Adsorption on surfaces Bonding at surfaces

Example: H 2/H/Pd(210) Theoretical description Lennard-Jones picture of dissociative adsorption Nature of surface bonds Adsorption of molecules on surfaces technolo- < gically of tremendous importance 4 Physisorption (E ad ∼ 0.1 eV): Noble gas ad- sorption, molecular adsorption through Van- Theoretical description by ab initio methods 3 der-Waals interaction possible A + B + S 2 Chemisorption (E ad ∼ 1 - 10 eV): Chemical Analysis of electronic structure very useful for bond between surface and adsorbate 1 D AB understanding of chemical trends E E a ad Nature of surface chemical bonds: 0 Potential energy (eV) A+B AB + S Approximate model Hamiltonian can pro- Ead vide qualitative insight: Newns-Anderson, -1 Metallic bonding Effective-Medium-Theory, Embedded-Atom- 0 1 2 Method . . . Distance from the surface z(Å) Alkali-metal bond (mainly ionic) Adsorption of molecular and atomic hydrogen on Covalent bonds Pd(210) Potential energy curves for molecular and dissociative adsorption

Potential energy surfaces (PES) Physisorption

PES central quantity to describe gas-surface interaction; Example: catalyst Physisorption mediated by Van der Waals forces

1D representation Multidimensional representation

1.2 without catalyst Adsorbed Activation barrier + - with catalyst e e reactants on the surface 1.0 ~ r’ -R R r R = (0 , 0, Z ) 0.8 - O + 0.6 ~r = ( x, y, z ) 0.4 metal vacuum 0.2

0.0 Potential energy (eV) -0.2 Gas phase -0.4 Reactants barrier Image potential of a hydrogen atom in front of a metal surface: -5 -4 -3 -2 -1 0 1 2 3 4 5 Products A+B Reaction path coordinate (Å) AB e2 1 1 1 1 A. Groß, Surf. Sci. Vol. 500 V = − + − − im ~ ~ ~ ~ ~ ~ 2 "|2R| |2R + ~r + r′| |2R + ~r | |2R + r′| # 1D representation misleading: e2 1 1 2 = − + − . (103) Catalysts provides detour in multi-dimensional configuration space 2 2Z 2( Z + z) ~ with lower activation barriers " |2R + ~r | # van der Waals interaction van der Waals interaction energy

Taylor expansion of image force in |~r |/|R~|: Frequency of the atomic oscillator

e2 x2 + y2 3e2 z m ω2 2 2 2 2 3 e 2 2 meω 2 Vim = − + z + (x + y ) + z + ... . (104) V = k x + y + ⊥ z . (107) 8Z3 2 16 Z4 2 atom 2 2   h i !
3 with van der Waals interaction ∝ Z− 2 2 Assumption: electronic motion in atom can be modeled by 3D-oscillator: e e ω = ωvib − 3 and ω = ωvib − 3 . (108) k 8meωvib Z ⊥ 4meωvib Z m ω2 V = e vib x2 + y2 + z2 . (105) atom 2 !
van der Waals binding energy: change in zero-point energy of atomic oscillator Atom potential in the presence of the surface: ~ −~e2 E (Z) = (ω + 2 ω − 3ω ) = . (109) 2 2 2 2 vdW vib 3 m ω e x + y 2 ⊥ k 4meωvib Z V = e vib x2 + y2 + z2 − + z2 + . . . atom 2 8Z3 2   m ω2 !
2 e 2 2 meω 2 ≈ k x + y + ⊥ z . (106) 2 2 !

van der Waals constant Zaremba-Kohn picture of physisorption

Atomic polarizability Taylor expansion of image force of the hydrogen atom corresponds basically to dipole-dipole interaction at distance 2Z e2 α = 2 . (110) However, hydrogen atom in the ground state has no permanent dipole moment ⇒ quantum meω vib treatment neccessary van der Waals binding energy: Quantum derivation of the long-range interaction between a neutral atom and a solid surface (Zaremba, Kohn) ~ωvib α Cv EvdW (Z) = − 3 = − 3 (111) 8Z Z H = Ha + Hs + Vas . (113)

Cv = ~ωvib α/ 8 van der Waals constant, related to the atomic polarizability a atom, s solid, Vas interaction term:

