reduction lin general: {nit: 1} Summary lin_basis: {nit: 1} Outlook lin_kernel: {nit: 100} frag: h2o: [ 1, 3 ] oh: [ 2 ] Applications of Wavelet-Based Simple Fragment Calculation IV DFT Laura Ratcli Calculation Setup Introduction • fragment SFs must be generated first Core Spectra in MADNESS Motivation Pseudopotentials in MADNESS Files and Directories Calculating Core Spectra h2o_oh_h2o.xyz h2o_oh_h2o.yaml Comparison with PW-PAW data-h2o_oh_h2o Core Hole Eects Summary data-h2o_oh_h2o: Applications of LS-BigDFT h2o.xyz h2o.yaml data-h2o Motivation oh.xyz oh.yaml data-oh LS-BigDFT Molecular Fragment Approach Simulating OLEDs Workflow Embedded Fragments Complexity Reduction cd data-h2o_oh_h2o Summary ./bigdft h2o Outlook ./bigdft oh cd ../ ./bigdft h2o_oh_h2o Applications of Wavelet-Based Noisy Fragments I DFT Laura Ratcli Interpreting the Output

Introduction • can identify when fragments have diering geometries Core Spectra in MADNESS Motivation log-h2o_oh_h2o.yaml Pseudopotentials in MADNESS ... Calculating Core Fragment transformations: Spectra Comparison with - Fragment name : h2o PW-PAW Angle (degrees) : 0.000000 Core Hole Eects Summary Axis : [ 0.577350, 0.577350, 0.577350 ] Wahba cost function : 3.944305E-30 Applications of LS-BigDFT - Fragment name : oh Motivation Angle (degrees) : 0.000000 LS-BigDFT Axis : [ 0.577350, 0.577350, 0.577350 ] Molecular Fragment Approach Wahba cost function : 2.366583E-30 Simulating OLEDs - Fragment name : h2o Embedded Fragments Complexity Reduction Angle (degrees) : 123.956174 Summary Axis : [ -0.759717, 0.637677, -0.127272 ] Outlook Wahba cost function : 2.115965E-01 #WARNING: Found 4 warning of high Wahba cost functions Average Wahba cost function value : 7.05E-02 Maximum Wahba cost function value : 2.12E-01 ... Applications of Wavelet-Based Noisy Fragments II DFT Laura Ratcli What Happens for Distorted Fragments?

Introduction • accuracy of energies, DoS, forces etc. correlates with value of J Core Spectra in MADNESS Motivation Rigid vs. Noisy Pseudopotentials in MADNESS Calculating Core E (Ha) ∆E (Ha) Av. J Max. J Spectra Comparison with Rigid -50.788 0.008 0.00 0.00 PW-PAW Noisy -50.689 0.114 0.07 0.21 Core Hole Eects Summary

Applications of LS-BigDFT Motivation LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary

Introduction • organic semiconductors have many advantages for Core Spectra in electronics – weight, cost, flexibility etc. MADNESS Motivation • simulation role: understanding and predicting properties, e.g. Pseudopotentials in MADNESS pre-screening candidate materials Calculating Core Spectra Comparison with • but materials tend to be disordered – simulation challenge PW-PAW Core Hole Eects Summary Modelling Charge Transport in Molecular Materials Applications of LS-BigDFT Motivation (1) generate morphology, e.g. using molecular mechanics or LS-BigDFT Molecular Fragment molecular dynamics methods Approach Simulating OLEDs (2) evaluate electronic parameters (on-site energies and transfer Embedded Fragments Complexity Reduction integrals) for a given morphology, e.g. using DFT-based Summary methods Outlook (3) simulate charge transport in the hopping regime using calculated parameters, e.g. using kinetic Monte Carlo → focus on (2) Applications of Wavelet-Based Simulation Challenge DFT Laura Ratcli Simulating OLEDs Introduction we want to calculate parameters Core Spectra in MADNESS like transfer integrals in a Motivation Pseudopotentials in disordered host-guest material MADNESS Calculating Core Spectra Comparison with PW-PAW Core Hole Eects Typical Procedure Summary

