Van der Waals density functional applied to adsorption systems

Transcription

1 Van der Waals density functional applied to adsorption systems Ikutaro Hamada Advanced Institute for Materials Research (AIMR) Tohoku University Contents Introduction The van der Waals density functional Application to C60/metal interfaces Summary 2

2 Ab initio surface/interface science: Charge separation/transport across an interface Molecular electronics: Electron transport through molecule(s) Photovoltaics: Charge separation at an interface excited Donor (P3HT) Acceptor (PCBM) Structure of a solid/liquid interface ϕ1 ϕ2 Electrochemical reaction at solid/liquid interface: charge transfer reaction 3

3 Outline Introduction The van der Waals density functional (vdw-df) Application of vdw-df - C60/Au(111) - C60/Ni(111) Summary 4

4 van der Waals density-functional (vdw-df) Divide exchange-correlation into local part and long-range nonlocal correlation E xc = E 0 xc + E nl c 5

5 van der Waals density functional (vdw-df) E xc = E GGA x + E LDA c + E nl c E nl c = 1 2 dr 1 dr 2 n(r 1 ) (q 1,q 2,r 12 )n(r 2 ) q i = q 0 (n(r i ), n(r i ) ) =0.0 =0.5 =0.9 r 12 = r 1 r 2 4 D 2 (Hartree) D = 1 2 (d + d ) = d d d + d Dion et al., Phys. Rev. Lett. 92, (2004). d = r r q 6 0 (r) d = r r q 0 (r ) D

6 vdw-df is able to describe vdw interaction Rare gas dimer GGA vdw-df Dion et al., Phys. Rev. Lett. 92, (2004). 7

7 vdw-df is able to describe covalent bonding Graphene vdw DF LDA PBE E tot (ev) PBE vdw-df Lattice constant (nm) IH and M. Otani, Phys. Rev. B 82, (2010). 8

8 vdw-df applied to an adsorption system Alq3/Mg(001) Adsorption energy (kj/mol) (a) meridional isomer (c) facial isomer PBE vdw-df vdw-df2 mer/up p mer/down fac/up (b) (d) fac/down Positive value: exothermic S. Yanagisawa, IH, K. Lee, D. C. Langreth, and Y. Morikawa, Phys. Rev. B 83, (2011). See also: S. Yanagisawa, K. Lee, and Y. Morikawa, J. Chm. Phys. 128, (2008). 9

9 Advantages/disadvantages of vdw-df vdw and covalent interactions in a seamless fashion H-bonding is too weak vdw attraction is too large near the equilibrium Binding distance is too large wrong (interfacial) electronic structure 10

10 Band-gap opening at the K point of graphene/ni(111) is not reproduced by vdw-df ARPES experiment vdw-df calculation A. Varykhalov, et al., Phys. Rev. Lett. 101, (2008) M. Vanin, et al., Phys. Rev. B 81, (R) (2010) 11

11 Adsorption energy is calculated reasonably well, while adsorption distance is generally overestimated by vdw-df Expt. GGA vdw-df DFT-D Expt. Z C Δφ (ev) K. Toyoda, IH, K. Lee, S. Yanagisawa, Y. Morikawa, J. Chem. Phys. 132, (2010) 12

12 Problems in vdw-df Equilibrium distance overestimated Too repulsive exchange (revpbe) at a short distance Rare gas dimer GGA vdw interaction near equilibrium overestimated Too large vdw attraction of nonlocal correlation at a short distance vdw-df E vdw-df xc = E revpbe x + E LDA c + E nl c Dion et al., Phys. Rev. Lett. 92, (2004). 13

13 Attempts to improve vdw-df vdw-df with the exact exchange - Thonhauser, Puzder, Langreth, J. Chem. Phys. 124, (2006). vdw-df with the PBE exchange - Gulans, Puska, and Nieminen, Phys. Rev. B 79, (R) (2009). vdw-df with the exchange of Cooper (C09) - Cooper, Phys. Rev. B 81, (R) (2010). vdw-df with an optimized exchange (OptPBE, OptB88, OptB86b) - Klimes, Bowler, and Michaelides, J. Phys. Condens. Matter 22, (2010). vdw-df2 - Lee, Murray, Kong, Lundqvist, Langreth, Phys. Rev. B 82, (2010). VV09/VV10 - Vydrov and Van Voorhis, Phys. Rev. Lett. 103, (2009), J. Chem. Phys. 133, (2010). Baysian error estimation functional with van der Waals correlation (BEEF-vdW) - Wellendorff et al., Phys. Rev. 85, (2012) 14

