dft and vdw interactions
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DFT and VdW interactionsDFT and VdW interactions
Marcus Elstner
Physical and Theoretical Chemistry, Technical University of Braunschweig
DFT and VdW interactionsDFT and VdW interactions
E ~ 1/R6
2 Problems:
- Pauli repulsion: exchange effect
~ exp(R) or 1/R12
- attraction due to correlation
~ -1/R6
DFT ProblemDFT Problem
- B88 exchange: too repulsive ?
- PBEx/PW91x: too attractive
already at Ex only level
- LDA finds often binding!
E ~ 1/R6
- fix Ex
- correlation Ec?Ec ??
Ex ??
Ar2 with Ex onlyAr2 with Ex only
• B too repulsive,
• PW91x too “attractive”
Complete mess with
DFTWu et al. JCP 115 (2001) 8748
Popular Functionals: role of ExPopular Functionals: role of Ex
Xu & Yang JCP 116 (2002) 515
BPW91
BLYP
B3LYP
PW91
B3LYP contains only 20% HF exchange!
• BPW91 vs PW91: attraction only due to exchange!!!!!
• Correlation not significant for PW91 and LYP
BPW91
BLYP
B3LYP
PW91
Popular Functionals: role of EcPopular Functionals: role of Ec
Xu & Yang JCP 116 (2002) 515
Perez-Jorda et al. JCP 110 (1999) 1916
DFT HFx + Ec:
some Ec lead to (over-) binding, some don’t!
Popular Functionals: role of EcPopular Functionals: role of Ec
Does overlap matter?Does overlap matter?
Xu & Yang JCP 116 (2002) 515
Elstner et al. JCP 114 (2001) 5149
GGA
DFTB
DFT and VdW interactions: the problemDFT and VdW interactions: the problem
E ~ 1/R6
Ec = 0
Exc = ??
DFT and VdW interactions: solutionsDFT and VdW interactions: solutions
Adding empirical dispersionElstner et 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 HFBecke & Johnson JCP 124 (2006) 014104
Put it into the pseudopotentialv. Lilienfeld et al. PRB 71 (2005) 195119
Find a new dispersion functionalDion, et al. Phys. Rev. Lett. 92 (2004) 246401; [JCP 124 (2006) 164106]
Kamiya et al. JCP 117 (2002) 6010.
Adding empirical dispersionAdding 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 interactionsElstner et al. JCP 114 (2001) 5149
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)
E ~ 1/R6
How to get Dispersion coefficients?Halgren JACS 114 (1992) 7827
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
DFTB inputDFTB input
f(R) = [1-exp(-3(R/R0)7)]3
Etot = ESCC-DFTB - f (R) C6 /R6
• R0: e.g. 3.8 for ONC
• Atomic polarizabilities:
hybridisation dependent
• Effective electron number (from Halgren)
DFTB + dispersionDFTB + dispersion
Sponer et al. J.Phys.Chem. 100 (1996) 5590; Hobza et al. J.Comp.Chem. 18 (1997) 1136
stacking energies in 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 generationDFT + 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 dispersionDFT and empirical dispersion
From Wu and Yang 2002
Does not work for all Exc functionals properly
Wu and Wang 2002
Zimmerli et al.2004
DFT + empirical dispersion: 2nd generationDFT + 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) C6 /R6
f (R) C6 /R6
-choice of C6 coefficients
-Choice of damping function
Choice of C6 coefficientsChoice of C6 coefficients
- hybridisation dependence vs. atomic values
- empirical values
Very similar in various approaches
Choice of damping functionChoice 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 fdampChoice 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 fdampChoice of fdamp
However, form of fdamp may be crucial
From Wu and Yang 2002
Location of minimum
For A-A stack
Grimme JCC 25 (2004) 1463Grimme JCC 25 (2004) 1463
- hybridisation dependence
- empirical vs. new fits
Very similar in various approaches
s6:
PW91: 0.7
BLYP: 1.4
Scaling:
-Basis set dependent
-functional dependent
DFT + empirical dispersion: 3rd generationDFT + 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 generationDFT + 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
DFT + empirical dispersion: 2nd generationDFT + empirical dispersion: 2nd generation
Grimme JCC 25 (2004) 1463:
scale BLYP + disp with 1.4
scale PW91 + disp with 0.7
3rd generation: revPBE, XLYP and s6=13rd generation: revPBE, XLYP and s6=1
Applications of DFTB-DApplications of DFTB-D
C
C
C
C
C
C
1.396
1.099
CC C
CC C
CCC
C CC
3.670
CCC
CC
C
CC
CC
C
C
5.295
CCC
CCC
CCC
CCC
6.403
3.325
CC
CC
CC
CC
CCCC
3.454
5.193
M S T
PD 1.108
3.556
DFTBDFTB-Dmonomer geometriesremain unchangedthroughout (but optimized)
(MP2/aug-cc-pVDZ (monomer frozen)){MP2/aug-cc-pVTZ (monomer frozen)}
(3.8){3.7}
(5.0){4.9}
(3.4){3.4}
(1.6){1.6}
Benzene (from Irle/Morokuma, Emory) Benzene (from Irle/Morokuma, Emory)
