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Unformatted text preview: DFT and VdW interactions DFT and VdW interactions Marcus Elstner Physical and Theoretical Chemistry, Technical University of Braunschweig DFT and VdW interactions 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 DFT Problem DFT ProblemB88 exchange: too repulsive ?PBEx/PW91x: too attractive already at Ex only levelLDA finds often binding! E ~ 1/R 6 fix E x correlation E c ? E c ?? E x ?? Ar 2 with E x only Ar 2 with E x 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 E x Xu & Yang JCP 116 (2002) 515 BPW91 B LYP B3 LYP PW91 B3LYP contains only 20% HF exchange! BPW91 vs PW91: attraction only due to exchange!!!!! Correlation not significant for PW91 and LYP B PW91 B LYP B3LYP PW91 Popular Functionals: role of E c Popular Functionals: role of E c Xu & Yang JCP 116 (2002) 515 PerezJorda 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 Popular Functionals: role of E c 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 problem DFT and VdW interactions: the problem E ~ 1/R 6 E c = 0 E xc = ?? DFT and VdW interactions: solutions 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 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 wellbehaved (i.e. like HF) Ec: double counting Dispersion forces  Van der Waals interactions Elstner et al. JCP 114 (2001) 5149 Dispersion forces  Van der Waals interactions Elstner et al. JCP 114 (2001) 5149 E tot = E SCCDFTB f (R ) C 6 /R 6 C 6 via SlaterKirckwood combination rules of atomic polarizibilities after Halgreen, JACS 114 (1992) 7827. damping f(R ) = [1exp (3(R /R )7 )] 3 R = 3.8 (fr O, N, C) E ~ 1/R 6 How to get Dispersion coefficients?...
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 Summer '06
 DuaneJohnson
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