Slide 1

DFT and VdW interactions Marcus Elstner Physical and Theoretical Chemistry, Technical University of Braunschweig Slide 2 DFT and VdW interactions E ~ 1/R 6 2 Problems: - Pauli repulsion: exchange effect ~ exp( R ) or 1 /R 12 - attraction due to correlation ~ -1 /R 6 Slide 3 DFT Problem - B88 exchange: too repulsive ? - PBEx/PW91x: too attractive already at Ex only level - LDA finds often binding! E ~ 1/R 6 - fix E x - correlation E c ? E c ?? E x ?? Slide 4 Ar 2 with E x only B too repulsive, PW91x too attractive Complete mess with DFT Wu et al. JCP 115 (2001) 8748 Slide 5 Popular Functionals: role of E x Xu & Yang JCP 116 (2002) 515 BPW91 BLYP B3LYP PW91 B3LYP contains only 20% HF exchange! Slide 6 BPW91 vs PW91: attraction only due to exchange!!!!! Correlation not significant for PW91 and LYP BPW91 BLYP B3LYP PW91 Popular Functionals: role of E c Xu & Yang JCP 116 (2002) 515 Slide 7 Perez-Jorda et al. JCP 110 (1999) 1916 DFT HF x + E c : some Ec lead to (over-) binding, some dont! Popular Functionals: role of E c Slide 8 Does overlap matter? Xu & Yang JCP 116 (2002) 515 Elstner et al. JCP 114 (2001) 5149 GGA DFTB Slide 9 DFT and VdW interactions: the problem E ~ 1/R 6 E c = 0 E xc = ?? Slide 10 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. Slide 11 Adding empirical dispersion Following the idea of HF+dis: Add f (R ) C 6 /R 6 to DFT total energy C 6 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 Slide 12 Dispersion forces - Van der Waals interactions Elstner et al. JCP 114 (2001) 5149 E tot = E SCC-DFTB - f (R ) C 6 /R 6 C 6 via Slater-Kirckwood combination rules of atomic polarizibilities after Halgreen, JACS 114 (1992) 7827. damping f(R ) = [1-exp(-3(R /R 0 )7 )] 3 R 0 = 3.8 (fr O, N, C) E ~ 1/R 6 Slide 13 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 Slide 14 DFTB input f(R ) = [1-exp(-3(R /R 0 )7 )] 3 E tot = E SCC-DFTB - f (R ) C 6 /R 6 R 0 : e.g. 3.8 for ONC Atomic polarizabilities: hybridisation dependent Effective electron number (from Halgren) Slide 15 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 Slide 16 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 Slide 17 DFT and empirical dispersion From Wu and Yang 2002 Does not work for all E xc functionals properly Wu and Wang 2002 Zimmerli et al.2004 Slide 18 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 Slide 19 f (R ) C 6 /R 6 -choice of C6 coefficients -Choice of damping function Slide 20 Choice of C6 coefficients - hybridisation dependence vs. atomic values - empirical values Very similar in various approaches Slide 21 Choice of damping function - various functional forms - Fermi-function - f(R ) = [1-exp(-3(R /R 0 )7 )] 3 - choice of cutoff radius from Grimme 2004 Slide 22 Choice of f damp f damp balances several effects - contribution from E x /E c in overlap region - double counting of E c - BSSE and BSIE - missing higher order terms 1/R**8 Determination completely empirical Choose, to reproduce interaction energies for large set of stacked compounds Slide 23 Choice of fdamp However, form of fdamp may be crucial From Wu and Yang 2002 Location of minimum For A-A stack Slide 24 Grimme 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 Slide 25 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 Slide 26 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 Slide 27 Applications of DFTB-D Slide 28 Benzene (from Irle/Morokuma, Emory) Slide 29 RHF, MP2 (both CP corrected) and DFTB E on benzene dimers: Benzene (from Irle/Morokuma, Emory) Slide 30 Hybride materials Slide 31 O(N)-QM/MM-molecular-dynamics for DNA-dodecamer in H 2 O Elstner et al. in preparation DNA-Dodecamer 758 + 2722 H 2 O + 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 Slide 32 Intercalation: Ethidium AT Reha et al JACS 2003 Slide 33 Secondary-structure elements for Glycine und Alanine- based polypeptides: -sheets, helices and turn Elstner, et a.. Chem. Phys. 256 (2000) 15 N = 1 (6 stable conformers) 3 10 - helix stabilization by internal H-bonds N-fold periodicity between i and i+3 N R -helix between i and i+4 For increasing N: energetics of different conformers, geometries, vibrations Slide 34 Glycine and Alanine based polypeptides in vacuo Elstner et al., Chem. Phys. 256 (2000) 15 N = 1 (6 stable conformers) N Relative energies, structures and vibrational properties: N=1-8 (6-31G*) C 7 eq C 5 ext C 7 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 Slide 35 Polypeptides in vacuo Effect of dispersion: favors more compact structures N = 2 (6-31G*) Ace-Ala 2 -Nme BLYP B3LYP MP2 HF SCC-DFTB C 7 eq C 5 ext BI BII BI` BII` DFT: relative stability of compact vs. extended structures? Slide 36 Secondary structure formation Elstner et al., Chem. Phys. 256 (2000) 15 DFT/DFTB ? 3 10 - helix R -helix peptide size DFT: crossover only for N~20 !! solvation?? E N Slide 37 Secondary structure : Influence of aqueous solution Cui et al, JPCB 105 (2001) 569 3 10 - helix R -helix 3 10 helix: occurence for N Slide 38 Molecular-dynamics for Crambin in H 2 O-solution O(N)-QM/MM simulation Liu et al. PROTEINS 44 (2001) 484 Crambin (639) + 2400 H 2 O MD simulation for 0.35 ns energy and interatomic forces parallel (16-node SP2): 2 sec. Slide 39 Influence of Dispersion Liu et al. PROTEINS 44 (2001) 484 QM/MM MD-Simulation Crambin in Solution HF DFT/DFTB ? SCC-DFTB + DIS MP2 Slide 40 Enkephalin: ~30 local minima 3 cluster Jalkanen et al. to be published Enkephalin: ~30 local minima 3 cluster Jalkanen et al. to be published C5 compact extended double bend single bend Slide 41 Enkephalin: MP2/6-31G* vs DFTB-dis//DFTB-dis compact extended conformer kcal Rel. energy (kcal) vs. conformer b a c Slide 42 Enkephalin: MP2/6-31G* vs DFTB//DFTB-dis compact extended conformer kcal Slide 43 Enkephalin: MP2 vs B3LYP//DFTB-dis compact extended conformer kcal Slide 44 Enkephalin: MP2 vs B3LYP-dis//DFTB-dis compact extended conformer kcal Slide 45 Enkephalin: MP2 vs PBE+dis//DFTB-dis compact extended conformer kcal Slide 46 Enkephalin: MP2 vs PBE//DFTB-dis compact extended conformer kcal Slide 47 Enkephalin: MP2 vs PBE+dis//DFTB-dis compact extended conformer kcal Slide 48 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... Slide 49 DFT+large soft matter structures: dont do without dispersion! - large impact on relative energies - stabilizes more compact structures: relevant secondary structures may not be stable without!