Applications of extract pairs of molecules from LS-BigDFT Motivation morphology and calculate LS-BigDFT transfer integrals for each pair Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary Environmental Eects Outlook BUT the environment can have a noticeable eect on the parameters – need large systems Applications of Wavelet-Based Electronic Parameters DFT Laura Ratcli Two Key antities Introduction Core Spectra in • transfer integrals • on-site energies MADNESS Motivation Pseudopotentials in MADNESS Calculating Core Spectra Comparison with PW-PAW Core Hole Eects Summary

Applications of LS-BigDFT Motivation LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary Fragment Approach Outlook how can we use the fragment approach to include the eect of the environment and account for statistics? Applications of Wavelet-Based Transfer Integrals I DFT Laura Ratcli

Introduction

Core Spectra in MADNESS Calculation Steps Motivation Pseudopotentials in MADNESS Fragment Orbital (FO) vs BigDFT fragment approach: Calculating Core i Spectra (1) calculate KS wvfns, |ϕ i, for isolated monomer(s) Comparison with 1,2 PW-PAW Core Hole Eects (2) use KS wvfns from isolated (2) use template SFs from Summary

Applications of monomers as a fixed basis isolated monomer(s) as a LS-BigDFT for the dimer fixed basis for the dimer Motivation LS-BigDFT (3) calculate FO Hamiltonian, (3) calculate FO Hamiltonian, Molecular Fragment Approach FO FO Simulating OLEDs H , without density H , aer self-consistent Embedded Fragments Complexity Reduction optimization density optimization Summary (4) calculate transfer integrals J12 and on-site energies e1,2 Outlook i using orthogonalized KS wvfns |ϕ˜1,2i: HOMO FO HOMO HOMO FO HOMO Jhole = hϕ˜ H ϕ˜ i ehole = hϕ˜ H ϕ˜ i 12 1 2 1 1 1

Applications of Wavelet-Based Transfer Integrals II DFT Laura Ratcli 1.00 DZ J12 LUMO −1.50 DZ e1,2 LUMO 0.80 TZP J LUMO TZP e LUMO Introduction 12 −2.00 1,2 TMB J12 LUMO TMB e1,2 LUMO 0.60 Core Spectra in −2.50 MADNESS 0.40 −3.00

Motivation Energy (eV) 0.20 Energy (eV) −3.50 Pseudopotentials in MADNESS 0.00 −4.00 Calculating Core 0 30 60 90 0 30 60 90 Spectra Rotation angle Rotation angle 1.00 Comparison with DZ J HOMO DZ e HOMO PW-PAW 12 −4.00 1,2 0.80 TZP J12 HOMO TZP e1,2 HOMO Core Hole Eects TMB J12 HOMO −4.50 TMB e1,2 HOMO 0.60 Summary −5.00 0.40 Applications of −5.50

LS-BigDFT Energy (eV) Energy (eV) 0.20 −6.00 Motivation 0.00 LS-BigDFT 0 30 60 90 0 30 60 90 Molecular Fragment Rotation angle Rotation angle Approach Simulating OLEDs Embedded Fragments Benchmark Results Complexity Reduction Summary • BigDFT (TMB) results are comparable to FO results for TZP Outlook basis • the fragment approach gives the correct sign for the transfer integrals (no ambiguity in phase factor) Applications of Wavelet-Based On-site Energies DFT Laura Ratcli

Introduction Beyond Fragment Orbital Approach Core Spectra in MADNESS Motivation how can we improve upon the one-electron picture of the FO Pseudopotentials in MADNESS approach? Calculating Core Spectra → use CDFT to introduce a net confined charge and thereby Comparison with PW-PAW Core Hole Eects include polarization eects Summary

Applications of LS-BigDFT Using CDFT Motivation LS-BigDFT • contrain a net charge (±1) on the molecule of interest Molecular Fragment Approach Simulating OLEDs • on-site energy for that molecule is defined as the dierence in Embedded Fragments Complexity Reduction total energies: Summary hole +1 0 electron −1 0 Outlook Eon-site = Etot − Etot Eon-site = Etot − Etot Applications of Wavelet-Based Constrained DFT with Fragments DFT Laura Ratcli Constrained DFT (CDFT)

Introduction • in CDFT we find the lowest energy state satisfying a given Core Spectra in (charge) constraint on the density MADNESS Motivation • we want to associate a charge with a particular fragment Pseudopotentials in MADNESS Calculating Core Spectra Comparison with CDFT with SFs PW-PAW Core Hole Eects Summary W [n, Vc]= EKS [n]+ Vc (2Tr [Kwc] − Nc) Applications of LS-BigDFT SF basis lends itself to a Löwdin like weight function: Motivation 1 1 2 2 LS-BigDFT wc = S PS Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction ZnBC-BC complex Summary

Outlook → use to find charge transfer states

CDFT and Fragments: LER, Genovese, Mohr and Deutsch, J. Chem. Phys. 142, 234105 (2015) Applications of Wavelet-Based OLED Morphology DFT Laura Ratcli

Introduction

Core Spectra in MADNESS Motivation Pseudopotentials in MADNESS Calculating Core Spectra Comparison with PW-PAW Core Hole Eects Summary

Applications of LS-BigDFT Motivation LS-BigDFT Molecular Fragment Approach Host-Guest OLED Morphology Simulating OLEDs Embedded Fragments Complexity Reduction • matrix of CBP doped with Ir(ppy)3 (∼ 6200 atoms) Summary • structures generated using Metropolis Monte Carlo combined Outlook with simulated annealing to mimic physical vapor deposition • perform calculations in clusters of nearest neighbours around each molecule to reduce computational cost Applications of Wavelet-Based Testing the Fragment Method I DFT Laura Ratcli Approximation 1: Fixed Neutral Basis Introduction

Core Spectra in • need to include an extra KS state in the SF optimization MADNESS Motivation • eigenvalues beer represented than for charged total energies Pseudopotentials in MADNESS • errors for electrons > holes Calculating Core Spectra Comparison with PW-PAW host guest Core Hole Eects Summary hole electron hole electron

Applications of Calculated, 1 e LS-BigDFT Cubic -5.22 -2.53 -4.63 -2.46 Motivation Linear -5.22 -2.51 -4.61 -2.46 host: CBP LS-BigDFT Molecular Fragment Fragment (+0 KS) -5.20 -2.15 -4.59 -2.15 Approach Fragment (+1 KS) -5.21 -2.51 -4.62 -2.43 Simulating OLEDs Embedded Fragments Complexity Reduction Calculated, all e Summary Cubic 6.60 -0.91 6.46 -0.96 Outlook Linear 6.65 -0.86 6.64 -0.96 Fragment (+0 KS) 6.68 -0.02 6.79 -0.48

Fragment (+1 KS) 6.69 -0.43 6.79 -0.81 guest: Ir(ppy)3 Applications of Wavelet-Based Testing the Fragment Method II DFT Laura Ratcli Approximation 2: Fragment Basis Introduction • fragment DoS is same quality as fully optimized SFs Core Spectra in MADNESS Motivation Pseudopotentials in MADNESS Calculating Core Spectra host: CBP Comparison with PW-PAW Core Hole Eects Summary

Applications of LS-BigDFT Motivation LS-BigDFT Molecular Fragment Approach Simulating OLEDs guest: Ir(ppy)3 Embedded Fragments Complexity Reduction Summary

Outlook Applications of Wavelet-Based Computational Protocol DFT (a) (b) Laura Ratcli

Introduction

Core Spectra in MADNESS Motivation Pseudopotentials in MADNESS + hole = ˜HOMO ˆFO ˜HOMO Ehole = E 1 − E0 Calculating Core Ji=k,j hϕi=k H ϕj i on-site tot tot Spectra Comparison with PW-PAW Core Hole Eects Template Calculations Summary

Applications of • generate SF basis for isolated host and guest molecules LS-BigDFT Motivation LS-BigDFT Neutral Calculation in Cluster k (Fixed Basis) Molecular Fragment Approach Simulating OLEDs • generate FO Hamiltonian using optimized density Embedded Fragments Complexity Reduction • calculate transfer integrals Ji=k,j for molecule k (a) Summary Outlook CDFT Calculations in Cluster k (Fixed Basis) • use CDFT to add ±1 charge to molecule k • calculate on-site energies for molecule k (b) Applications of Wavelet-Based On-Site Energies DFT Laura Ratcli

