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                Alexandre Tkatchenko                   Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin, Germany QMC@TTI, Apuan Alps, Jul 29, 2013                             When (2 + 2)  4 ? 

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Page 1: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

                Alexandre Tkatchenko                  Fritz­Haber­Institut der Max­Planck­Gesellschaft, 

Berlin, Germany

QMC@TTI, Apuan Alps, Jul 29, 2013                             

When (2 + 2)  4 ? 

Page 2: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

When (2 + 2)  4 

orVan der Waals Interactions in Complex 

(and Simple) Materials 

                Alexandre Tkatchenko                  Fritz­Haber­Institut der Max­Planck­Gesellschaft, 

Berlin, Germany

QMC@TTI, Apuan Alps, Jul 29, 2013                             

Page 3: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Acknowledgments

Robert A. DiStasio Matthias Scheffler

Roberto CarAnatole 

von Lilienfeld

Page 4: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Acknowledgments

Robert A. DiStasio Matthias Scheffler

Roberto CarAnatole 

von Lilienfeld

Alberto Ambrosetti

Anthony ReillyVivekGobre

Page 5: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Textbook picture of vdW interactions

A B

Page 6: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

A B

A B­ +

A B­ + ­ +

R

Textbook picture of vdW interactions

Page 7: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

A B

A B­ +

A B­ + ­ +

R

Textbook picture of vdW interactions

Page 8: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Beguin et al.PRL 110, 263201 (2013).

Reality check for vdW from experiment

Page 9: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Beguin et al.PRL 110, 263201 (2013).

Page 10: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Beyond textbook model of vdW interactions: Electrodynamic response effects

A BRAB

r1

r2

Page 11: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

A BRAB

r1

r2

Beyond textbook model of vdW interactions: Electrodynamic response effects

Page 12: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

1

A BRAB

r1

r2

AccurateMicroscopicModeling of CoulombResponse

Full (All­Order)Many­Body

van der WaalsEnergy

2

Beyond textbook model of vdW interactions: Electrodynamic response effects

Page 13: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

1

A BRAB

r1

r2

AccurateMicroscopicModeling of CoulombResponse

Full (All­Order)Many­Body

van der WaalsEnergy

2

Beyond textbook model of vdW interactions: Electrodynamic response effects

We know how to solve the problem, albeit not very efficiently

Page 14: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Electrodynamic treatment of vdW interactions: beyond “hybridized atoms”

Page 15: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Multi­layered graphene

Electrodynamic treatment of vdW interactions: beyond “hybridized atoms”

Page 16: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Electrodynamic treatment of vdW interactions: beyond “hybridized atoms”

Page 17: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

VivekGobre

Electrodynamic treatment of vdW interactions: beyond “hybridized atoms”

V. V. Gobreand A. Tkatchenko,Nature Comm. (2013)

Page 18: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

How long­ranged are vdW interactions? … Direct experimental evidence

P. Loskill, H. Hähl, T. Faidt, S. Grandthyll, F. Müller, and K. Jacobs, Adv. Coll. Interf. Sci. 107, 179182 (2012).

P. Loskill, J. Puthoff, M. Wilkinson, K. Mecke, K. Jacobs and K. Autumn, J. R. Soc. Interface, to be published (2013).

Si

SiO2

Page 19: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

How long­ranged are vdW interactions? … Direct experimental evidence

P. Loskill, H. Hähl, T. Faidt, S. Grandthyll, F. Müller, and K. Jacobs, Adv. Coll. Interf. Sci. 107, 179182 (2012).

P. Loskill, J. Puthoff, M. Wilkinson, K. Mecke, K. Jacobs and K. Autumn, J. R. Soc. Interface, to be published (2013).

Si

SiO2

Page 20: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Towards Efficient Many­Body Treatment of vdW Interactions

The conventional approach(Grimme, Johnson­Becke/Corminboeuf, 

Tkatchenko­Scheffler, Langreth­Lundqvist vdW­DF, Vydrov­van Voorhis, ...)

Effective screening and two­body energy

A

B

Valid for small molecules or homogeneous dielectrics

Page 21: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Towards Efficient Many­Body Treatment of vdW Interactions

The conventional approach(Grimme, Johnson­Becke/Corminboeuf, 

Tkatchenko­Scheffler, Langreth­Lundqvist vdW­DF, Vydrov­van Voorhis, ...)

Effective screening and two­body energy

A

B

The new state­of­the­art:Full many­body response and energy for a system of 

quantum oscillators (DFT+MBD)

A

CD

F E

B

Valid for small molecules or homogeneous dielectrics

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).

Page 22: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

The Model: Quantum Harmonic Oscillator (QHO)

Model proposed by W. L. Bade (1957); and used by B. J. Berne; A. Donchev; M. W. Cole; G. Martyna; K. Jordan; and others. 

