Theory of Thermodynamics and Kinetics of Benzene Adsorption on Ag(111)

1. Theory of Thermodynamics and Kinetics of Benzene Adsorption on Ag(111) ShafatMubin 24th October, 2016

2. Introduction Aromatic Molecules and Organic Electronics: • Possible electronic material • Properties depend on ordering of thin-film structure • Little work done on MD of aromatic molecules on metal substrates

3. Contents Benzene on Ag(111): • Binding configurations and energies - develop force-field • Overlayer - model order-disorder • Desorption - generate TPD spectra

4. 1. Benzene Binding on Ag(111) I. Dispersion Corrected DFT Calculations (W. Liu,  V. G. Ruiz, G-X Zhang, B. Santra, X. Ren, M. Scheffler, and A . Tkatchenko. New J. Phys.15, 2013) i) Binding energies (eV) ATOP BRI HCP FCC ii) Equilibrium heights () dHM = 2.95 dCM = 2.96

5. 1. Benzene Binding on Ag(111) (A. D. MacKerell et al, J. Phys. Chem. B., 102, 1998, A. Nemkevich et al, Phys. Chem. Chem. Phys.,12, 2010) II. Quantum to Classical - Force-field : CHARMM (Chemistry at HARvard Macromolecular Mechanics) - C-Ag and H-Ag : Morse + Grimme’svdW(S. Grimme, J. Comp. Chem. 2006) - Fictitious atom at center (“X”) X • Massless (in practice, mass is 1.0amu) • Joined to C ring by almost rigid bonds and dihedrals • Interacts only with Ag via a Morse potential - Final Model : C : Morse + vdW : , , H : Morse + vdW : , , X : Morse : , , s6 Total: 10 parameters

6. 1. Benzene Binding on Ag(111) - Results Binding energy obtained from single-molecule TPD (discussed later) = 0.64 eV Experimental binding energy = 0.62 ± 0.03 eV(Liu et al, PRL, 115, p.03614, 2015 )

7. 2. Overlayer of Benzene on Ag(111) I. Experimental Work - Experiments by LEED, UPS, 2PPE, NEXAFS, ARUPS, etc. - Summary: - overlayer is hexagonal 3x3 (nearest neighbor: 8.65 ) - FCC or HCP sites are occupied - overlayer is flat with respect to surface - LEED pattern not observed above 160 K - repulsion exists between molecules ( K. H. Frank et al, J. Chem. Phys., 89, 1988 ) ( R. Dudde et al, Surf. Sci.225, 1990 ) ( Yannoulis et al, Surf. Sci., 189/190, 1987 ) ( K. C. Gaffney et al, Chem. Phys., 251, 2000 ) ( T. J. Rockey et al, J. Phys. Chem. B, 2006 )

8. 2. Overlayer of Benzene II. Intermolecular Potentials - Lennard-Jones (LJ) and Coulomb (from CHARMM forcefield) 8.65 • minimum located below 8.65 • attractive (beyond the minimum) • short-ranged denser than 3x3 packing

9. 2. Overlayer of Benzene - Intermolecular Potentials (contd.) Other interactions: - Dipole-dipole interaction : too weak to counter dispersion - dipole moment induced by surface electric field - perpendicular to surface and creates repulsion - p ≈ 1 D at 1 ML calculated from experimental change in work function - p=1.24 D calculated from DFT (W. Kohn, K. H. Lau, Solid State Communications, 1976 ) (K. J. Gaffney, et al, Chem. Phys. 2000 )

10. 2. Overlayer of Benzene - Intermolecular Potentials (contd.) (A. D. McLachlan, J. Mol. Phys. 7, 1964 ) - McLachlan interaction : too weak - substrate-mediated fluctuating dipole-image interaction between adsorbates - depends on polarizability of benzene - 10% of dispersion energy - insignificant contribution to the adsorbed system

11. 2. Overlayer of Benzene - Intermolecular Potentials (contd.) - Shockley scattering: - Theory: - Friedel oscillations of surface states (Shockley states) - creates interaction between adsorbates - Pair-interaction: (P. Hyldgaard and T. Einstein. Journal of Crystal Growth,275, 2005)

