When (2 + 2) 4? Alexandre Tkatchenko Fritz Haber Institut der Max Planck Gesellschaft, Berlin, Germany
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1 When (2 + 2) 4? Alexandre Tkatchenko Fritz Haber Institut der Max Planck Gesellschaft, Berlin, Germany QMC@TTI, Apuan Alps, Jul 29, 2013
2 When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko Fritz Haber Institut der Max Planck Gesellschaft, Berlin, Germany QMC@TTI, Apuan Alps, Jul 29, 2013
3 Acknowledgments Robert A. DiStasio Anatole von Lilienfeld Matthias Scheffler Roberto Car
4 Acknowledgments Robert A. DiStasio Matthias Scheffler Anatole von Lilienfeld Alberto Ambrosetti Roberto Car Vivek Gobre Anthony Reilly
5 Textbook picture of vdw interactions A B
6 Textbook picture of vdw interactions B A + B A + + B A R
7 Textbook picture of vdw interactions B A + B A + + B A R
8 Reality check for vdw from experiment Beguin et al. PRL 110, (2013).
9 Beguin et al. PRL 110, (2013).
10 Beyond textbook model of vdw interactions: Electrodynamic response effects r1 A RAB r2 B
11 Beyond textbook model of vdw interactions: Electrodynamic response effects r1 A RAB r2 B
12 Beyond textbook model of vdw interactions: Electrodynamic response effects 1 Accurate Microscopic Modeling of Coulomb Response 2 r1 A RAB r2 B Full (All Order) Many Body van der Waals Energy
13 Beyond textbook model of vdw interactions: Electrodynamic response effects 1 2 r1 Accurate Microscopic Modeling of Coulomb Response A RAB r2 B Full (All Order) Many Body van der Waals Energy We know how to solve the problem, albeit not very efficiently
14 Electrodynamic treatment of vdw interactions: beyond hybridized atoms
15 Electrodynamic treatment of vdw interactions: beyond hybridized atoms Multi layered graphene
16 Electrodynamic treatment of vdw interactions: beyond hybridized atoms
17 Electrodynamic treatment of vdw interactions: beyond hybridized atoms Vivek Gobre V. V. Gobre and A. Tkatchenko, Nature Comm. (2013)
18 How long ranged are vdw interactions? Direct experimental evidence SiO2 Si P. Loskill, H. Hähl, T. Faidt, S. Grandthyll, F. Müller, and K. Jacobs, Adv. Coll. Interf. Sci. 107, (2012). P. Loskill, J. Puthoff, M. Wilkinson, K. Mecke, K. Jacobs and K. Autumn, J. R. Soc. Interface, to be published (2013).
19 How long ranged are vdw interactions? Direct experimental evidence SiO2 Si P. Loskill, H. Hähl, T. Faidt, S. Grandthyll, F. Müller, and K. Jacobs, Adv. Coll. Interf. Sci. 107, (2012). P. Loskill, J. Puthoff, M. Wilkinson, K. Mecke, K. Jacobs and K. Autumn, J. R. Soc. Interface, to be published (2013).
20 Towards Efficient Many Body Treatment of vdw Interactions The conventional approach (Grimme, Johnson Becke/Corminboeuf, Tkatchenko Scheffler, Langreth Lundqvist vdw DF, Vydrov van Voorhis,...) Effective screening and two body energy A B Valid for small molecules or homogeneous dielectrics
21 Towards Efficient Many Body Treatment of vdw Interactions The conventional approach (Grimme, Johnson Becke/Corminboeuf, Tkatchenko Scheffler, Langreth Lundqvist vdw DF, Vydrov van Voorhis,...) Effective screening and two body energy A The new state of the art: Full many body response and energy for a system of quantum oscillators (DFT+MBD) F A B B Valid for small molecules or homogeneous dielectrics E D C Valid for small and large molecules, insulators, metals, interfaces,... A. Tkatchenko and M. Scheffler, Phys. Rev. Lett. (2009). A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, Phys. Rev. Lett. (2012). R. A. DiStasio Jr., O. A. von Lilienfeld, A. Tkatchenko, Proc. Natl. Acad. Sci. (2012).
22 The Model: Quantum Harmonic Oscillator (QHO) Nucleus (q) Harmonic bond ( ) Electron ( q,m) Model proposed by W. L. Bade (1957); and used by B. J. Berne; A. Donchev; M. W. Cole; G. Martyna; K. Jordan; and others.