Nucleus (q)

Harmonic bond ()

“Electron” (­q,m)

Page 23: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

The Model: Quantum Harmonic Oscillator (QHO)

Model proposed by W. L. Bade (1957); and used by B. J. Berne; A. Donchev; M. W. Cole; G. Martyna; K. Jordan; and others. 

Nucleus (q)

Harmonic bond ()

“Electron” (­q,m)

In the dipole approximation:

( ,) fully characterize the QHO 

Page 24: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

First­Principles Model: QHOs in Molecules and Solids

α0 and ω0 include short­range hybridization 

 C6 = C6[n(r)],   RvdW = RvdW[n(r)]

A. Tkatchenko and M. Scheffler, Phys. Rev. Lett. (2009)

Page 25: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

The Method: DFT+MBDTS­vdW method

Self­consistent electrodynamic response (Dyson)

Many­body vdW energy for a system of coupled oscillators (RPA)

A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, Phys. Rev. Lett. (2012).

Page 26: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

● Seamless treatment of short­range (quantum) and long­range (classical) electrodynamic response

● Full correlation energy of coupled QHOs is equivalent to the random­phase approximation or ring­CCD (JCP 138, 074106 (2013))

● Computes many­body vdW energy to infinite order 

● Negligible computational cost compared to DFT (MBD calculations can be easily done for > 10,000 atoms)

Salient Features of the MBD Method

A

CD

F E

B

Page 27: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Coupling DFT and MBD by range separation of the Coulomb potential

(bohr)

(Har

tree

)

EDFT+MBD=EDFT+EMBD

See work on range separation by A. Savin, H. Stoll, G. Scuseria, K. Hirao, ... 

Page 28: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Performance of DFT+MBD for gas­phase intermolecular interactions

S22 CCSD(T): Jurecka, Sponer, Cerny, Hobza, PCCP (2006); Sherrill et al., JCP (2010).

Page 29: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Large many­body vdW effects in complex molecular geometries

R. A. DiStasio Jr., O. A. von Lilienfeld, and A. Tkatchenko, PNAS (2012)

Page 30: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

 “Chemically Accurate” Predictionsfor Molecular Materials

A. M. Reilly

A. M. Reilly and A. Tkatchenko, J. Phys. Chem. Lett. 4, 1028 (2013).; J. Chem. Phys. 139, 024705 (2013).

Page 31: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

PBE0+MBD overall accuracy: 0.8 kcal/mol; 4.6%

 “Chemically Accurate” Predictionsfor Molecular Materials

A. M. Reilly

AnthonyReilly

A. M. Reilly and A. Tkatchenko, J. Phys. Chem. Lett. 4, 1028 (2013). 

Page 32: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

DFT+MBD correctly discriminates between crystal polymorphs: Example of glycine

Page 33: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

DFT+MBD correctly discriminates between crystal polymorphs: Example of glycine

Angew. Chem. (2013).

Overall

Page 34: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Long­range double­screening in DFT+MBDTS­vdW method

Self­consistent electrodynamic response (Dyson)

Many­body vdW energy for a system of coupled oscillators (RPA)

A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, Phys. Rev. Lett. (2012).

Page 35: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Supram

olecu

lar sy

stems: 

a link

 betw

een 

gas­p

hase 

molecu

les 

and m

olecu

lar cr

ystals

S. Grimme et al., JCTC (2013).

Page 36: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

 6 systems out of S12L database

Diffusion Quantum Monte Carlo: A. Tkatchenko, D. Alfe, K. S. Kim, JCTC (2012);and D. Alfe et al., to be published.

S. Grimme, Chem. Eur. J. (2012)

Page 37: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

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).

26.5                     29.9                              27.7

33.4                     34.8                              32.6

81.1                     77.4                              81.6

Page 38: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Binding in supramolecular systems: DMC vs. “Experiment” vs.PBE+MBD*

26.5                     29.9                              27.7

33.4                     34.8                              32.6

81.1                     77.4                              81.6

(kcal/mol, DMC sampling error is +/­ 1.5 kcal/mol)“Experimental” values: S. Grimme, Chem. Eur. J. (2012).

Page 39: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

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

Alberto Ambrosetti

S. Grimme (2012)

Page 40: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Reconciling theory and experiment: Measurement of vdW potential for single adsorbed molecule

to be published, Phys. Rev. Lett. (2013)

Page 41: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Single­molecule measurement of adsorption energy by AFM

C. Wagner et al.,PRL 109, 076102 (2012).  

Page 42: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Single­molecule measurement of adsorption energy by AFM

C. Wagner et al.,PRL 109, 076102 (2012).  

Page 43: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Summary

Page 44: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

Summary

Page 45: When (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · When (2 + 2) 4 or Van der Waals Interactions in Complex (and Simple) Materials Alexandre Tkatchenko FritzHaberInstitut

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 effectsSystematic scaling to larger systems

...