Monomer S-Dimer T-Dimer PD-DimerE [kcal/mol] E [kcal/mol] E [kcal/mol] E [kcal/mol]
RHF/cc-pVDZ//MP2/aug-cc-pVTZ 0.00 4.36 0.82 4.00RHF/aug-cc-pVDZ//MP2/aug-cc-pVDZ 0.00 3.60 -0.11 4.04RHF/aug-cc-pVTZ//MP2/aug-cc-pVTZ 0.00 5.10 1.42 5.02 MP2/cc-pVDZ//MP2/aug-cc-pVTZ 0.00 -2.71 -3.76 -4.23MP2/aug-cc-pVDZ//MP2/aug-cc-pVDZ 0.00 -2.90 -3.16 -4.28MP2/aug-cc-pVTZ//MP2/aug-cc-pVTZ 0.00 -3.26 -3.46 -4.67MP2/aug-cc-pVQZ//MP2/aug-cc-pVTZ 0.00 -3.37 -3.54 -4.79CCSD(T)/CBS (based on MP2-R12) 0.00 -1.81 -2.74 -2.78
DFTB//MP2/aug-cc-pVTZ 0.00 0.56 -0.31 0.38DFTB//MP2/aug-cc-pVTZ w/DISP 0.00 -4.02 -2.68 -4.36DFTB//DFTB 0.00 0.54 -0.34 -0.16DFTB//DFTB w/DISP 0.00 -4.54 -2.74 -4.60
RHF, MP2 (both CP corrected) and DFTB E on benzene dimers:
Benzene (from Irle/Morokuma, Emory) Benzene (from Irle/Morokuma, Emory)
Hybride materials Hybride materials
O(N)-QM/MM-molecular-dynamics for DNA-dodecamer in H2O
Elstner et al. in preparation
O(N)-QM/MM-molecular-dynamics for DNA-dodecamer in H2O
Elstner 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
Intercalation: Ethidium – ATReha et al JACS 2003
Intercalation: Ethidium – ATReha et al JACS 2003
Secondary-structure elements for Glycine und Alanine-based polypeptides: ß-sheets, helices and turn
Elstner, et a.. Chem. Phys. 256 (2000) 15
Secondary-structure elements for Glycine und Alanine-based polypeptides: ß-sheets, helices and turn
Elstner, et a.. Chem. Phys. 256 (2000) 15
N = 1 (6 stable conformers) 310 - helix
stabilization by internal H-bonds
N-fold periodicity
between i and i+3N
R-helix
between i and i+4
For increasing N: energetics of different conformers, geometries, vibrations
Glycine and Alanine based polypeptides in vacuoElstner et al., Chem. Phys. 256 (2000) 15
Glycine and Alanine based polypeptides in vacuoElstner et al., Chem. Phys. 256 (2000) 15
N = 1 (6 stable conformers)
N
Relative energies, structures and vibrational properties: N=1-8
2 L P
(6-31G*)
C7
eq C5ext C7
ax
MP4-BSSE
MP2
B3LYP
SCC-DFTB
E relative energies (kcal/mole)
MP4-BSSE: Beachy et al, BSSE ‚corrected‘ at MP2 level
Ace-Ala-Nme
Polypeptides in vacuoEffect of dispersion: favors more compact structures
Polypeptides in vacuoEffect of dispersion: favors more compact structures
N = 2
(6-31G*)
Ace-Ala2-Nme
BLYPB3LYP
MP2
HF
SCC-DFTB
C7eq C5
ext 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 formation Elstner et al., Chem. Phys. 256 (2000) 15
DFT/DFTB ? 310 - helix R-helix
peptide size
DFT: crossover only for N~20 !! solvation??
E
N
Secondary structure:Influence of aqueous solutionCui et al, JPCB 105 (2001) 569
Secondary structure:Influence of aqueous solutionCui et al, JPCB 105 (2001) 569
310 - helix R-helix
310 – helix: occurence for N<8 in database
QM/MM MD of octa-Alanine:
310 - helix converts into R-helix within 10 ps
Situation in Protein?
Molecular-dynamics for Crambin in H2O-solution O(N)-QM/MM simulation
Liu et al. PROTEINS 44 (2001) 484
Molecular-dynamics for Crambin in H2O-solution O(N)-QM/MM simulation
Liu et al. PROTEINS 44 (2001) 484
Crambin (639) + 2400 H2O
MD simulation for 0.35 ns energy and interatomic forcesparallel (16-node SP2): 2 sec.
Influence of Dispersion Liu et al. PROTEINS 44 (2001) 484
Influence of Dispersion Liu et al. PROTEINS 44 (2001) 484
QM/MM MD-Simulation Crambin in Solution
HF
DFT/DFTB ?
SCC-DFTB + DIS
MP2
Enkephalin: ~30 local minima 3 clusterJalkanen et al. to be published
Enkephalin: ~30 local minima 3 clusterJalkanen et al. to be published
C5
compact
extended
double bendsingle bend
Enkephalin: MP2/6-31G* vs DFTB-dis//DFTB-disEnkephalin: MP2/6-31G* vs DFTB-dis//DFTB-dis
compact extended
conformer
kcal
Rel. energy (kcal) vs. conformer
b a
c
Enkephalin: MP2/6-31G* vs DFTB//DFTB-disEnkephalin: MP2/6-31G* vs DFTB//DFTB-dis
compact extended
conformer
kcal
Enkephalin: MP2 vs B3LYP//DFTB-disEnkephalin: MP2 vs B3LYP//DFTB-dis
compact extended
conformer
kcal
Enkephalin: MP2 vs B3LYP-dis//DFTB-disEnkephalin: MP2 vs B3LYP-dis//DFTB-dis
compact extended
conformer
kcal
Enkephalin: MP2 vs PBE+dis//DFTB-disEnkephalin: MP2 vs PBE+dis//DFTB-dis
compact extended
conformer
kcal
Enkephalin: MP2 vs PBE//DFTB-disEnkephalin: MP2 vs PBE//DFTB-dis
compact extended
conformer
kcal
Enkephalin: MP2 vs PBE+dis//DFTB-disEnkephalin: MP2 vs PBE+dis//DFTB-dis
compact extended
conformer
kcal
CONCLUSIONS 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!
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