12. 2. Overlayer of Benzene - Intermolecular Potentials (contd.) - Substrate-mediated interaction(contd.) - Asymptotic form : - Alternative form (including bulk-state absorption) : (P. Hyldgaard and M. Persson. J. Phys. Cond.Matter,12, 2000) (P. Hyldgaard and T. Einstein. Journal of Crystal Growth,275, 2005) r = reflectance = phase shift

13. 2. Overlayer of Benzene - Intermolecular Potentials (contd.) - Substrate-mediated interaction(contd.) - Asymptotic formplot : Ag surface states: (O. Jeandupeux et al, PRB, 1999) - Oscillatory - Long ranged Bulk states create similar interaction but it is negligibly small

14. 2. Overlayer of Benzene - Intermolecular Potentials (contd.) - Substrate-mediated interaction(contd.) - Previous work : benzene overlayer on Cu(111) (K. Berland, T. Einstein and P. Hyldgaard. Phys. Rev. B. 80, 2009) Cu surface states: Two phases: - - Short-cutoff Key Difference: Only one phase (3x3) in Ag(111) Bz-Bz interaction minimum substrate-mediated minimum

15. 2. Overlayer of Benzene - Intermolecular Potentials (contd.) - Modifications • Two scattered waves (from C and H separately) - two sets of phase shifts and reflectances (r) - four parameters - two potentials • Non-Asymptotic form : Fit for and

16. 2. Overlayer of Benzene - Intermolecular Potentials (contd.) - Fitting and : - Competing overlayers 3x3 centre of benzene 7.5 8.65 • - 3x3 is most favoured at all cutoffs • A long cutoff (30 ) can be chosen • Overlayer energy is positive (i.e. repulsive force) • Disorder temperature can be controlled by adjusting the difference between 3x3 and the next favouredoverlayer 7.5 7.5-8.65-10.3 8.5 7.5 favoured by CHARMM forcefield 10.3

17. 2. Overlayer of Benzene - Intermolecular Potentials (contd.) - Overall intermolecular potential

18. 2. Overlayer of Benzene III. Z-Decay of Substrate-mediated Interactions How does substrate-mediated interaction decay with height? determined by trial-and-error: Fraction First layer 1.0 Second layer ? 0 z

19. 2. Overlayer of Benzene - Z-Decay of Substrate-mediated Interactions (contd.) DFT calculations of benzene energy as a function of height (W. A. Saidi, U.Pitt)

20. 2. Overlayer of Benzene - Z-Decay of Substrate-mediated Interactions (contd.) Determination of decay function: obtained from fitted force-field Finding • Trial-and-error

21. 2. Overlayer of Benzene - Implementation (contd.) - Setup • Large simulation box to accommodate a long cutoff (60 78 ) • 72 benzene molecules, initially ordered at FCC in 3x3 • Substrate-mediated interaction modeled as X-X pair potential • Temperature range : 50 K – 200 K • Simulation time: 5 ns

22. 2. Overlayer of Benzene 200 K 100 K 150 K

23. 2. Overlayer of Benzene Average PE per molecule Measures deviation from a perfect hexagon Hexagonal Order Parameter () V. Results • with z-decay • without z-decay • with z-decay • without z-decay Simulated disorder temperature ≈ 160 K Experimental ≈ 160 K ( K. C. Gaffney et al, Chem. Phys., 251, 2000 ) j (C. Williges, W. Chen, C. Morhard, J. P. Spatz, and R. Brunner. Langmuir29, 2013)

24. 3. Desorption of Benzene - Experimental Work - Temperature-programmed desorption (T. J. Rockey et al, J. Phys. Chem. B, 2006) = heating rate (coverage dependent) = binding energy Simulate TPD spectrum at a low coverage (weak intermolecular interaction) to determine

25. 3. Desorption of Benzene II. Simulating TPD Spectrum - Transition state (TS) and desorption - a thin region (b) far above the surface - zero interaction with Ag in TS - a molecule in TS is considered desorbed - rate constant (k) calculation: b TS Region Distance longer than cutoff SURFACE

26. 3. Desorption of Benzene - Accelerated MD: Bond-boost Method Rate constant: With boost:

27. 3. Desorption of Benzene - Simulating TPD Spectrum(contd.) • Arrhenius equation: Single Molecule Arrhenius Plot eV

28. 3. Desorption of Benzene - Simulating TPD Spectrum(contd.) - Results (Single Molecule) - Simulated TPD spectrum: • Simulated • Experiment ( T. J. Rockey et al, J. Phys. Chem. B, 2006 )