23 The Model: Quantum Harmonic Oscillator (QHO) Nucleus (q) Harmonic bond ( ) In the dipole approximation: (, ) fully characterize the QHO Electron ( q,m) Model proposed by W. L. Bade (1957); and used by B. J. Berne; A. Donchev; M. W. Cole; G. Martyna; K. Jordan; and others.
24 First Principles Model: QHOs in Molecules and Solids α0 and ω0 include short range hybridization C6 = C6[n(r)], RvdW = RvdW[n(r)] A. Tkatchenko and M. Scheffler, Phys. Rev. Lett. (2009)
25 The Method: DFT+MBD TS vdw method Self consistent electrodynamic response (Dyson) Many body vdw energy for a system of coupled oscillators (RPA) A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, Phys. Rev. Lett. (2012).
26 Salient Features of the MBD Method F A B E D C Seamless treatment of short range (quantum) and long range (classical) electrodynamic response Full correlation energy of coupled QHOs is equivalent to the random phase approximation or ring CCD (JCP 138, (2013)) Computes many body vdw energy to infinite order Negligible computational cost compared to DFT (MBD calculations can be easily done for > 10,000 atoms)
27 (Hartree) Coupling DFT and MBD by range separation of the Coulomb potential EDFT+MBD=EDFT+EMBD (bohr) See work on range separation by A. Savin, H. Stoll, G. Scuseria, K. Hirao,...
28 Performance of DFT+MBD for gas phase intermolecular interactions S22 CCSD(T): Jurecka, Sponer, Cerny, Hobza, PCCP (2006); Sherrill et al., JCP (2010).
29 Large many body vdw effects in complex molecular geometries R. A. DiStasio Jr., O. A. von Lilienfeld, and A. Tkatchenko, PNAS (2012)
30 Chemically Accurate Predictions for Molecular Materials A. M. Reilly A. M. Reilly and A. Tkatchenko, J. Phys. Chem. Lett. 4, 1028 (2013).; J. Chem. Phys. 139, (2013).
31 Chemically Accurate Predictions for Molecular Materials A. M. Reilly Anthony Reilly PBE0+MBD overall accuracy: 0.8 kcal/mol; 4.6% A. M. Reilly and A. Tkatchenko, J. Phys. Chem. Lett. 4, 1028 (2013).
32 DFT+MBD correctly discriminates between crystal polymorphs: Example of glycine
33 DFT+MBD correctly discriminates between crystal polymorphs: Example of glycine Angew. Chem. (2013). Overall
34 Long range double screening in DFT+MBD TS vdw method Self consistent electrodynamic response (Dyson) Many body vdw energy for a system of coupled oscillators (RPA) A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, Phys. Rev. Lett. (2012).
35 s: m e t s y s n s r e e a e u l ls l u tw c ta c e be o l e ys l o k m cr m in e r a r l as l a p a h cu u S e p l s o a g dm an S. Grimme et al., JCTC (2013).
36 6 systems out of S12L database S. Grimme, Chem. Eur. J. (2012) Diffusion Quantum Monte Carlo: A. Tkatchenko, D. Alfe, K. S. Kim, JCTC (2012); and D. Alfe et al., to be published.
37 Binding in supramolecular systems: DMC vs. Experiment vs.pbe+mbd* (kcal/mol, DMC sampling error is +/ 1.5 kcal/mol) Experimental values: S. Grimme, Chem. Eur. J. (2012).
38 Binding in supramolecular systems: DMC vs. Experiment vs.pbe+mbd* (kcal/mol, DMC sampling error is +/ 1.5 kcal/mol) Experimental values: S. Grimme, Chem. Eur. J. (2012).
39 Binding in supramolecular systems: PBE+MBD performance within DMC error bar MAE of PBE+MBD* vs. DMC: 1.6 kcal/mol MAE of PBE+MBD* vs. Exp. 2.9 kcal/mol S. Grimme (2012) Alberto Ambrosetti
40 Reconciling theory and experiment: Measurement of vdw potential for single adsorbed molecule to be published, Phys. Rev. Lett. (2013)
41 Single molecule measurement of adsorption energy by AFM C. Wagner et al., PRL 109, (2012).
42 Single molecule measurement of adsorption energy by AFM C. Wagner et al., PRL 109, (2012).
43 Summary
44 Summary
45 Summary First step towards general treatment of vdw interactions in molecules and condensed matter. Many possible extensions: Delocalized excitations Relativistic effects (retardation) Finite temperature Higher multipole effects Systematic scaling to larger systems...
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