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DFT and VdW interactions. Marcus Elstner Physical and Theoretical Chemistry, Technical Universi ty of Braunschweig. E ~ 1/ R 6. DFT and VdW interactions. 2 Problems: Pauli repulsion: exchange effect ~ exp( R  ) or 1 /R 12  - attraction due to correlation

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dft and vdw interactions
DFT and VdW interactions

Marcus Elstner

Physical and Theoretical Chemistry, Technical Universityof Braunschweig

dft and vdw interactions2

E ~ 1/R6

DFT and VdW interactions
  • 2 Problems:
  • Pauli repulsion: exchange effect
  • ~ exp(R) or 1/R12
  • - attraction due to correlation
  • ~ -1/R6
dft problem

E ~ 1/R6

DFT Problem
  • B88 exchange: too repulsive ?
  • PBEx/PW91x: too attractive
  • already at Ex only level
  • LDA finds often binding!

Ex ??

  • fix Ex
  • correlation Ec?

Ec ??

ar 2 with e x only
Ar2 with Ex only
  • B too repulsive,
  • PW91x too “attractive”
  • Complete mess with
  • DFT

Wu et al. JCP 115 (2001) 8748

popular functionals role of e x
Popular Functionals: role of Ex

BPW91

BLYP

B3LYP

PW91

B3LYP contains only 20% HF exchange!

Xu & Yang JCP 116 (2002) 515

slide6

Popular Functionals: role of Ec

Xu & Yang JCP 116 (2002) 515

BPW91

BLYP

B3LYP

PW91

  • BPW91 vs PW91: attraction only due to exchange!!!!!
  • Correlation not significant for PW91 and LYP
slide7

Popular Functionals: role of Ec

Perez-Jorda et al. JCP 110 (1999) 1916

DFT HFx + Ec:

some Ec lead to (over-) binding, some don’t!

does overlap matter
Does overlap matter?

GGA

DFTB

Xu & Yang JCP 116 (2002) 515

Elstner et al. JCP 114 (2001) 5149

dft and vdw interactions solutions
DFT and VdW interactions: solutions

Adding empirical dispersion

Elstneret al. JCP 114 (2001) 5149

Xu & Yang JCP 116 (2002) 515

Zimmerli et al. JCP 120 (2004) 2693

Grimme JCC 25 (2004) 1463

DFT model for empircal dispersion on top of HF

Becke & Johnson JCP 124 (2006) 014104

Put it into the pseudopotential

v. Lilienfeld et al. PRB 71 (2005) 195119

Find a new dispersion functional

Dion, et al. Phys. Rev. Lett. 92 (2004) 246401; [JCP 124 (2006) 164106]

Kamiya et al. JCP 117 (2002) 6010.

adding empirical dispersion
Adding empirical dispersion

Following the idea of HF+dis:

Add f (R) C6 /R6to DFT total energy

C6 empirical values

Elstner, Hobza et al. JCP 114 (2001) 5149

To be successfull: Ex should be well-behaved (i.e. like HF)

Ec: double counting

dispersion forces van der waals interactions elstner et al jcp 114 200 1 5149

E ~ 1/R6

Dispersion forces - Van der Waals interactionsElstner et al. JCP 114 (2001) 5149

Etot = ESCC-DFTB - f (R) C6 /R6



C6 via Slater-Kirckwood combination rules of atomic polarizibilities after Halgreen, JACS 114 (1992) 7827.

damping f(R) = [1-exp(-3(R/R0)7)]3

R0 = 3.8Å (für O, N, C)

slide13

How to get Dispersion coefficients?Halgren JACS 114 (1992) 7827

London, Phys. Chem. (Leipzig) B 11(1930) 222

Slater & Kirkwood. Phys. Rev. 37 (1931) 682.

Kramer & Herschbach J. Chem. Phys. 53 (1970) 2792

effective electron number

slide14

DFTB input

Etot = ESCC-DFTB - f (R) C6 /R6

f(R) = [1-exp(-3(R/R0)7)]3

  • R0: e.g. 3.8 for ONC
  • Atomic polarizabilities:
  • hybridisation dependent
  • Effective electron number (from Halgren)
dftb dispersion
DFTB + dispersion

Sponer et al. J.Phys.Chem. 100 (1996) 5590; Hobza et al. J.Comp.Chem. 18 (1997) 1136stacking energiesin MP2/6-31G* (0.25), BSSE-corrected ( + MP2-values)

  • Hartree-Fock, no stacking
  • AM1, PM3, repulsive interaction (2-10) kcal/mole
  • MM-force fields strongly scatter in results

vertical dependence twist-dependence

dft empirical dispersion 1st generation
DFT + empirical dispersion: 1st generation

1) Problem of unbalanced Ex:

2) Problem of Ec?? Which one to choose?

 Large variation in results when adding dispersion

Wu and Wang 2002

Zimmerli et al 2004

dft and empirical dispersion
DFT and empirical dispersion

Does not work for all Exc functionalsproperly

Wu and Wang 2002

Zimmerli et al.2004

From Wu and Yang 2002

dft empirical dispersion 2nd generation
DFT + empirical dispersion: 2nd generation

1) Problem of unbalanced Ex:

2) Problem of Ec?? Which one to choose?

 Large variation when adding dispersion

Grimme 2004: scale BLYP + dispersion with 1.4

scale PW91 + dispersion with 0.7

f r c 6 r 6
f (R)  C6 /R6
  • choice of C6 coefficients
  • Choice of damping function
choice of c6 coefficients
Choice of C6 coefficients
  • hybridisation dependence vs. atomic values
  • empirical values
  •  Very similar in various approaches
choice of damping function
Choice of damping function
  • various functional forms
  • - Fermi-function
  • - f(R) = [1-exp(-3(R/R0)7)]3
  • choice of “cutoff” radius

from Grimme 2004

choice of f damp
Choice of fdamp
  • fdamp balances several effects
  • - contribution from Ex/Ec in overlap region
  • - double counting of Ec
  • BSSE and BSIE
  • missing higher order terms 1/R**8 …
  • Determination completely empirical

Choose, to reproduce interaction energies for large set of stacked compounds

choice of fdamp
Choice of fdamp

However, form of fdamp may be crucial

Location of minimum

For A-A stack

From Wu and Yang 2002

grimme jcc 25 2004 1463
Grimme JCC 25 (2004) 1463
  • s6:
  • PW91: 0.7
  • BLYP: 1.4
  • Scaling:
  • -Basis set dependent
  • functional dependent
  • hybridisation dependence
  • empirical vs. new fits
  •  Very similar in various approaches
dft empirical dispersion 3rd generation
DFT + empirical dispersion: 3rd generation
  • 1) Problem of unbalanced Ex:
  • 2) Problem of Ec?? Which one to choose?
  •  Large variation in results when adding dispersion
  • mix PW91x and Bx
  • revPBE
  • meta GGA??
  • + balanced damping function, no scaling
dft empirical dispersion 1st generation26

DFT + empirical dispersion: 2nd generation

Grimme JCC 25 (2004) 1463:

scale BLYP + disp with 1.4

scale PW91 + disp with 0.7

DFT + empirical dispersion: 1st generation

1) Problem of unbalanced Ex:

2) Problem of Ec?? Which one to choose?

 Large variation in results when adding dispersion

Wu and Wang JCP 116 (2002) 515

Zimmerli et al. JCP 120 (2004) 2693

3rd generation: revPBE, XLYP and s6=1

slide29

Benzene (from Irle/Morokuma, Emory)

RHF, MP2 (both CP corrected) and DFTB DE on benzene dimers:

o n qm mm molecular dynamics for dna dodecamer in h 2 o elstner et al in preparation
O(N)-QM/MM-molecular-dynamics for DNA-dodecamer in H2OElstner et al. in preparation
  • DNA-Dodecamer 758 + 2722 H2O + 22 Na
  • periodic BC-Ewald-summation
  • dispersion in QM-region
  • MD-simulation at 300 K
  • parallel-16 processors SP2energy/forces: 1 – 2 sec.  10 ps/day

1-st stable QM/MM ns-scale dynamic simulation

slide33

N

Secondary-structure elements for Glycine und Alanine-based polypeptides: ß-sheets, helices and turnElstner, et a.. Chem. Phys. 256 (2000) 15

For increasing N: energetics of different conformers, geometries, vibrations

N = 1 (6 stable conformers)

aR-helix

310 - helix

N-fold periodicity

stabilization by internal H-bonds

between i and i+4

between i and i+3

glycine and alanine based polypeptides in vacuo elstner et al chem phys 256 2000 15

N

Glycine and Alanine based polypeptides in vacuoElstner et al., Chem. Phys. 256 (2000) 15

Relative energies, structures and vibrational properties: N=1-8

N = 1 (6 stable conformers)

E relative energies (kcal/mole)

B3LYP

(6-31G*)

MP2

MP4-BSSE

SCC-DFTB

Ace-Ala-Nme

C7eq C5ext C7ax

MP4-BSSE: Beachy et al, BSSE ‚corrected‘ at MP2 level

polypeptides in vacuo effect of dispersion favors more compact structures
Polypeptides in vacuoEffect of dispersion: favors more compact structures

(6-31G*)

N = 2

BLYP

B3LYP

HF

MP2

SCC-DFTB

Ace-Ala2-Nme

C7eq C5ext BI BII BI` BII`

DFT: relative stability of compact vs. extended structures?

secondary structure formation elstner et al chem phys 256 2000 15
Secondary structure formationElstner et al., Chem. Phys. 256 (2000) 15

E

DFT/DFTB ?

310 - helix

aR-helix

N

peptide size

DFT: crossover only for N~20 !!  solvation??

secondary structure influence of aqueous solution cui et al jpcb 105 2001 569
Secondary structure:Influence of aqueous solutionCui et al, JPCB 105 (2001) 569

310 – helix: occurence for N<8 in database

QM/MM MD of octa-Alanine:

310 - helix converts into aR-helix within 10 ps

310 - helix

aR-helix

Situation in Protein?

slide38

energy and interatomic forces

parallel (16-node SP2): 2 sec.

MD simulation for 0.35 ns

Molecular-dynamics for Crambin in H2O-solution O(N)-QM/MM simulationLiu et al. PROTEINS 44 (2001) 484

Crambin (639) + 2400 H2O

influence of dispersion liu et al proteins 44 2001 484
Influence of DispersionLiu et al. PROTEINS 44 (2001) 484

QM/MM MD-Simulation

Crambin in Solution

HF

DFT/DFTB ?

MP2

SCC-DFTB + DIS 

slide40

Enkephalin: ~30 local minima 3 cluster

Jalkanen et al. to be published

single bend

double bend

compact

extended

C5

slide41

Enkephalin: MP2/6-31G* vs DFTB-dis//DFTB-dis

compact  extended

kcal

c

a

b

conformer

Rel. energy (kcal) vs. conformer

slide42

Enkephalin: MP2/6-31G* vs DFTB//DFTB-dis

compact  extended

kcal

conformer

slide43

Enkephalin: MP2 vs B3LYP//DFTB-dis

compact  extended

kcal

conformer

slide44

Enkephalin: MP2 vs B3LYP-dis//DFTB-dis

compact  extended

kcal

conformer

slide45

Enkephalin: MP2 vs PBE+dis//DFTB-dis

compact  extended

kcal

conformer

slide46

Enkephalin: MP2 vs PBE//DFTB-dis

compact  extended

kcal

conformer

slide47

Enkephalin: MP2 vs PBE+dis//DFTB-dis

compact  extended

kcal

conformer

slide48

CONCLUSIONS

  • Dispersion favors compact structures ~ 15 kcal/mole
  • MP2/6-31G*:
  • - internal BSSE
  • - higher level correlation contribution
  • -PBE and B3LYP differ in stability of extended (C5) confs
  • -B3LYP overestimates Pauli repulsion: N-H...
dft large soft matter structures don t do without dispersion
DFT+large soft matter structures: don‘t do without dispersion!
  • large impact on relative energies
  • stabilizes more compact structures:
  • relevant secondary structures may
  • not be stable without!