Free energy sampling for electrochemical systems

Transcription

1 Free energy sampling for electrochemical systems Mira Todorova, Anoop Kishore Vatti, Suhyun Yoo and Jörg Neugebauer Department of Computational Materials Design Düsseldorf, Germany IPAM,

2 Challenge: Structural and Phase Complexity Example: Galvanised steel surface Material Protective Coating layer Environment + Frank Appel + - Very different materials classes Find a suitable descriptor Steel Zinc Zinc oxide Water Translate materials complexity into representative atomistic structures

3 Approach: Employ chemical potentials Combine density functional theory with thermodynamic concepts chemical potentials + Gibbs free energy H H H H H + = Steel Zinc Zinc oxide - Water Number of atoms of species a Chemical potentials allow to compute the relevant structural units separately (divide and conquer)

4 Solvent description Solvation via explicit solvent Free energies: accessible time scales for MD simulations Æ Energy æ ~100 ps + flexibility solvation shell and its dynamics different types of bonding and charge electronic structure time - computationally expensive restricted number of atoms (e.g. 32 H 2 O) min configurations band gap problem (xc-functional)

5 Solvent description: coarse graining Solvation via explicit solvent Solvation via implicit solvent H 2 O r e in =1 e out ~ 78 Rough Smooth Energy Energy Reaction coordinate Reaction coordinate

6 Solvent description: coarse graining Solvation via explicit solvent Solvation via implicit solvent H 2 O r e in =1 e out ~ 78 + flexibility solvation shell and its dynamics different types of bonding and charge electronic structure - computationally expensive + computationally efficient - cavity (extend and shape) - bonding - electronic structure (i.e. distinction between optical and thermodynamic charge transition (redox) levels) K. Mathew, et al., J. Chem. Phys. 140, (2014),

7 Suhyun Yoo Surface stability in electrochemical environment e out ~ 80 S.Yoo, M. Todorova and J. Neugebauer (submitted)

8 Solid/liquid interface

9 ZnO: some general remarks 1/2 e - per Zn E Zn(sp 3 ) CB O(sp 3 ) VB Bulk ZnO (wurtzite structure) Zn(0001) polar surfaces Energy gain if: Zn-sp 3 is empty O-sp 3 is filled Wide band-gap semiconductor Atoms: sp 3 hybridised Electron transfer fromzntoo

10 Solid/liquid interface Surface reconstructions (also relevant for 2D materials) Easy availability of OH and H surface adsorption Screening capabilities of the solvent

11 Solid/liquid interface Energy Reaction coordinate Surface reconstructions (also relevant for 2D materials) Easy availability of OH and H surface adsorption Screening capabilities of the solvent

12 Solid/liquid interface Find for each set of (ph, U) the phase with the lowest Gibbs free energy of formation Energy Reaction coordinate Surface reconstructions (also relevant for 2D materials) Easy availability of OH and H surface adsorption Screening capabilities of the solvent

13 Phase diagrams and chemical potentials Find for each set of (ph, U) the phase with the lowest Gibbs free energy of formation Evaluate excess Gibbs free energy: a a DG» E tot - E clean - i N i m i (ph,u) water stability D f G (m O, m H, m Zn ) ZnO stability m Zn (m O ) m O (ph, U) = D f G[H 2 O] -2{e(U - U SHE ) - k B T ln10 ph} M. Todorova and J. Neugebauer, Phys. Rev. Appl. 1, (2014)

14 Considered surface phases on ZnO (0001) Considered ~ 50 surface phases Clean surface OH-adsorbed phases 0.11ML ~ 1ML OH Triangular phases n2~n7 n6n3~n7n3 p(2x2)-0.5ml OH Clean Zn(0001)-Zn p(2x2) models p( 48X 48)-n7 p( 48X 48)-n7n3 p( 12X 12) -1/6ML O and 1/6ML OH p(2x2)-v Zn p(2x2)-o ad G. Kresse, O. Dulub, and U. Diebold, Phys. Rev. B 68, (2003) M. Valtiner, M. Todorova, G. Grundmeier, and J. Neugebauer, Phys. Rev. Lett. 103, (2009)

15 Surface Pourbaix Diagram of ZnO(0001) Calculation without solvent p(2 2)-OH 0.50 ML p(3 3)-OH 0.44 ML U U SHE [V] AFM image for ZnO (0001)-Zn in electrolyte p( 48 48)-n7 ph An OH adsorbate phase is stable at conditions where triangular reconstructions are observed M. Valtiner, S. Borodin, and G. Grundmeier, Langmuir 24, 5350 (2008)

16 Selective stabilization by the solvent Calculation with solvent p( 48 48)-n7n3-4OH p( 48 48)-n7n3 p( 48 48)-n7n3-4H U U SHE [V] ph AFM image for ZnO (0001)-Zn in electrolyte Solvation leads to the stabilization of structures which are thermodynamically unstable under normal conditions. M. Valtiner, S. Borodin, and G. Grundmeier, Langmuir 24, 5350 (2008)

