Dispersion Correcting Atom Centered Potentials (DCACP) and Many-Body Dispersion (MBD) contributions to interatomic vdw forces
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1 Dispersion Correcting Atom Centered Potentials (DCACP) and Many-Body Dispersion (MBD) contributions to interatomic vdw forces O. Anatole von Lilienfeld Current: Argonne Leadership Computing Facility From 2013: Chemistry Department, Basel University
2 Overview Introduction Why do we care? What's the problem with vdw? Atom-Electron approach (DCACP) Motivation First attempts Applications Atom-Atom approach (MBD) Many-body dispersion in DFT 3-body dispersion effects Many-body dispersion effects
3 Why do we care? ``There is plenty of room at the bottom'' (Feynman) Intermolecular bonds are weaker than chemical bond, yet crucial for many highly relevant processes Self-assembly Supra-molecular Adhesion, adsorption, physisorption Liquid phase (Solid covalent, Gas ideal) Nano- and meso-scale objects Soft matter Biological systems
4 Why do we care? Papers by D. Andrienko et al, OAvL & Andrienko, JCP (2007)
5 Why do we care? Low-dimensional systems Supra-molecular systems, liquids, and solids Hybrid organic/inorganic interfaces Physico-chemical Properties and reactions Ionic systems Metals, alloys, Semi-conductors, defects
6 Why do we care? compound design Science (1991) Many more Norskov et al (Stanford/DTU) Curtarolo&Beratan&Yang (Duke) Ceder (MIT) Wolverton (Northwestern) Zunger (NREL) Yamashita (UT) von Lilienfeld (ANL) A Franceschetti & A Zunger, Nature (1999) 6
7 What's the problem with vdw? Ar Ar
8 What's the problem with vdw? vdw-dft: Non-local functionals (depend explicitly on r and r') (Dion, Langreth, Lundqvist et al. PRL (2004)). SAPT-DFT: Explicit energy expansion for weakly interacting moieties (Jeziorski, Szalewicz, Podeszwa et al. CR (1994), Hesselmann, Jansen) Empirical density functionals (Truhlar et al. JCP (2006), Goddard PNAS (2004),...) Empirical atom centered potentials (von Lilienfeld, Tavernelli, Roethlisberger, Sebastiani PRL (2004), DiLabio CPL (2008)) Interatomic (pairwise or beyond) dispersion corrections Ahlrichs, Scoles et al (70's and 80's); Elstner, Hobza, Frauenheim, Kaxiras et al (2001); Wu and Yang JCP (2002); Grimme J. Comp. Chem. (2004,2006); Johnson and Becke JCP ( ); Silvestrelli PRL (2008); Tkatchenko and Scheffler PRL (2009); and others...
9 What's the problem with vdw? Langreth-Lundqvist functional Dion, Rydberg, Schroeder, Langreth, Lundqvist, PRL (2004). Lee, Murray, Kong, Lundqvist, Langreth, PRB (2010).
10 What's the problem with vdw? Langreth-Lundqvist functional (vdw-df-04 and vdw-df-10) vdw-df-04 vdw-df-10 Exchange: revpbe Exchange: PW86 Local corr.: LDA Local corr.: LDA No free parameters 2 parameters C6 error: ~ 20% C6 error: ~ 60%(*) (*) Vydrov and van Voorhis, PRA (2010).