29. 3. Desorption of Benzene - Results (low coverage) - Simulating TPD Spectrum(contd.) - Low-coverage TPD simulation (with intermolecular interaction): - Run simulation until all adsorbates desorb - Record temperature of desorption and plot ( T. J. Rockey et al, J. Phys. Chem. B, 2006 )

30. 3. Desorption of Benzene - Simulating TPD Spectrum(contd.) - Results (higher coverages) Simulated Experiment Simulated Experiment trailing-edge discrepancy presumably caused by surface defects ( T. J. Rockey et al, J. Phys. Chem. B, 2006 )

31. 3. Desorption of Benzene III. Simulating Surface Defects • Defect Structures: • Islands, edges and vacancies (presumably not periodic) • Expected to increase binding energy and broaden TPD spectra • Concentration and types present in experiment unknown (although assumed to be unchanged for experiments performed by Rockey, 2006)

32. 3. Desorption of Benzene - Simulating Surface Defects Islands on surface Isolated Ag atoms Rectangular Island Step-edge

33. 3. Desorption of Benzene - Simulating Surface Defects Isolated Ag atoms Isolated Ag atoms have negligible effect on TPD at high coverages

34. 3. Desorption of Benzene - Simulating Surface Defects Effect of Types of Defects on TPD (1 ML) • No defect • Rectangular Island • Row of Atoms • Experiment Rectangular Island Row of Atoms ( T. J. Rockey et al, J. Phys. Chem. B, 2006 )

35. 3. Desorption of Benzene - Simulating Surface Defects TPD (0.05, 0.21, 0.42, 0.63 ML) • No defect • Rectangular Island • Row of Atoms • Experiment ( T. J. Rockey et al, J. Phys. Chem. B, 2006 )

36. 3. Desorption of Benzene - Simulating Surface Defects Combining Defect Contributions • Divide domain into independent sections containing specific defect types and concentrations • Three types of defects: - Defect 0 (no defect) - Defect 1 (rectangular island) - Defect 2 (step-edge) • Vary concentrations to match experimental spectra

37. 3. Desorption of Benzene - Simulating Surface Defects Combining Defect Contributions Fit :

38. 3. Desorption of Benzene - Simulating Surface Defects Combining Defect Contributions: • No defect • Combined Defect • Experiment

39. 3. Desorption of Benzene - Simulating Surface Defects Combining Defect Contributions: Coverage and TPD (0.05, 0.21, 0.42, 0.63, 1.0 ML) Dashed Experiment Solid Simulation

40. Conclusion • Single benzene simulations (force-field,TPD • Intermolecular forces and z-decay • Desorption spectra (with defects) • Future Work: extend to other aromatic systems (e.g. NTCDA/Ag)

41. Questions?

42. Limitations of Pairwise Model • Many-body effects represented as pairwise interactions (i.e. additive approach)

43. Limitations of Pairwise Model [1] Exact vs Additive At large z above surface: Exact (for an isotropic particle): dynamic polarizability of adsorbate dielectric response function of substrate Additive (sum of ’s over pairs on a slab): ; atomic density of substrate Impossible to find consistent ’s that produce theoretical ’s for all known geometries (e.g. slab, sphere, cavity, cylinder) (Bruch, L. W., M. W. Cole, and E. Zaremba (1997) Physical Adsorption Forces and Phenomena)

44. Limitations of Pairwise Model [2] Orientation Dependence of Anisotropic Particle Exact (for an anisotropic particle): calculated for isotropic polarizability calculated for Additive : negligible orientation dependence (Harris, J., Feibelman, P., Surf. Sci., 1982)

45. Inverse-cube Decay Benzene Exact (parallel to surface) = 7.159 eV Benzene Exact (perpendicular to surface) = 8.253 eV Benzene Additive (from simulation parameters) = 8.58 eV • [slide 22]: • z-dependence of Bz-Ag interaction • Morse Fit: fitted force-field • Inverse-cube Fit:

46. Inverse-cube Decay [slide 22]: Finding Bz-Bz interaction z-dependence Benzene Exact (parallel to surface) = 7.159 eV • [slide 22]: • z-dependence of Bz-Ag interaction • Morse Fit: fitted force-field • Inverse-cube Fit: