Transcript Kein Folientitel

DFT and VdW interactions
Marcus Elstner
Physical and Theoretical Chemistry, Technical
University of Braunschweig
DFT and VdW interactions
2 Problems:
- Pauli repulsion: exchange effect
~ exp(R) or 1/R12
- attraction due to correlation
E ~ 1/R6
~ -1/R6
DFT Problem
- B88 exchange: too repulsive ?
- PBEx/PW91x: too attractive
already at Ex only level
- LDA finds often binding!
Ex ??
E ~ 1/R6
- fix Ex
Ec ??
- correlation Ec?
Ar2 with Ex only
• B too repulsive,
• PW91x too “attractive”
Complete mess with
Wu et al. JCP 115 (2001) 8748
DFT
Popular Functionals: role of Ex
BPW91
BLYP
B3LYP
PW91
B3LYP contains only 20% HF exchange!
Xu & Yang JCP 116 (2002) 515
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
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?
GGA
DFTB
Elstner et al. JCP 114 (2001) 5149
Xu & Yang JCP 116 (2002) 515
DFT and VdW interactions: the problem
Exc = ??
E ~ 1/R6
Ec = 0
DFT 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.
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 (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
E~
1/R6
R0 = 3.8Å (für O, N, C)
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 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
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 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
Does not work for all
Exc functionals properly
Wu and Wang 2002
Zimmerli et al.2004
From Wu and Yang 2002
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)  C6 /R6
-choice of C6 coefficients
-Choice of damping function
Choice of C6 coefficients
- hybridisation dependence vs. atomic values
- empirical values
 Very similar in various approaches
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 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
However, form of fdamp may be
crucial
Location of minimum
For A-A stack
From Wu and Yang 2002
Grimme JCC 25 (2004) 1463
s6:
PW91: 0.7
BLYP: 1.4
Scaling:
- hybridisation dependence
- empirical vs. new fits
 Very similar in various approaches
-Basis set dependent
-functional dependent
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 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 generation
Grimme JCC 25 (2004) 1463:
scale BLYP + disp with 1.4
scale PW91 + disp with 0.7
3rd generation: revPBE, XLYP and s6=1
Applications of DFTB-D
Benzene (from Irle/Morokuma, Emory)
C
C
C
C
C
C
C
C
C
C
C
C
C
C
1.396
C
C
C
C
C
C
1.099
C
C
C
C
(5.0)
{4.9}
S
M
DFTB
DFTB-D
monomer geometries
remain unchanged
throughout (but optimized)
C
C
C
T
C
C
C
C
C
C
C
C
C
C
C
C
3.556
3.325
(3.4)
{3.4}
C
C
5.295
5.193
C
C
C
C
C
C
(MP2/aug-cc-pVDZ (monomer frozen))
{MP2/aug-cc-pVTZ (monomer frozen)}
C
3.670
3.454
(3.8)
{3.7}
6.403
(1.6)
{1.6}
C
PD
C
C
C
1.108
C
C
Benzene (from Irle/Morokuma, Emory)
RHF, MP2 (both CP corrected) and DFTB E on benzene dimers:
Monomer
E [kcal/mol]
S-Dimer
E [kcal/mol]
T-Dimer
E [kcal/mol]
PD- Dimer
E [kcal/mol]
RHF/cc-pVDZ//MP2/aug- cc-pVTZ
RHF/aug- cc-pVDZ//MP2/aug -cc-pVDZ
RHF/aug- cc-pVTZ//MP2/aug- cc-pVTZ
0.00
0.00
0.00
4.36
3.60
5.10
0.82
-0.11
1.42
4.00
4.04
5.02
MP2/cc- pVDZ//MP2/aug- cc-pVTZ
MP2/aug - cc-pVDZ//MP2/aug- cc-pVDZ
MP2/aug - cc-pVTZ//MP2/aug- cc-pVTZ
MP2/aug - cc-pVQZ//MP2/aug- cc-pVTZ
CCSD(T) /CBS ( based on MP2-R12)
0.00
0.00
0.00
0.00
0.00
-2.71
-2.90
-3.26
-3.37
-1.81
-3.76
-3.16
-3.46
-3.54
-2.74
-4.23
-4.28
-4.67
-4.79
-2.78
DFTB//MP2/aug -cc-pVTZ
DFTB//MP2/aug -cc-pVTZ w/DISP
DFTB//DFTB
DFTB//DFTB w/DISP
0.00
0.00
0.00
0.00
0.56
-4.02
0.54
-4.54
-0.31
-2.68
-0.34
-2.74
0.38
-4.36
-0.16
-4.60
Hybride materials
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 SP2
energy/forces: 1 – 2 sec.  10 ps/day
1-st stable QM/MM ns-scale dynamic simulation
Intercalation: Ethidium – AT
Reha et al JACS 2003
Secondary-structure elements for Glycine und Alaninebased polypeptides: ß-sheets, helices and turn
Elstner, et a.. Chem. Phys. 256 (2000) 15
For increasing N: energetics of different conformers, geometries, vibrations
N = 1 (6 stable conformers)
310 - helix
R-helix
N-fold periodicity
stabilization by internal H-bonds
between i and i+3
N
between i and i+4
Glycine and Alanine based polypeptides in vacuo
Elstner 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

N

Ace-Ala-Nme
C7eq
C5ext
C7ax

2

L
MP4-BSSE: Beachy et al, BSSE ‚corrected‘ at MP2 level

P
Polypeptides in vacuo
Effect 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
 E
310 - helix
DFT/DFTB ?
R-helix
N
peptide size
DFT: crossover only for N~20 !!  solvation??
Secondary structure:
Influence of aqueous solution
Cui et al, JPCB 105 (2001) 569
310 – helix: occurence for N<8 in database
310 - helix
QM/MM MD of octa-Alanine:
310 - helix converts into R-helix within 10 ps
Situation in Protein?
R-helix
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 forces
parallel (16-node SP2): 2 sec.
Influence of Dispersion
Liu et al. PROTEINS 44 (2001) 484
QM/MM MD-Simulation
Crambin in Solution
HF
DFT/DFTB ?
MP2
SCC-DFTB + DIS 
Enkephalin: ~30 local minima 3 cluster
Jalkanen et al. to be published
single bend
compact
extended
C5
double bend
Enkephalin: MP2/6-31G* vs DFTB-dis//DFTB-dis

compact
extended
kcal
c
b
a
Rel. energy (kcal) vs. conformer
conformer
Enkephalin: MP2/6-31G* vs DFTB//DFTB-dis
compact

extended
kcal
conformer
Enkephalin: MP2 vs B3LYP//DFTB-dis
compact

extended
kcal
conformer
Enkephalin: MP2 vs B3LYP-dis//DFTB-dis
compact

extended
kcal
conformer
Enkephalin: MP2 vs PBE+dis//DFTB-dis
compact

extended
kcal
conformer
Enkephalin: MP2 vs PBE//DFTB-dis
compact

extended
kcal
conformer
Enkephalin: MP2 vs PBE+dis//DFTB-dis
compact

extended
kcal
conformer
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!
- large impact on relative energies
- stabilizes more compact structures:
relevant secondary structures may
not be stable without!