14 Higher accuracy vdw-df: vdw-df2 C09x E vdw-df xc = E GGA x + E LDA c + E nl c Exchange functional of Cooper (C09) Cooper, Phys. Rev B 81, (R) (2010) Nonlocal correlation of Lee et al. (vdw-df2) Lee et al., Phys. Rev. B 82, (R) (2010). for improved description of interface geometry and electronic structure of adsorption systems IH and M. Otani, Phys. Rev. B 82, (2010). 15

15 Exchange enhancement factor E GGA x = drne unif x (n)f x (s) s = n /(2k F n) PBE revpbe C09 Reproduce revpbe asymptote at a large reduced gradient F x Obey gradient expansion at a small reduced gradient to reduce repulsion at short distance s C09 [V. R. Cooper, Phys. Rev. B 81, (R) (2010)] 16

16 vdw-df2c 09x improves the adsorption distance of graphene 300 Graphene/Ni(111) 200 PBE vdw-df Binding energy (mev) Expt. vdw-df2 C09 x Adsorption distance (nm) IH and M. Otani, Phys. Rev. B 82, (2010). 17

17 vdw-df2 C09x band structure ARPES experiment IH and M. Otani, Phys. Rev. B 82, (2010). A. Varykhalov et al., Phys. Rev. Lett. 101, (2008) 18

18 vdw-df2c 09x improves the adsorption distance of graphene Graphene/Pt(111) Binding energy (mev) Expt. vdw-df vdw-df2 vdw-df C09 x vdw-df2 C09 x Adsorption distance (nm) IH and M. Otani, Phys. Rev. B 82, (2010). 19

19 Interaction energy of water with graphene from vdw-df2 C09x agrees well with those from accurate RPA and DMC Interaction energy (ev) vdw-df2 C09 x vdw-df2 vdw-df PBE RPA DMC Separation (nm) DMC and RPA results: Ma, Michaelides, Alfe, Schimka, Kresse, Wang, Phys. Rev. B 84, (2011). vdw-df results: IH, submitted 20

20 Interaction energy of water with graphene from vdw-df2 C09x agrees well with those from accurate RPA and DMC Interaction energy (ev) vdw-df2 C09 x vdw-df2 vdw-df PBE RPA DMC Separation (nm) DMC and RPA results: Ma, Michaelides, Alfe, Schimka, Kresse, Wang, Phys. Rev. B 84, (2011). vdw-df results: IH, submitted 21

21 A benchmark calculation: Sandwich-shaped benzene dimer Separation Interaction energy (kj mol -1 ) vdw-df vdw-df2 vdw-df-c09 vdw-df2-c09 estd. CCSD(T)-CBS Separation (Å) vdw-df2 C09x is less accurate than other vdw-dfs for molecular duplex 22

22 S22 dataset Hydrogen bonded complex 1. ammonia dimer 2. water dimer 3. formic acid dimer 4. formamide dimer 5. uracil dimer HB 6. 2-pyridoxine 2-aminopyridine 7. adenine thymine WC Dispersion dominated complex 8. methane dimer 9. ethene dimer 10. benzene methane 11. benzene dimer (C2h) 12. pyrazine dimer 13. uracil dimer stack 14. indole benzene stack 15. adenine thymine stack Mixed complex 16. ethene ethine 17. benzene water 18. benzene ammonia 19. benzene HCN 20. benzene dimer (C2v) 21. indole benzene T- shape 22. phenol dimer 23

23 Benchmark calculation with S22 dataset Deviation of binding energies from reference CCSD(T) results Hydrogen-bonded complex Dispersion dominated complex Mixed complex Deviation (mev) vdw-df vdw-df2 vdw-df-c09x vdw-df2-c09x Overestimate Underestimate Index vdw-df2 C09x tends to underestimate the binding energy of molecular complexes, especially those of dispersion dominated complexes 24