Introduction

Core Spectra in pure host pure host MADNESS Motivation Pseudopotentials in MADNESS Calculating Core host host Spectra Comparison with PW-PAW Core Hole Eects Summary guest guest

Applications of LS-BigDFT Motivation 4.4 4.6 4.8 5.0 5.2 5.4 5.6 6.2 6.4 6.6 6.8 7.0 7.2 7.4 LS-BigDFT Energy (eV) Energy (eV) Molecular Fragment Approach Simulating OLEDs Embedded Fragments Hole On-Site Energies – Environment and Statistics Complexity Reduction Summary • dierences between FO-DFT [le] and CDFT [right] Outlook • disorder → dispersion of values for both methods

• CDFT: polarization leads to shi in average Eon-site (- - -) vs isolated molecules (—) Applications of Wavelet-Based Transfer Integrals DFT Laura Ratcli

Introduction 0.10 0.10 Core Spectra in MADNESS Motivation 0.05 0.05 Pseudopotentials in MADNESS Calculating Core Spectra 0.00 0.00 Comparison with PW-PAW Core Hole Eects

Summary transfer integrals (eV) 0.05 transfer integrals (eV) 0.05

Applications of LS-BigDFT 0.10 0.10 Motivation 4 6 8 10 12 14 4 6 8 10 12 14 distance (Å) distance (Å) LS-BigDFT Molecular Fragment Approach Hole Transfer Integrals – Statistics Simulating OLEDs Embedded Fragments Complexity Reduction • some dependence on distance Summary

Outlook • poor correlation between relative orientation and Jij → importance of both environment and statistics

Host-Guest Application: LER, Grisanti, Genovese, Deutsch, Neumann, Danilov, Wenzel, Beljonne and Cornil, J. Chem. Theory Comput. 11, 2077 (2015) Applications of Wavelet-Based Outline DFT 1 Introduction Laura Ratcli 2 Core Spectra in MADNESS Introduction Motivation Core Spectra in MADNESS Pseudopotentials in MADNESS Motivation Pseudopotentials in Calculating Core Spectra MADNESS Calculating Core Spectra Comparison with PW-PAW Comparison with PW-PAW Core Hole Eects Core Hole Eects Summary Summary Applications of 3 Applications of LS-BigDFT LS-BigDFT Motivation Motivation LS-BigDFT Molecular Fragment LS-BigDFT Approach Simulating OLEDs Molecular Fragment Approach Embedded Fragments Complexity Reduction Simulating OLEDs Summary Embedded Fragments Outlook Complexity Reduction Summary 4 Outlook Applications of Wavelet-Based Fragments in SiCNT I DFT Laura Ratcli SF Repetition in Extended Systems Introduction

Core Spectra in • can we also exploit repetition in non-molecular systems? MADNESS Motivation • for a finite NT the SFs feel the eects of the edges Pseudopotentials in MADNESS • quantitative measure of basis similarity (onsite overlap matrix) Calculating Core Spectra Comparison with PW-PAW Core Hole Eects Summary

Applications of LS-BigDFT Motivation LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary

Outlook Applications of Wavelet-Based Fragments in SiCNT II DFT Laura Ratcli Introduction Embedded Pseudo-Fragments Core Spectra in MADNESS Motivation • fragments are rings of the NT Pseudopotentials in MADNESS • generate fragments in an environment Calculating Core Spectra Comparison with • for finite NT need more than one fragment type PW-PAW Core Hole Eects Summary Template Fragment Template Fragment Applications of Calculation Calculation Calculation Calculation optimize LS-BigDFT support optimize functions Motivation support LS-BigDFT functions Molecular Fragment Approach

Simulating OLEDs replicate replicate Embedded Fragments support support functions functions Complexity Reduction Summary

Outlook ¡ xed ﬁxed support support functions functions Applications of Wavelet-Based Fragments in SiCNT III DFT Laura Ratcli Embedded Pseudo-Fragments

Introduction • errors converge with number of unique pseudo-fragments Core Spectra in • MADNESS fragments are not rigid (J 6= 0) Motivation Pseudopotentials in MADNESS Energy Convergence Calculating Core Spectra Comparison with PW-PAW E E − Ecubic Band Gap Wahba Cost Function Core Hole Eects eV/atom meV/atom eV Average Maximum Summary Periodic NT Applications of LS-BigDFT Cubic -130.802 - 2.37 - - Motivation Linear -130.793 9.6 3.79 - - LS-BigDFT 1 PFrag -130.789 13.0 3.74 0.000 0.000 Molecular Fragment Approach Finite NT Simulating OLEDs Cubic -130.729 - 2.22 - - Embedded Fragments Complexity Reduction Linear -130.719 9.9 3.63 - - Summary 2 PFrags -125.087 5642.3 1.81 185.000 235.000 Outlook 4 PFrags -129.771 958.0 3.03 1.220 1.970 6 PFrags -130.676 53.4 3.58 0.112 0.221 8 PFrags -130.713 16.4 3.61 0.007 0.015 10 PFrags -130.715 14.2 3.61 0.002 0.009 Applications of Wavelet-Based Fragments in SiCNT IV DFT Laura Ratcli Embedded Pseudo-Fragments Introduction • need to go ∼ 10 Å before the SFs stop ‘feeling’ the edges Core Spectra in MADNESS • Motivation agrees with the values of the onsite overlap matrix Pseudopotentials in MADNESS Calculating Core Spectra Comparison with PW-PAW Core Hole Eects Summary

Applications of LS-BigDFT Motivation LS-BigDFT Molecular Fragment Approach Simulating OLEDs Embedded Fragments Complexity Reduction Summary

Outlook Applications of Wavelet-Based Fragments in Defective Systems DFT Laura Ratcli Defect Calculations in Graphene Introduction • extend the above approach to 2D material Core Spectra in MADNESS • use atomic pseudo-fragments Motivation Pseudopotentials in • MADNESS can use to assess defect ‘extension’ Calculating Core Spectra Comparison with PW-PAW Core Hole Eects Summary

Applications of LS-BigDFT Motivation LS-BigDFT Molecular Fragment −1 Approach 10 Simulating OLEDs

Embedded Fragments (eV/atom) Complexity Reduction − Summary 2 linear 10 E

Outlook − frag

E − 10 3 0 2 4 6 8 10 12 14 Distance from Si (Å) Embedded Fragments: LER and Genovese, in preparation (2018) Applications of Wavelet-Based Outline DFT 1 Introduction Laura Ratcli 2 Core Spectra in MADNESS Introduction Motivation Core Spectra in MADNESS Pseudopotentials in MADNESS Motivation Pseudopotentials in Calculating Core Spectra MADNESS Calculating Core Spectra Comparison with PW-PAW Comparison with PW-PAW Core Hole Eects Core Hole Eects Summary Summary Applications of 3 Applications of LS-BigDFT LS-BigDFT Motivation Motivation LS-BigDFT Molecular Fragment LS-BigDFT Approach Simulating OLEDs Molecular Fragment Approach Embedded Fragments Complexity Reduction Simulating OLEDs Summary Embedded Fragments Outlook Complexity Reduction Summary 4 Outlook Applications of Wavelet-Based Bridging the Gap – Beyond QM DFT Laura Ratcli

Introduction Core Spectra in Overlapping Length-Scale Regimes MADNESS Motivation Pseudopotentials in how can we connect LS-DFT and classical simulations? MADNESS Calculating Core Spectra → use SFs to map quantum information to localized DoF (i.e. Comparison with PW-PAW reduce the complexity) Core Hole Eects Summary Applications of Extracting Local Information LS-BigDFT Motivation LS-BigDFT • partial densities of states Molecular Fragment Approach • Hamiltonian and DM Simulating OLEDs Embedded Fragments • Complexity Reduction atomic charges/multipoles – can connect with classical Summary methods (e.g. electrostatic embedding) Outlook Applications of Wavelet-Based Charge Analysis for Solvated DNA I DFT Laura Ratcli DNA Fragment in Solution Introduction Core Spectra in • 11 base pairs in Na/H2O solution (15,613 atoms) MADNESS Motivation • full DFT calculation in 2h15m (800 MPI, 8 OMP) Pseudopotentials in MADNESS Calculating Core H O* O Na Spectra C OH O H 2 Comparison with N H2O PW-PAW P Core Hole Eects Summary

Applications of normalized occurence LS-BigDFT -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 Motivation atomic net charge LS-BigDFT Molecular Fragment Approach Atomic → Fragment Charge Analysis Simulating OLEDs Embedded Fragments Complexity Reduction • Mulliken (and Löwdin) values are strongly basis-dependent – Summary can be unphysical Outlook • atomic charges are not (in general) physical observables • solution: calculate charges only for independent fragments Applications of Wavelet-Based Purity Indicator: Identifying Fragments DFT Laura Ratcli Can we Predict if a Fragmentation is Meaningful?

Introduction suppose a QM system (with Fˆ = |ΨihΨ|) can be split into M ′ Core Spectra in independent fragments F, i.e. hΨF |ΨF i = δ ′ , MADNESS FF F Motivation ⇒ there exists a projection operator Wˆ such that Pseudopotentials in F F MADNESS Wˆ |Ψi = |Ψ i Calculating Core Spectra Comparison with the fragment DM should satisfy (separability, idempotency) PW-PAW 2 Core Hole Eects ˆF ˆ ˆ F F F ˆF Summary F = FW = |Ψ ihΨ | = F Applications of LS-BigDFT when expressed in a localized basis Motivation ˆ αβ ˆ F αβ LS-BigDFT F = |φαiK hφβ|; W = |φαiRF hφβ| Molecular Fragment X X Approach αβ αβ Simulating OLEDs Embedded Fragments ⇒ a good choice of fragment should satisfy Complexity Reduction Summary 1 2 Π= Tr (KSF ) − KSF ≃ 0; SF = SRF S Outlook QF

−1 we can define dierent RF , e.g. Mulliken: RF = TF S or −1/2 −1/2 Löwdin: RF = S TF S , (TF selects the indices α ∈ F) Applications of Wavelet-Based Testing the Purity Indicator DFT Laura Ratcli 100 Molecule Water Droplet

Introduction Π explicitly depends on the fragment choice, population analysis Core Spectra in scheme and SFs MADNESS Motivation Pseudopotentials in Optimized SFs Atomic Orbitals MADNESS non-optimized atomic orbitals Calculating Core optimized quasi-orthogonal support functions

Spectra ) reference ) Fermi energy reference Fermi energy -1 sp/s Comparison with -1 sp/s - type spd/sp spd/sp - type spdf/spd PW-PAW spdf/spd - type

Core Hole Eects DoS (ha DoS (ha Summary -1 -0.8 -0.6 -0.4 -0.2 0 -1 -0.8 -0.6 -0.4 -0.2 0 energy (ha) energy (ha) Mulliken-Type Projector Mulliken-Type Projector Applications of Mulliken-Type Projector Mulliken-Type Projector spdf/spd spdf/spd LS-BigDFT spdf/spd - type spdf/spd - type spd/sp spd/sp Motivation spd/sp - type spd/sp - type occurence occurence sp/s sp/s occurence LS-BigDFT occurence sp/s - type sp/s - type

Molecular Fragment 0 0.05 0.1 0.15 0.2 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.05 0.1 0.15 0.2 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Purity Indicator Norm of water Dipole moment (D) Approach Purity Indicator Norm of water Dipole moment (D) Simulating OLEDs Embedded Fragments optimizedSFs atomicorbitals Complexity Reduction Summary sp/s spd/sp spdf/spd sp/s spd/sp spdf/spd ✔ ✔ ✔ ✘ ✔ ✔ Outlook DoS non-purity ✔ ✘ ✘ ✔ ✘ ✘ H2O dipole ✔ ✘ ✘ ✔/✘✘ ✘ → optimized minimal basis set provides reliability Applications of Wavelet-Based Charge Analysis for Solvated DNA II DFT Laura Ratcli Complexity Reduction Cytosine Introduction • Mulliken projector Core Spectra in MADNESS • minimal optimized basis -0.80 -0.75 -0.70 -0.65 -0.60 -0.55 Motivation nucleotide net charge

Pseudopotentials in Guanine MADNESS • small Π ↔ chemically Calculating Core Spectra sound charges Comparison with

PW-PAW -0.80 -0.75 -0.70 -0.65 -0.60 -0.55 nucleotide net charge Core Hole Eects • can connect QM and MM Summary via fragment multipoles Applications of LS-BigDFT Motivation Atoms: Unphysical Charges Fragments: Chemically Sound LS-BigDFT Molecular Fragment H O* H2O Approach O Na PO4 C OH O Cytosine nucleotide H 2 Simulating OLEDs N H2O Guanine nucleotide P Embedded Fragments Complexity Reduction Summary normalized occurence normalized occurence Outlook -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 -1.5 -1.0 -0.5 0.0 0.5 atomic net charge fragment net charge ∗ H C N OO Na P PO4 Cyt Gua H2O Π 0.48 0.48 0.32 0.15 0.12 0.04 0.34 Π 0.05 0.01 0.01 0.01

Complexity Reduction: Mohr, Masella, LER and Genovese, J. Chem. Theory Comput. 13, 4079 (2017) Applications of Wavelet-Based Outline DFT 1 Introduction Laura Ratcli 2 Core Spectra in MADNESS Introduction Motivation Core Spectra in MADNESS Pseudopotentials in MADNESS Motivation Pseudopotentials in Calculating Core Spectra MADNESS Calculating Core Spectra Comparison with PW-PAW Comparison with PW-PAW Core Hole Eects Core Hole Eects Summary Summary Applications of 3 Applications of LS-BigDFT LS-BigDFT Motivation Motivation LS-BigDFT Molecular Fragment LS-BigDFT Approach Simulating OLEDs Molecular Fragment Approach Embedded Fragments Complexity Reduction Simulating OLEDs Summary Embedded Fragments Outlook Complexity Reduction Summary 4 Outlook 50

Applications of 40 Wavelet-Based Summary 30 DFT 20

Walltime (min.) 10

Laura Ratcli 0 5000 10000 15000 20000 25000 LS-DFT and Fragments Number of atoms Introduction

Core Spectra in • large and complex systems

MADNESS support function reformatting Motivation • systematic approach support function optimization Pseudopotentials in MADNESS • exploit repetition Calculating Core Spectra Comparison with PW-PAW Example Applications Core Hole Eects Summary • disordered supramolecular Applications of LS-BigDFT materials Motivation LS-BigDFT • extended systems Molecular Fragment Approach Simulating OLEDs • solvated DNA Embedded Fragments Complexity Reduction Future Challenges Summary

Cytosine Outlook • implement new functionalities

-0.80 -0.75 -0.70 -0.65 -0.60 -0.55 (hybrid functionals, excitations, nucleotide net charge Guanine spin, fragment forces...)

-0.80 -0.75 -0.70 -0.65 -0.60 -0.55 nucleotide net charge Applications of Wavelet-Based Bringing it all Together DFT Laura Ratcli Controlling Errors Across Methods and Lengthscales Introduction • (multi-)wavelets provide a framework for assessing and Core Spectra in MADNESS controlling numerical errors Motivation Pseudopotentials in • could quantify errors for DFT approaches across lengthscales MADNESS Calculating Core Spectra Comparison with PW-PAW Core Hole Eects Summary QM/MM Applications of LS-BigDFT Implicit Solvent Motivation Fragments LS-BigDFT Molecular Fragment Fixed Basis Approach O(N) BigDFT Simulating OLEDs Embedded Fragments Complexity Reduction Localization O(N³) BigDFT Summary MADNESS PSP

Outlook of Approximation Level PSP MADNESS AE

Number of Atoms Applications of Wavelet-Based Acknowledgments DFT Laura Ratcli MADNESS Introduction Nick Romero Álvaro Vázquez-Mayagoitia Sco Thornton Core Spectra in MADNESS Robert Harrison et al., SIAM J. Sci. Comput. 38, S123 (2016) Motivation https://github.com/m-a-d-n-e-s-s/madness Pseudopotentials in MADNESS Calculating Core Spectra BigDFT and Applications Comparison with PW-PAW Core Hole Eects Michel Masella Summary Luigi Genovese Luca Grisanti Applications of Stephan Mohr LS-BigDFT David Beljonne Motivation Thierry Deutsch LS-BigDFT Jérome Cornil Molecular Fragment Paul Boulanger Approach Tobias Neumann Simulating OLEDs Damien Caliste Embedded Fragments Denis Danilov Complexity Reduction Stefan Goedecker Summary Wolfgang Wenzel Outlook www.bigdft.org Thank you for your aention!