17 Selectivity of solvation effects: Size effects semiconducting Increasing electrostatic penalty Increasing solvation energy Poisson equation: Df = r Solvation energy is highly discriminating High electrostatic penalty in vacuum leads to a higher solvation energy gain it favours non-metallic surfaces over ones with metallic character

18 Selectivity of solvation effects: Metallicity 10-4 e/bohr 3 semiconducting e/bohr e/bohr 3 metallic e/bohr 3 Solvation energy is highly discriminating High electrostatic penalty in vacuum leads to a higher solvation energy gain non-metallic surfaces are favoured over ones with metallic character

19 Beyond the coarse graining model Coarse graining water: useful when accounting for the screening properties of the solvent is sufficient Explicit information about the geometric and/or the electronic structure is needed: Dissolution Reactions Redox levels, level alignment

20 Anoop Kishore Vatti Benchmark: Ion formation energies in water Cl 2 Cl -

21 Semiconductor defect chemistry in a nutshell Formation energies: D ( ) q ZnO : V + mo Fermi q f Gdefect O tot O + ( ZnO : V ) = DE qe Defect concentration: c defect = e -D f G defect k B T m O O 2 e - E Fermi

22 Semiconductor defect chemistry in a nutshell q q f defect O tot O + Formation energies: D G ( ZnO : V ) = DE ( ZnO : V ) + mo qefermi D f G (ev) q = 2 q = 0 V O Fermi Energy (ev) Defect energy for a given point defect in any charge state can be computed Single defect rather than a charge neutral reaction can be computed

23 Semiconductor defect chemistry in a nutshell q q f defect O tot O + Formation energies: D G ( ZnO : V ) = DE ( ZnO : V ) + mo qefermi D f G (ev) position of the charge transition level (redox level) e 2+/0 q = 2 q = 0 V O Fermi Energy (ev) Defect energy for a given point defect in any charge state can be computed Single defect rather than a charge neutral reaction can be computed E gap CB VB E Fermi

24 Calculating ion formation energies D f - - G( Cl ) = Etot (Cl : H 2O) + Etot (H2O) - m T, p T, p Cl + qe Fermi + TDS configurations m e m vac e m CB e E gap m e VB Æ E tot (Cl - : H 2 O) æ Æ E tot (H 2 O) æ m Cl m e ~ E F Ab initio MD Reservoirs for the defect species and the charge ( fi Alignment) Y. Marcus, J. Chem. Soc., Faraday Trans. 1, 87, 2995 (1991)

25 Band gap CB CB Energy VB X q- /X 0 X q- /X 0 VB Experiment DFT

26 Importance of correct alignment Conventional DFT exchange correlation potential: GGA-PBE 0 Formation energy (ev) VBM(exp) Valence band Is this real? Cl 0 Cl - Conduction band CBM (exp) Conduction band E F (ev)

27 Importance of correct alignment Hybrid DFT exchange correlation potential: PBE0 Formation energy (ev) VBM(exp) Valence band VBM (PBE) Cl 0 Cl - CBM (exp) 0 Conduction band E F (ev)

28 Band gap of water and alignment 0 Vacuum level CB CB Use electrostatic potential to align the band gaps Work function (metals) Ionization Potential/ Electron affinity (semiconductors) z Energy VB VB Experiment DFT

29 Band gap of water and alignment Surface dipole Solid Use electrostatic potential to align the band gaps Work function (metals) Ionization Potential/ Electron affinity (semiconductors) z <Surface dipole> Water

30 Band gap of water Sample phase space using a classical potential (TIP3P) Extract from the obtained trajectory uncorrelated structures Perform DFT calculations at different levels of xc-functionals T.A.Pham et al., Phys. Rev. B 89, (2014) C.Freysoldt et al., Rev. Mod. Phys. 86, 253 (2014)

31 Band gap of water Sample phase space using a classical potential (TIP3P) Extract from the obtained trajectory uncorrelated structures Perform DFT calculations at different levels of xc-functionals T.A.Pham et al., Phys. Rev. B 89, (2014) C.Freysoldt et al., Rev. Mod. Phys. 86, 253 (2014)

32 Correlations in water e/bohr 3 0 x [Å] e/bohr 3 10 y [Å] Can we utilize our knowledge about the correlations in water to develop coarse graining models?

33 Conclusions Coarse graining models for water - extremely efficient to account for the solvent - useful for accessing stability and constructing phase diagrams - limited applicability when the structure of the solvent becomes important Explicit water - computationally expensive - contain all the needed information about electronic and geometric structure Can we use the knowledge we have about the correlations in water to design better sampling strategies?

34 Acknowledgement Group (former & present): Su-Ting Cheng Klaus-Dieter Bauer Mehmet Ilhan Anoop Kishore Vatti Suhyun Yoo Sudarsan Surendralal Moloud Aghayarzadeh Colleagues at the MPIE Jörg Neugebauer Funding: