when (2 + 2) 4 › tti_talks › qmcitaa_13 › tkatchenko_tti2013.pdf · when (2 + 2) 4 or van der...
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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](https://reader033.vdocuments.us/reader033/viewer/2022060401/5f0e26c17e708231d43ddb53/html5/thumbnails/1.jpg)
Alexandre Tkatchenko FritzHaberInstitut der MaxPlanckGesellschaft,
Berlin, Germany
QMC@TTI, Apuan Alps, Jul 29, 2013
When (2 + 2) 4 ?
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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
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Acknowledgments
Robert A. DiStasio Matthias Scheffler
Roberto CarAnatole
von Lilienfeld
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Acknowledgments
Robert A. DiStasio Matthias Scheffler
Roberto CarAnatole
von Lilienfeld
Alberto Ambrosetti
Anthony ReillyVivekGobre
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Textbook picture of vdW interactions
A B
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A B
A B +
A B + +
R
Textbook picture of vdW interactions
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A B
A B +
A B + +
R
Textbook picture of vdW interactions
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Beguin et al.PRL 110, 263201 (2013).
Reality check for vdW from experiment
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Beguin et al.PRL 110, 263201 (2013).
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Beyond textbook model of vdW interactions: Electrodynamic response effects
A BRAB
r1
r2
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A BRAB
r1
r2
Beyond textbook model of vdW interactions: Electrodynamic response effects
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1
A BRAB
r1
r2
AccurateMicroscopicModeling of CoulombResponse
Full (AllOrder)ManyBody
van der WaalsEnergy
2
Beyond textbook model of vdW interactions: Electrodynamic response effects
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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
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Electrodynamic treatment of vdW interactions: beyond “hybridized atoms”
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Multilayered graphene
Electrodynamic treatment of vdW interactions: beyond “hybridized atoms”
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Electrodynamic treatment of vdW interactions: beyond “hybridized atoms”
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VivekGobre
Electrodynamic treatment of vdW interactions: beyond “hybridized atoms”
V. V. Gobreand A. Tkatchenko,Nature Comm. (2013)
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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
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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
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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
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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).
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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)
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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
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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)
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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).
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● 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
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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, ...
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Performance of DFT+MBD for gasphase intermolecular interactions
S22 CCSD(T): Jurecka, Sponer, Cerny, Hobza, PCCP (2006); Sherrill et al., JCP (2010).
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Large manybody vdW effects in complex molecular geometries
R. A. DiStasio Jr., O. A. von Lilienfeld, and A. Tkatchenko, PNAS (2012)
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“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).
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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).
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DFT+MBD correctly discriminates between crystal polymorphs: Example of glycine
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DFT+MBD correctly discriminates between crystal polymorphs: Example of glycine
Angew. Chem. (2013).
Overall
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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).
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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).
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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)
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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
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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).
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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)
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Reconciling theory and experiment: Measurement of vdW potential for single adsorbed molecule
to be published, Phys. Rev. Lett. (2013)
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Singlemolecule measurement of adsorption energy by AFM
C. Wagner et al.,PRL 109, 076102 (2012).
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Singlemolecule measurement of adsorption energy by AFM
C. Wagner et al.,PRL 109, 076102 (2012).
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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](https://reader033.vdocuments.us/reader033/viewer/2022060401/5f0e26c17e708231d43ddb53/html5/thumbnails/44.jpg)
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](https://reader033.vdocuments.us/reader033/viewer/2022060401/5f0e26c17e708231d43ddb53/html5/thumbnails/45.jpg)
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
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