11 Overview Introduction Why do we care? What's the problem with vdw? Atom-Electron approach (DCACP) Motivation First attempts Applications Atom-Atom approach (MBD) Many-body dispersion in DFT 3-body dispersion effects Many-body dispersion effects
12 Dispersion corrected atom centered potentials (DCACP)
13 Motivation General idea electron-electron atom-atom atom-electron Feynman, Phys Rev (1939)
14 Motivation General idea electron-electron atom-atom atom-electron Feynman, Phys Rev (1939)
15 Motivation Feynman, Phys Rev (1939) R
16 Motivation Feynman, Phys Rev (1939) R R R 1/R7
17 Motivation Add atom centered potential to external potential in SCF Act weakly on electrons in outer low density regions Atom-electron corrections not unusual in solid state physics relativistic effects for heavy atoms DFT+U dispersion corrected atom centered potentials (DCACP) in 2004 self-interaction correction (Pollmann (2006)) band-gap correction (van de Walle (2007))
18 Overview Introduction Why do we care? What's the problem with vdw? Atom-Electron approach (DCACP) Motivation First attempts Applications Atom-Atom approach (MBD) Many-body dispersion in DFT 3-body dispersion effects Many-body dispersion effects
19 First attempts von Lilienfeld, Tavernelli, Sebastiani, Roethlisberger, PRL (2004)
20 First attempts von Lilienfeld, Tavernelli, Sebastiani, Roethlisberger, PRL (2004); von Lilienfeld et al, PRB (2005)
21 DCACP applications Tapavizca, Lin, von Lilienfeld, Tavernelli, Coutinho-Neto, Roethlisberger, JCTC (2007)
22 DCACP applications Lin, von Lilienfeld, Coutinho-Neto, Tavernelli, Roethlisberger, JCPA (2007)
23 DCACP applications Roethlisberger group:
24 DCACP applications Tavernelli et al, Phys Rev B (2009)
25 Overview Introduction Why do we care? What's the problem with vdw? Atom-Electron approach (DCACP) Motivation First attempts Applications Atom-Atom approach (MBD) Many-body dispersion in DFT 3-body dispersion effects Many-body dispersion effects
26 Many-body dispersion in DFT Pair-wise corrected DFT A RAB B Tkatchenko & von Lilienfeld, PRB (2008)
27 Many-body dispersion in DFT r1 Coulomb Screening A RAB r2 B Many-body vdw Energy
28 Many-body dispersion in DFT Many-body vdw Energy
29 Many-body dispersion in DFT Many-body vdw Energy Tkatchenko & von Lilienfeld, PRB (2008)
30 Many-body dispersion in DFT Many-body vdw Energy Tkatchenko & von Lilienfeld, PRB (2008)
31 Many-body dispersion in DFT For rare gas crystals, experimental MBC estimated to be up to 10% of cohesive energy Many-body vdw Energy Tkatchenko & von Lilienfeld, PRB (2008) Functional MBC LDA 35 % PBE 50 % TPSS 80 %
32 Overview Introduction Why do we care? What's the problem with vdw? Atom-Electron approach (DCACP) Motivation First attempts Applications Atom-Atom approach (MBD) Many-body dispersion in DFT 3-body dispersion effects Many-body dispersion effects
33 3-body dispersion effects Many-body vdw Energy von Lilienfeld & Tkatchenko, JCP (2010)
34 3-body dispersion effects von Lilienfeld & Tkatchenko, JCP (2010) Tkatchenko&Scheffler, PRL (2009)
35 3-body dispersion effects Many-body vdw Energy von Lilienfeld & Tkatchenko, JCP (2010)
36 3-body dispersion effects Damping according to Tang&Toennis von Lilienfeld & Tkatchenko, JCP (2010) Tkatchenko&Scheffler, PRL (2009)
37 3-body dispersion effects Many-body vdw Energy von Lilienfeld & Tkatchenko, JCP (2010)
38 3-body dispersion effects Many-body vdw Energy von Lilienfeld & Tkatchenko, JCP (2010)
39 3-body dispersion effects Many-body vdw Energy von Lilienfeld & Tkatchenko, JCP (2010)
40 Overview Introduction Why do we care? What's the problem with vdw? Atom-Electron approach (DCACP) Motivation First attempts Applications Atom-Atom approach (MBD) Many-body dispersion in DFT 3-body dispersion effects Many-body dispersion effects
41 Many-body dispersion effects Many-body vdw Energy Tkatchenko, von Lilienfeld, DiStasio, accepted in PNAS (2012)
42 Many-body dispersion effects r1 Coulomb Screening A RAB r2 B Many-body vdw Energy Use DFT+MBD method A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, PRL (2012).
43 TS-vdW method Self-consistent electrostatic screening (SCS) Many-body vdw energy for a system of coupled oscillators (CFDM) A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, PRL (2012).
44 Many-body dispersion effects SCS: Polarization and anisotropy in H6 TS-vdW: +SCS: LR-CCSD: C6 C6 C6iso (Reference) All values in HartreeBohr6
45 Many-body dispersion effects C6 coefficients: from small to large silicon clusters 27% error TDLDA: S. Botti et al., PRB (2008)
46 PBE(0)+MBD: S22 database PBE+vdW PBE+MBD PBE0+MBD MARE PBE+vdW 9.1% PBE+MBD 5.4% PBE0+MBD 4.2% S22 CCSD(T): Jurecka, Sponer, Cerny, Hobza, PCCP (2006); Sherrill et al., JCP (2010).
47 Many-body dispersion effects Important features of DFT+MBD F A B E D C Seamless treatment of short-range (quantum) and long-range (classical) screening Models anisotropy, polarization, and depolarization for non-metallic molecules and solids Computes many-body dipole vdw energy to infinite order with a single parameter Negligible computational cost compared to DFT (MBD calculation takes 1 min. for 1000 atoms on 1 processor) A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, PRL (2012).
48 Many-body dispersion effects Many-body vdw Energy Tkatchenko, von Lilienfeld, DiStasio, accepted in PNAS (2012)
49 Many-body dispersion effects Many-body vdw effects at play: Benzene molecular crystal PBE+vdW 690 mev/molecule PBE+MBD 565 mev/molecule 2.9 kcal/mol due to screening and many-body VdW effects Experiment mev/molecule Tkatchenko, von Lilienfeld, DiStasio, accepted in PNAS (2012)
50 Many-body dispersion effects Many-body vdw effects at play: Ellipticine BLYP+DCACP -37 kcal/mol PBE+vdW kcal/mol PBE+MBD kcal/mol Lin, von Lilienfeld, Coutinho-Neto, Tavernelli, Rothlisberger, J. Phys. Chem. B (2007); von Lilienfeld and Tkatchenko, J. Chem. Phys. (2010). Tkatchenko, von Lilienfeld, DiStasio, accepted in PNAS (2012)
51 Many-body dispersion effects Many-body vdw Energy Tkatchenko, von Lilienfeld, DiStasio, accepted in PNAS (2012)
52 Overview Introduction Why do we care? What's the problem with vdw? Atom-Electron approach (DCACP) Motivation First attempts Applications Atom-Atom approach (MBD) Many-body dispersion in DFT 3-body dispersion effects Many-body dispersion effects
53 Outlook BG/Q (Mira) Argonne Leadership Computing Facility promotes open science internationally through INCITE program ( Systems: Large and crowded Many Methods: High quality (QMC, MBPT, CCSD(T)...)
54 Acknowledgments Rothlisberger, EPFL Tkatchenko, FHI Tavernelli, EPFL DiStasio, Princeton Sebastiani, FU Berlin Dobson, Griffith U This research used resources of the Argonne Leadership Computing Facility at Argonne National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under contract DE-AC02-06CH11357.
55 S22 database: Comparison with other approaches S22 CCSD(T): Jurecka, Sponer, Cerny, Hobza, PCCP (2006); Scherrill et al., JCP (2010).
56 Many-body dispersion effects The current state-of-the-art (Grimme, Becke, Tkatchenko/Scheffler) Effective screening and two-body energy The new state-of-the-art: Full many-body screening and energy for a system of quantum oscillators F A A B Valid for small molecules or homogeneous dielectrics B E C Valid for small and large molecules, insulators, metals, interfaces,... D
57 Many-body dispersion effects C6 coefficients: 1225 atomic/molecular dimers TS-vdW TS-vdW+SCS A. Tkatchenko and M. Scheffler, PRL (2009)
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