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