Accurate van der Waals interactions from ground state electron density

Size: px

Start display at page:

Download "Accurate van der Waals interactions from ground state electron density"

Meredith Carr
5 years ago
Views:

Department, Fritz Haber Institut der MPG Berlin,

1 Accurate van der Waals interactions from ground state electron density Alexandre Tkatchenko Theory Department, Fritz Haber Institut der MPG Berlin, Germany berlin.mpg.de Haber Institute EXCITCM09, Nov 2, 2009

2 Back to Basics A R B No orbital overlap (large enough R):

3 Back to Basics A R B No orbital overlap (large enough R): 20% error in Cn coefficients leads to 20% error in binding energy

4 Role of vdw asymptotics at equilibrium distance Xe Xe 4.36 Å, 24 mev Tang and Toennies JCP (2003)

5 Role of vdw asymptotics at equilibrium distance 4.36 Å, 24 mev Xe Xe Cn increased by 20% 4.21 Å, 36 mev

6 Asymptotics do matter: RG dimers ~ 60% ~ 30% ~ 10% 4.36 Å, 24 mev Xe Xe Cn increased by 20% 4.21 Å, 36 mev Increasing Cn by 20% increases the binding energy by 50%

7 Asymptotics do matter: Benzene dimer exc h Total d an ge n o i s r e p is SAPT: Podeszwa, Bukowski, Szalewicz, JPCA (2006) Error of 20% in the dispersion energy leads to 50% error in binding

8 Can we get dispersion coefficients (from ground state theory) to better than 5%?

9 Accurate reference C6 database (1) Differential dipole oscillator strength (DOS) Transition energy (ground state excited state) (1) W. J. Meath and co workers (1977 present)

10 Accurate reference C6 database (1) Experimental data (DOSD) Theory (pseudo DOSD) Using different sets of exp. S(k) data, C6AB is typically accurate to 1 2% (1) W. J. Meath and co workers (1977 present)

11 Accurate reference C6 database (1) Experimental data (DOSD) Theory (pseudo DOSD) Using different sets of exp. S(k) data, C6AB is typically accurate to 1 2% Data available for atoms, alkanes, alkenes, alkynes, alcohols, H2, N2, H2S, NH3, SO2, COS, CO2, CS2, SiH4, CCl4, etc. (50 atoms and molecules 1225 interaction pairs) (1) W. J. Meath and co workers (1977 present)

12 Can we get accurate dispersion coefficients? MP2: C6 Error 18% Energy Error ~ 36%

13 Can we get accurate dispersion coefficients? LL: Andersson and Rydberg, Physica Scripta (1999). C6 Error MP2: 18% Langreth Lundqvist: 16% Energy Error ~ 36% ~ 32%

14 Can we get accurate dispersion coefficients? C6 Error MP2: 18% Langreth Lundqvist: 16% Becke Johnson: 13% Becke Johnson: Johnson and Becke, JCP (2005) Energy Error ~ 36% ~ 32% ~ 26%

15 Let us start from first principles...

16 Atom atom dispersion energy A No multipole moments on A and B B Eint = Edisp

17 Atom atom dispersion energy A No multipole moments on A and B B Eint = Edisp To leading order (long range approximation):

18 Atom atom dispersion energy A No multipole moments on A and B B Eint = Edisp C6 coefficient To leading order (long range approximation):

19 TS vdw method: Basic ingredients 1) Only relative polarizability is used avoiding inaccurate absolute polarizability of (semi ) local DFT or Hartree Fock. 2) Ab initio reference free atom C6 coefficients (Chu and Dalgarno). 3) Accurate combination rule for heteronuclear coefficients. 4) Atom in a molecule/solid polarizability from Hirshfeld partitioning of the electron density (Becke and Johnson). 5) C6 = C6[n(r)]: C6 becomes a functional of the electron density. A. Tkatchenko and M. Scheffler PRL (2009).

20 C6 is a functional of the density (Carbon Carbon C6 coefficient) 24.1 HartreeBohr6 sp HartreeBohr6 2 sp 38.6 HartreeBohr6 sp 3

21 Performance of TS vdw for molecules MAE of 5.5% for 1225 molecular pairs from DOSD reference data of W. J. Meath et al.

22 Performance of TS vdw for molecules Results depend negligibly (1% deviation) on the employed xc functional

23 S. Grimme J. Comput. Chem. 27, 1787 (2006) Comparison to fixed C6 schemes TS scheme: 5% Grimme: 15%... and we can treat all elements in the periodic table

24 DFT+vdW & MP2+ vdw (1) (2) Leading dispersion term (or C6 term) is added to DFT or MP2 total energy, damped at short distances, Effective vdw parameters are functionals of the electron density: C6 = C6[n(r)], RvdW = RvdW[n(r)] One damping parameter for DFT (for each functional), no parameters for MP2 (1) DFT+vdW: Tkatchenko and Scheffler PRL (2009) (2) MP2+ vdw: Tkatchenko, DiStasio Jr., Head Gordon, Scheffler JCP (2009)

25 Short range damping function 1.0 fn(r) n= 8 10 R [bohr] Analytic: Aziz, Koide, Meath, Tang, Toennies, et al. HF&DFT: Scoles, Yang, Grimme, Bechstedt, Hobza, et al. Damping function: Analytical form known exactly for dispersion energy in H H Law of corresponding states for other spherical atoms (rare gas, alkaline earth, mercury) Parameterized when used with DFT or quantum chemical methods

26 Performance for intermolecular interactions (S22*) 118 mev PBE Gulans, Puska, 59 mev Nieminen, PRB (2009) Langreth-Lundqvist 33 mev MP2 20 mev PBE+vdW(Hobza) 13 mev PBE+vdW(TS) 3 mev MP2+ vdw(16 systems) Mean absolute error to CCSD(T) [mev] *Jurecka, Sponer, Cerny, Hobza PCCP 8, 1985 (2006) S22 database: Organic dimers, including vdw, electrostatics and H bonding

27 Importance of vdw asymptotics (large molecules) GGA&Hybrids M06 Marom, Tkatchenko, Scheffler, Kronik, JCTC, submitted. GGA(h)+vdW M06+vdW

28 Outlook Extending the method to solids and adsorption (dielectric screening in metals, etc.) Short range damping function Anisotropic and non additive many body vdw interactions

29 Summary Developed accurate first principles method for the long range van der Waals interactions Can be coupled to DFT (DFT+vdW) or MP2 (MP2+ΔvdW) Consistently accurate results for a variety of applications Can be coupled to hybrid functionals for improved electronic structure (Marom, Tkatchenko, Scheffler, Kronik, submitted) or followed by GW calculations

Methods for van der Waals Interactions

Methods for van der Waals Interactions Alexandre Tkatchenko Theory Department, Fritz Haber Institut der MPG Berlin, Germany tkatchen@fhi berlin.mpg.de Haber Institute FHI DFT and Beyond Workshop, Jul.