Title: DFT and VdW interactions
1DFT and VdW interactions
Marcus Elstner Physical and Theoretical
Chemistry, Technical University of Braunschweig
2DFT and VdW interactions
- 2 Problems
- Pauli repulsion exchange effect
- exp(R??) or 1/R12??
- - attraction due to correlation
- -1/R6??
3DFT Problem
- B88 exchange too repulsive ?
- PBEx/PW91x too attractive
- already at Ex only level
- LDA finds often binding!
Ex ??
Ec ??
4Ar2 with Ex only
- B too repulsive,
- PW91x too attractive
- Complete mess with
- DFT
Wu et al. JCP 115 (2001) 8748
5Popular Functionals role of Ex
BPW91 BLYP B3LYP PW91
B3LYP contains only 20 HF exchange!
Xu Yang JCP 116 (2002) 515
6Popular 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
7Popular Functionals role of Ec
Perez-Jorda et al. JCP 110 (1999) 1916 DFT
HFx Ec some Ec lead to (over-) binding,
some dont!
8Does overlap matter?
GGA
DFTB
Xu Yang JCP 116 (2002) 515
Elstner et al. JCP 114 (2001) 5149
9DFT and VdW interactions the problem
Exc ??
Ec 0
10DFT and VdW interactions solutions
Adding empirical dispersion Elstner 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 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.
11Adding empirical dispersion
Following the idea of HFdis 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
12Dispersion 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)
13How 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
14DFTB 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)
15DFTB dispersion
Sponer et al. J.Phys.Chem. 100 (1996) 5590 Hobza
et al. J.Comp.Chem. 18 (1997) 1136stacking
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
16DFT 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
-
17DFT and empirical dispersion
Does not work for all Exc functionals properly Wu
and Wang 2002 Zimmerli et al.2004
From Wu and Yang 2002
18DFT 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
19???f (R??) ? C6 /R6??
- choice of C6 coefficients
- Choice of damping function
20Choice of C6 coefficients
- hybridisation dependence vs. atomic values
- empirical values
- ? Very similar in various approaches
21Choice of damping function
- various functional forms
- - Fermi-function
- - f(R??) 1-exp(-3(R??/R0)7)3
- choice of cutoff radius
from Grimme 2004
22Choice 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/R8
- Determination completely empirical
- Choose, to reproduce interaction energies for
large set of stacked compounds
23Choice of fdamp
However, form of fdamp may be crucial
Location of minimum For A-A stack
From Wu and Yang 2002
24Grimme 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
25DFT 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
26DFT 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 s61
27Applications of DFTB-D
28Benzene (from Irle/Morokuma, Emory)
29Benzene (from Irle/Morokuma, Emory)
RHF, MP2 (both CP corrected) and DFTB DE on
benzene dimers
30Hybride materials
31O(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
32Intercalation Ethidium ATReha et al JACS 2003
33Secondary-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 i3
between i and i4
34Glycine and Alanine based polypeptides in
vacuoElstner et al., Chem. Phys. 256 (2000) 15
Relative energies, structures and vibrational
properties N1-8
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
35Polypeptides 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?
36Secondary structure formation Elstner et al.,
Chem. Phys. 256 (2000) 15
E
DFT/DFTB ?
310 - helix
aR-helix
N
peptide size
DFT crossover only for N20 !! ? solvation??
37Secondary structureInfluence of aqueous
solutionCui et al, JPCB 105 (2001) 569
310 helix occurence for Nlt8 in database
QM/MM MD of octa-Alanine 310 - helix
converts into aR-helix within 10 ps
310 - helix
aR-helix
Situation in Protein?
38Molecular-dynamics for Crambin in H2O-solution
O(N)-QM/MM simulationLiu et al. PROTEINS 44
(2001) 484
Crambin (639) 2400 H2O
39Influence of Dispersion Liu et al. PROTEINS 44
(2001) 484
QM/MM MD-Simulation Crambin in Solution
HF?
DFT/DFTB ?
MP2
SCC-DFTB DIS ?
40Enkephalin 30 local minima? 3 cluster Jalkanen
et al. to be published
single bend
double bend
compact
extended
C5
41Enkephalin MP2/6-31G vs DFTB-dis//DFTB-dis
compact ? extended
kcal
c
a
b
conformer
Rel. energy (kcal) vs. conformer
42Enkephalin MP2/6-31G vs DFTB//DFTB-dis
compact ? extended
kcal
conformer
43Enkephalin MP2 vs B3LYP//DFTB-dis
compact ? extended
kcal
conformer
44Enkephalin MP2 vs B3LYP-dis//DFTB-dis
compact ? extended
kcal
conformer
45Enkephalin MP2 vs PBEdis//DFTB-dis
compact ? extended
kcal
conformer
46Enkephalin MP2 vs PBE//DFTB-dis
compact ? extended
kcal
conformer
47Enkephalin MP2 vs PBEdis//DFTB-dis
compact ? extended
kcal
conformer
48CONCLUSIONS
- 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...
-
-
49DFTlarge soft matter structures dont do
without dispersion!
- large impact on relative energies
- stabilizes more compact structures
- relevant secondary structures may
- not be stable without!