24 vdw-df2 C09x predicts accurate geometry of layered materials Graphite c (nm) Eb (mev) LDA PBE vdw-df vdw-df vdw-df2 C09x QMC ±5 RPA Interlayer binding energy (mev) LDA PBE vdw-df vdw-df2 vdw-df C09 x vdw-df2 C09 x Expt. Expt ± Lattice constant c (nm) QMC: Spanu, Sorella, and Galli, Phys. Rev. Lett. 103, (2009). RPA: Lebegue, Harl, Gould, Angyan, Kresse, and Dobson, Phys. Rev. Lett. 105, (2010). Expt. Baskin and Mayer, Phys. Rev. B 100, 544 (1955); Zacharia, Ulbricht, and Hertel, Phys. Rev. B 69, (2004). 25

25 vdw-df2 C09x predicts accurate geometry of layered materials h-bn c (nm) Eb (mev) LDA PBE vdw-df vdw-df vdw-df2 C09x Interlayer binding energy (mev) Experimental interlayer distance LDA PBE vdw-df vdw-df2 vdw-df C09 x vdw-df2 C09 z RPA Expt Lattice constant c (nm) RPA: Marini, Garcia-Gonzalez, Rubio, Phys. Rev. Lett. 96, (2006). Expt. Paszkowicz et al., Appl. Phys. A: Mater. Sci. Process. 75, 431 (2002). 26

26 Lattice constants of solids vdw-df vdw-df2 optb88-vdw OptB86b-vdW PBE vdw-df2 C09x ME (A ) MAE (A ) MRE (%) MARE (%) vdw-df2 C09x gives good lattice constants of typical solids! 28

27 Outline Introduction The van der Waals density functional (vdw-df) Applications of vdw-df - C60/Au(111) - C60/Ni(111) Summary 29

28 C60 as a component of molecular electronic devices - Franck-Condon blockade in a single-c60 transistor (Au/C60/Au) Park et al., Nature 407, 57 (2000). - Bright lines in differential conductance which correspond to C60 center of mass motion - Kondo effect in single-c60 transistors with Au and Ni electrodes Pasupathy et al., Science 306, 86 (2004). Yu and Natelson, Nano Lett. 4, 79 (2004). - Peak in conductance at zero bias Park et al., Nature 407, 57 (2000). - Negative differential resistance Danilov et al., Faraday Discuss. 131, 337 (2006). - Superconductivity Winkelmann, et al., Nature Phys. 5, 876 (2009). Yu and Natelson, Nano Lett. 4, 79 (2004). - Theoretical calculations Ono and Hirose, Phys. Rev. Lett. 98, (2007) Schull, Frederiksen, et al., Phys. Rev. Lett. 103, (2009) Sogo,..., Yanagisawa, Morikawa, J. Phys. Chem. C 114, 3504 (2010) and many more... Ono and Hirose, Phys. Rev. Lett. 98, (2007). 30

29 C60/Au(111): accurate binding energy with vdw-df2 C09x 1 Binding energy (ev) 0-1 PBE Distance vdw-df2 C09 x -2 Expt Distance (nm) IH and M. Tsukada, Phys. Rev. B 83, (2011). 31

30 PDOS and COOP analysis 3.00 PDOS (b) HOMO(1) HOMO(2) HOMO(3) HOMO(4) HOMO(5) LUMO(1) LUMO(2) Charge density difference 0.50 LUMO(3) (c) COOP E-E F (ev) White (blue): Charge accumulation (depletion) There are weak covalent-like interfaces, owing to hybridization of C60 LUMOs and substrate wave-functions 32 IH and M. Tsukada, PRB 83, (2011).

31 Binding energy curve of C60 on Ni(111) as a function of distance 2 1 PBE vdw-df Binding energy (ev) Distance Distance (nm) Equilibrium binding energy (E0) and distance (d0) from curve fitting: PBE: E0= (ev), d0=0.198 (nm) vdw-df: E0= (ev), d0=0.188 (nm) IH, in preparation 33

32 Summary Introduction of vdw-df for adsorption systems and solids vdw-df2 with the C09 exchange (vdw-df2 C09x ) Application of vdw-df2 C09x to C60 on metal surfaces IH and M. Otani, Phys. Rev. B 82, (2010). IH and M. Tsukada, Phys. Rev. B 83, (2011). 36

33 Acknowledgment Yoshitada Morikawa (Osaka University) Minoru Otani (AIST) Susumu Yanagisawa (University of the Ryukyus) Kyoho Lee (Rutgers University) Masaru Tsukada (Tohoku University) Masaaki Araidai (Tsukuba University) Funding: World Premier International Research Institute Initiative (WPI) Grant-in-aid for Scientific Research on Innovative area JSPS Core-to-core Program, A, Advanced Research Networks 37