Fourth-order correction defines dynamical image plane at Z0 s a 3 3 ρˆ (~r )ˆρ (~r ′) s,a s,a s,a V = d ~rd ~r ′ with ρˆ (~r ) = n (~r ) − nˆ (~r ) . (114) Cv 3CvZ0 5 Cv 5 as + |~r − ~r ′| Vim (Z) = − 3 − 4 + O(Z− ) = − 3 + O(Z− ) (112) Z Z (Z − Z0) Z Pertubation treatment of physisorption Pertubation treatment of physisorption II

Assumption: negligible overlap of the wave functions ⇒ C H = H + H + V . (115) (2) v 5 a s as E (Z) = − 3 + O(Z− ) (117) (Z − Z0) First-order contribution vanishes; second order: with a s a s |h ψ ψ |V ′ |ψ ψ i| (2) 0 0 as α β 1 ∞ ǫ(iω ) − 1 E = a a s s (E − E ) + ( E − E ) Cv = dω α (iω ) (118) α=0 β=0 0 α 0 β 4π ǫ(iω ) + 1 X6 X6 Z 1 1 0 = − d3~r d3~r d3~x d3~x ′ ′ ~ ~ Z Z Z Z |R + ~x − ~r | |R + ~x ′ − ~r ′| ∞ dω 1 ∞ ǫ(iω ) − 1 × χa(~x, ~x ′, iω )χs(~r, ~r ′, iω ) (116) Z0 = dω α (iω ) z¯(iω ) (119) 2π 4πC v ǫ(iω ) + 1 Z0 Z0

χa,s retarded response functions α atomic polarizability, ǫ dielectric function, z¯ centroid of induced charge density

Physisorption potential for He on noble metals van der Waals interaction in DFT

Physisorption potential Theoretical description Localized electron hole in current exchange-correlation functionals αz ⇒ veff (z) ∝ e− for z → ∞ instead of veff (z) → 1/z Zaremba and Kohn, PRB 15, 1769 (1977): et al. Interaction potential divided in two parts: Hult : Adiabatic connection formula:

Short-range Hartree-Fock term 2 1 1 3 3 e E [n] = d ~rd ~r ′ dλ [hn˜(~r )˜n(~r ′)i − δ(~r − ~r ′)h(~r )i] (122) Longe-range van der Waals interaction xc 2 |~r − ~r | n,λ Z ′ Z0

V (Z) = VHF (Z) + VvdW(Z) (120) ⇒ Second order

Noble gas: repulsive interaction proporptio- ∆E (R~) = E − d3~r d3~r d3~x d3~x V (R~ + ~x − ~r ) V (R~ + ~x − ~r ) nal to surface charge density xc xc∞ ′ ′ as as ′ ′ V (Z) ∝ n(Z) (121) Z Z Z Z HF ∞ dω × χa(~x, ~x ′, iω )χs(~r, ~r ′, iω ) (123) Potential as a function of Z 2π Z0 Approximations: Response treated in Random Phase Approximation (RPA) local approximation for screened response Chemisorption Newns-Anderson Model

Chemisorption corresponds to the creation of a true chemical bond between adsorbate and Developed by Newns based on a model proposed by Anderson for bulk impurities substrate Describes the interaction of a adatom orbital φ with metal states φ Energetic contributions to chemisorption discussed within DFT: a k Model Hamiltonian (ignoring spin) N

Etot = εi + Exc [n] − vxc (~r )n(~r ) d~r − EH + Vnucl nucl + + − H = εa na + εk nk + (Vak ba bk + Vka b ba) (125) i=1 Z k X k k N X X = εi + Exc [n] − veff (~r )n(~r ) d~r + EH + Vel nucl + Vnucl nucl − − i=1 Z X + N ni = bi bi i = a,k . (126) = εi + Exc [n] − veff (~r )n(~r ) d~r + Ees (124) i=1 X Z + ni number operator, bi , bi creation and annihilation operator of the orbital φi, respectively.

Adsorbate LDOS in the Newns-Anderson Model Adsorbate level in the Newns-Anderson Model

Direct solution of the Schr ¨odinger equation Single-particle Green function

H ~c i = εi ~c i (127) 1 Gaa (ε) = (130) ε − εa − Σ( ε) intractable due to the infinite number of metal states Self-energy Σ( ε) = Λ( ε) − i∆( ε): Consider local density of states (LDOS) on the adsorbate level: ∆( ε) = π |V |2 δ(ε − ε ) (131) 1 ak k ρ (ε) = |h i|ai| 2 δ(ε − ε ) = − Im G (ε) (128) k a i π aa X i X G single particle Green function ( δ = 0 +): P ∆( ε′) Λ( ε) = dε ′ , (132) π ε − ε Z ′ |iih i| G(ε) = (129) ε − ε + iδ P denotes principal part integral i i X Parameters in the Newns-Anderson Model Variation of adsorbate levels Ionization energy and affinity level Level variation Adsorbate LDOS: Ionization energy I: energy to remove an A: Gain additional energy due to the inter- electron from a neutral atom and bring it action of the electron with its own image: 1 ∆( ε) e2 ρa(ε) = 2 2 . (133) to infinity π (ε − εa − Λ( ε)) + ∆ (ε) Aeff (z) = A + . (136) Electron affinity A: energy that is gained 4z when an electron is taken from infinity to 6 vacuum level ∆( ε) lifetime broadening 2 the valence level of an atom 4 A = A + e /4z v (z) eff Φ eff Position of affinity level εa(z) + Λ( z) and level width ∆( z) usually enter as parameters in the I and A modified in front of a surface: 2

Newns-Anderson model Let us consider a hydrogen atom in front (eV) 0 F ε of a perfect conductor F ε−ε -2 Newns-Anderson model rather for explanatory purposes than for predictive purposes helpful 2 2 I = I - e /4z e 1 1 2 -4 eff V = − + − (134)

im Energy Recently Newns-Anderson model predominantly used to describe charge transfer processes in 2 2Z 2z (Z + z) -6 molecule-surface scattering   -8 I: attraction of electron to its own image -10 charge overcompensated by repulsion with -1 0 1 2 3 4 respect to the image of the nucleus Distance from the surface z(Å)

∞ 2 ∂V im e ∆I = dz ′ = − . (135) ∂z ′ 4z z=ZZ Occupied levels increase and affinity levels decrease in front of a surface

Adsorbate affinity level variation Effective medium theory

Schematic picture Theoretical description Idea: Adsorbate can be considered as being embedded in an inhomogeneous electron gas set up by the substrate 4 Initially empty affinity levels shifts down: Determine average electron density in the vicinity of the adsorbate v (z) e 2 eff 2 ∆(z) εa(z) = ε − (137) ∞ 4z 0 Width of the level increases: n¯i = < nj(~r ) > (139) εF (eV)

F 2 ∆(z) αz j=i -2 ∆( z) = ∆ 0 e− (138) X6 ε−ε -4 When εa(z) crosses the Fermi level, the

Energy cohesive -6 level becomes filled Energy estimated as the embedding energy of the adsorbate ε (z) -8 a in a homogeneous electron gas, the effective medium: Close to the surface adsorbate is then ne- -10 -1 0 1 2 gatively charged E ≈ Eci (¯ni) (140) Distance from the surface z(Å)

Variation of affinity level εa(z) Cohesive energy Ec(¯n) universal function Embedding cohesive energies Qualitative picture of hydrogen adsorption

Cohesive energies Discussion Hydrogen embedding energy as a function of the electron density

Two contributions to Ec: kinetic and elec- Electron density and potential variation Energetics 5 trostatic energy ) -3 3 4 He Kinetic energy: increases with density due Vacancy Dashed line: Optimum density 3 O to the Pauli principle 2 (n) (eV) 2

c H 1 Electrostatic energy: becomes more attrac- Bulk Surface Chemisorption minimum direct reflecti- 0 tive at higher densities 1 on of the minimum of the Ec(n) curve -1 Competition of kinetic and electrostatic 0 -2 energy leads to a minimum (except for Hydrogen sits off-center in the vacancy -3

Cohesive energy E noble gases) since the electron density is to low in -4 -1 the center of the vacancy 0,00 0,05 0,10 0,15 0,20 -3 n → 0: Ec → A: electron affinity Electron density ( Å ) -2

Embedding energy for H,O and He obtained by LDA-DFT et al. -3 (M.J. Puska , PRB 24, 3037 (1981)) Cohesion energy (eV) Electron density x 10 (Å -10 -8 -6 -4 -2 0 2 4 Distance from the surface z(Å)

Qualitative explanations given by embedding energy Effective medium theory II

Chemisorption bond length: Problems associated with simple form Etot = Ec(n) : adsorbate-metal bond lengths are the shorter, the lower the adsorbate coordination is Adsorption energy independent of substrate Adsorbate-metal vibrational frequency: No diffusion barrier on the surface

⇒ Electrostatic interaction of the cores and band-structure effects have to be taken into d2E (n(~r )) d2E (n) dn c c acccount: ωvib ∝ 2 = 2 (141) r dz r dn dz εF Assumption: natom ∝ exp( −βr ) ⇒ E = E (¯n ) + φ (~r )∆ ρ(~r )d3(~r ) + δ ∆g(ε) ε dε (143) tot c 0 0   Za Z dn −∞ = β n sin α (142)   dz 0 Final result:

eff α: angle of the metal-adsorbate line with the surface plane Etot = Ec (¯n0) + ∆ Ehyb (144) top bridge (111)hollow (100)hollow ⇒ ωvib > ω vib > ω vib > ω vib

2 |Vad | ∆Ehyb = −2 (1 − f) (145) Cd − V0(~r ) EMT adsorption energies on 3d and 4d metals Embedded Atom Method (EAM)

3d metals 4d metals Idea (Daw and Baskes (1983)): Total energy is a sum of an embedding energy plus an electrostatic core-core repulsion

-4 -1,5 1 Etot = Fi(nh,i ) + φij (rij ) (146) -2 Experiment 2 Effective Medium Theory Experiment i i=j Homogeneous contribution X X6 0 Effective Medium Theory Hydrogen -2 2 Homogeneous contribution nh,i : host density at atom i due to the remaining atoms of the system 4 φij (rij ): core-core pair repulsion between atoms i and j separated by rij 6 -2,5 n estimated as superposition of atomic densities 8 h,i Oxygen 10 -3 a 12 H adsorption energy (eV) nh,i = nj (rij ) (147) Atomic adsorption energy (eV) 14 j(=i) -3,5 X6 Sc Ti V Cr Mn Fe Co Ni Cu Y Zr Nb Mo Tc Ru Rh Pd Ag φ (r) represented by interaction of two neutral, screened atoms For atomic oxygen adsorption, the deviations between experiment and theory are already ij much larger ( ∼ 2 eV) φij (r) = Zi(r) Zj(r) /r . (148)

Embedding energy and effective charge in the EAM Hydrogen atomic chemisorption energies

Embedding energy F (n) and effective charge Z(r) fitted to reproduce lattice and elastic Embedding energy F (n) and effective charge Z(r) fitted to reproduce lattice and elastic constants, cohesive and vacancy formation energy, and energy difference between fcc and constants, cohesive and vacancy formation energy, and energy difference between fcc and bcc phases. bcc phases. Method Pd(100) Pd(111) Embedding energy Effective charge hollow bridge top fcc hollow hcp hollow bridge top EAM 0.53 0.45 0.10 0.53 0.53 – 0.03 GGA-DFT 0.468 0.426 -0.047 0.554 0.518 0.410 0.010 0 1 GGA-DFT results for 2 2 structure with the PW91-GGA functional (courtesy of A. Roudgar) -1 ×

o 0,8 H H Ni EAM gives reasonable description of hydrogen chemisorption energies -2 Pd 0,6 H EAM used extensively for bulk and surface properties of metals and alloys -3 Ni Ni Ni Pd 0,4 Pd -4 Pd H Effective charge Z(r)/Z 0,2

Embedding energy F(n) (eV) -5

-6 0 0 0,01 0,02 0,03 0,04 0,05 0 1 2 -3 Electron density n (Å ) Distance r (Å) Covalent bonding Lang-Williams Theory of Atomic Chemisorption

Interaction of adsorbates with sp bonded metals (Al,Na): EMT and EAM give reasonable description of metal bonding and atomic chemisorption DFT-LDA calculations of atomic adsorption on jellium surfaces EMT and EAM do not satisfactorily describe covalent bonding Theory of Atomic Chemisorption on Simple Metals, PRB 18 , 616 (1978). EDIM method (Embedded diatomics in molecules; Truong, Truhlar): Solution of Kohn-Sham equations can be regarded as being equivalent to solving a scattering EAM combined with semiempirical bond theory Lippmann-Schwinger equation:

EDIM: Expresses Coulomb and exchange integral in modified four-body LEPS form plus 3 embedded atom ideas ψMA (~r ) = ψM (~r ) + d ~r ′ GM (~r, ~r ′) δv eff (~r ′) ψMA (~r ′) (149) Z M: unperturbed metal; MA : metal-adsorbate system

δv eff (~r ): Change of the effective potential due to the presence of the adsorbate

Interpretation: elastic scattering of metal states ψM (~r ) by the adsorbate induced effective potential δv eff (~r )

⇒ Charge density and local density of states in atomic chemisorption

Charge density in atomic chemisorption Change of the density of states upon adsorption Charge density plots Type of chemisorption Density of states Type of chemisorption Lithium Silicon Chlorine Lithium: Li 2 s derived state primarily above εF Li Cl 3 p Si 3 p Li 2 s ⇒ positive ionic chemisorption charge transfer to substrate 1,0 Si Cl Li Si Cl ⇒ positive ionic chemisorption 0,8 Cl 3 p derived state primarily below εF s ⇒ negative ionic chemisorption

1Å s Charge density Chlorine 0,6 Si 3 s Si 3 p derived state half-filled bonding charge transfer to adsorbate anti-bonding 0,4 ⇒ covalent bonding ⇒ negative ionic chemisorption

0,2

¢£

¡ ¡ Charge contour plots:

Change in state density (arb. units) 0,0

difference Silicon Lower parts of the resonances add charge

Charge density ε charge accumulation in bond region -15 -10 -5 F 0 to the bond region, upper parts substract ⇒ covalent bonding Energy relative to vacuum (eV) charge from this region Upper panel: Total charge density of states; lower panel: charge density Change of the density of states (Lang and Williams). ⇒ bonding – anti-bonding character Electron density corresponds to Al ( r = 2 ). difference, broken lines correspond to charge depletion (Lang and Williams). Spatial information about charge re- s Charge density plots alone are often not very distribution supplemented by analy- instructive sis of the density of states: ⇒ Energetics corresponds to a ba- ⇒ Charge density difference plot: lance between band-structure and electrostatic contributions ∆n(r) = n(r)total − n(r)substrate − n(r)atom (150) Bonding character of resonances Resonance energy

Lang and Williams: Bonding – anti-bonding character of resonances derived from charge Let εα be the energy where Re Dα(ε) vanishes contour plots Taylor expansion: Re Dα(ε) ≈ (dRe Dα(εα)/dε )( ε − εα) ⇒ Alternative derivation: Phase shift of scattering states Γ tan δα(ε) = − (154) Im Dα(ε) ε − εα tan δα(ε) = − (151) Re Dα(ε) with with Im D (ε) Γ = α (155) D (ε) = det[1 − G (ε) δv ] (152) (dRe Dα(ε)/dε ) α M eff  ε=εα Change in the density of states related to phase shift ⇒ Change in the density of states g dδ (ε) δn (ε) = α α (153) π dε gα Γ δn (ε) = 2 2 . (156) π (ε − εa) + Γ gα dimension of the representation the state α belongs to Compare with Newns-Anderson expression

Phase shift at the resonance energy Variation of resonance level

⇒ resonance at energies εα where Re Dα(ε) vanishes Density of states of H atomic adsorption Level variation Phase shift Resonance levels broadens and shifts to -4 Γ Fermi level lower energies due to the metal–adatom tan δα(ε) = − (157) -6 interaction ε − εα -8 Resonance narrows again close to and in -10 ⇒ phase shift increases through π/ 2 as the energy goes through εα from below the substrate

Energy (eV) -12 ⇒ Small metal density of states at the Lower energy side of the resonance: phase of the reflected wave is shifted such that the -14 bottom of the metal band electron density is accumulated in the region of the adatom-substrate bond r veff ( ) Bonding character -16 Resonance level follows the bare-metal ef- -1,0 -0,5 0,0 0,5 1,0 1,5 2,0 fective potentials Higher energy side of the resonance: phase shift leads to a reduction of the the electron Distance from the surface z(Å) density in the region of the adatom-substrate bond Plausible within first-order perturbation Variation of the density of states as a function of the atomic theory Anti-bonding character distance from the surface (Lang and Williams). Electron density corresponds to Al ( rs = 2 ). Reactivity concepts for transition and noble metals Adsorption on transition and noble metals

Goal: Gain an understanding of the reactivity of a system from properties of the reactand Interaction of atomic level with a Level variation systems alone transition metal Resonance levels broadens and shifts to Gas-phase reactivity concepts based on the frontier orbital concept (Fukui): 4 lower energies due to the sp -metal–adatom anti- 2 bonding s interaction Interaction dominated by the highest occupied molecular orbital (HOMO) and the lowest ⇒ Renormalization of energy level 0 ε ε unoccupied molecular orbital (LUMO). F F (eV) F -2 d-band Renormalized level splits due to the strong Corresponding reactivity concept for reactions at surfaces: ε − -4 hybridization with metal d-states in a bon- -6 ding and anti-bonding contribution Reactivity determined by metal local density of states at the Fermi energy (Feibelman and bonding Energy Hamann) or by the number of holes in the metal d-band (Harris and Andersson). -8 s Up-shift of anti-bonding state larger than -10 Concept of softness (Cohen et al.) free atom + sp interaction + d interaction bare metal down-shift of bonding state -12 ⇒ Overall repulsive effect for complete fil- ∂n (ε, ~r ) 1 Projected density of states (arb. units) ling of both the bonding and the anti- s(~r ) = = d~r ′ K− (~r, ~r ′)n(εF , ~r ) (158) ∂µ Schematic drawing of the interaction of an atomic level with bonding resonance ε=εF Z a transition metal surface

Hammer and Nørskov: d-band hybridization picture

Dissociation of H 2 at metal surfaces Approximate reactivity measure in the d-band model

Interaction of molecular levels with a d band Interaction Atomic chemisorption energy metal 2 * Both σg and σu∗ split into bonding and anti- σu derived antibonding V 2 bonding levels with respect to the surface– δE chem ≈ − 2(1 − f) + αV (159) ε ε − ε adsorbate interaction d H

s ε center of d-band, ε renormalized H adsorbate resonance, f filling factor of d-band, σ − d interaction attractive since the an- d H * u∗ σu first term energy gain due to the hybridization tibonding level is unoccupied 2 σg derived antibonding ε noble metal second term αV repulsion due to energetic cost of orthogonalization d F εd ε transition metal F Position of the Fermi energy determines Dissociative adsorption of H 2: * σu derived bonding whether the σg derived antibonding state σg Dissociation barrier determined by the interaction of the renormalized H 2 bonding σg and s is occupied or not the anti-bonding σu∗ states:

metal H 2 molecule If it is not occupied, the σg − d interaction σ derived bonding 2 2 g is attractive and the H-H bond is weakened V V 2 δE ts = −2 − 2(1 − f) + αV (160) Schematic drawing of the interaction of the H 2 σg and σu∗ levels with due to the occupied σu∗ level εσu∗ − εd εd − εσg a transition metal surface

MHMd Estimate for V : V = η r3 Dissociation barriers and d-band model Activation barrier for H 2 dissociative adsorption

2 2 DFT Metal ε V 2 −2 V 2(1 − f) V αV 2 δE EDFT Correlation between δE ts and Ets Discussion d ε ε ε εσ ts ts σu∗− d d− g DFT Cu -2.67 2.42 -1.32 0 1.02 -0.30 0.70 Close correlation between δE ts and Ets Cu:Cu 3Pt -2.35 2.42 -1.44 0 1.02 -0.42 0.80 Pt:Cu 3Pt -2.55 9.44 -5.32 -0.42 3.96 -1.78 -0.33 Transition state energies calculated at Pt -2.75 9.44 -5.03 -0.44 3.96 -1.51 -0.28 (rH H, Z ) = (1.2 A,˚ 1.5 A).˚ − Ni -1.48 2.81 -2.27 -0.10 1.18 -1.19 -0.15 Ni:NiAl -1.91 2.81 -1.93 -0.11 1.18 -0.86 0.48 Hydrogen dissociates spontaneously on Au -3.91 8.10 -3.30 0 3.40 0.10 1.20 transition metal surfaces. Noble metals show largest dissocation bar- B. Hammer and J.K. Nørskov. Surf. Sci. 343 , 211 (1995). All energies in eV. Transition state energies calculated at (rH H, Z ) = (1.2 A,˚ 1.5 A).˚ riers. − d-band center alone not sufficient to explain reactivity

B. Hammer and J.K. Nørskov. Surf. Sci. 343 , 211 (1995).

Hydrogen adsorption on Pd surfaces: H-Pd gas phase chemistry a model system for chemisorption

Pd-H and Pd-H 2 complexes determined on the CASSCF/MRSDCI level Adsorption of hydrogen on Pd interesting since

Pd−H Pd−H 2 • Pd can be used as a catalyst for hydrogenation and dehydrogenation reactions

• Pd can act as a hydrogen storage device ( → fuel cell technology)

PdHPdH HPdH Electronic structure of the free Pd atom: 2 10 0 closed-shell configuration 4d 5s 2 PdH: binding energy D = 2 .34 eV, bond length re = 1 .545 A˚ Open-shell 4d95s1 0.95 eV higher 1 PdH 2: H-H bond length rH H = 0 .864 A,˚ Pd-H bond length rPd H = 1 .67 A,˚ − − Despite the closed-shell configuration of the free atom, Pd shows the reactivity characteristic 3 HPdH: Pd-H bond length rPd H = 1 .50 A,˚ Energy 0.25 eV higher than PdH 2 for a transition metal −

PdH 2 weakly bound van der Waals complex, unfortunately no binding energy evaluated Electronic structure of Pd bulk and surfaces Reactivity model for the description of transition metals

Local density of states (LDOS) Discussion d-band shift due to the lower coordination at surfaces or steps (B. Hammer et al. , Catal. Lett. 43 , 31 (1997), M. Mavrikakis et al. , PRL 81 , 2819 (1998).) 4 Layer 1 Third-layer LDOS already very close to the 3 ⇒ Higher reactivity bulk DOS of Pd 2 1 d-band density of states Smaller overlap leads to Charge conservation causes 0 Pd d-band extends over the Fermi energy to a narrowing of the d-band a shift of the d-band 4 eV Layer 2 in the bulk ⇒ high reactivity 3 ε ε ε states 2 At the open (210) surface the two upper 1 layers show a significant narrowing and ups-

LDOS 0 4 Layer 3 hift of the d-band

3 εF ε ε Change of d-band at the surface can be DOS F DOS F DOS 2 6 1 understood within a tight-binding picture

0

8 6 4 2 0 E EF eV

Layer-resolved LDOS of the three topmost layers of Pd(210).

Hydrogen adsorption on Pd(100) Coverage dependence of H adsorption energies on Pd

Adsorption energy Coverage dependence Adsorption energy per H atom Coverage dependence

0,6 Coverage dependence can be understood 0,6 Adsorption energies determined by DFT- 0,5 within electrostatic considerations GGA calculations with the PW91 exchange- (eV) (eV) ad ad 0,4 0,5 correlation functional Adsorption properties for Θ = 1 : 0,3 Ads. Ead h0 ∆Φ Pd(110): missing-row structure 0,2 0,4 H/Pd(111) site (eV) ( A)˚ (meV) H/Pd(100) hollow site H/Pd(110) Adsorption energy E Adsorption energy E 0,1 bridge site H/Pd(210) General trend: H-H interaction repulsive hollow site (GGA) hollow 0.47 0.11 180 0 0,3 0 0,25 0,5 0,75 1 bridge 0.14 1.01 390 0 0,5 1 1,5 2 2,5 3 Hydrogen coverage Θ Hydrogen coverage Θ Reason: repulsive dipole-dipole interaction Adsorbate-adsorbate interaction due to Pd(111) and Pd(100): A. Roudgar Coverage dependence of the adsorption energy of hydrogen dipole-dipole repulsion Pd(110): V. Ledentu et al. , PRB 57, 12482 (1998) determined by LDA-FP-LMTO calculations (S. Wilke et al., Pd(210): M. Lischka and A. Groß, PRB 65, Feb. 2002 Surf. Sci. 307 , 76 (1994)). GGA calculations: A. Roudgar Hydrogen adsorption on Pd(110) Adsorbate-induced reconstructions of Pd(110)

H adsorption on unreconstructed Pd(110) Adsorption structure Pairing-row reconstruction Missing-row reconstruction

Experiments find a (2 ×1) structure of H on the unreconstructed Pd(210) surface

GGA-DFT: (2 ×1) structure 29 meV/H more stable than (1 ×1) H/Pd(110) struc- ture

Zigzag chains: maximize H-H distance and H screening by the Pd top layer atoms Hydrogen coverage Θ = 1 .5 Hydrogen coverage Θ = 1 .0 Pd(110): V. Ledentu et al. , PRB 57, 12482 (1998) Driving force: H-H repulsion of the Driving force: better adsorbate-substrate Both effects reduce dipole-dipole repulsion adatoms adsorbed in the same trough interaction and reduced H-H repulsion between adsorbates Hydrogen-induced missing-row reconstruction most stable but kinetically hindered

Steps as active centers: H/Pd(210) Dissociative adsorption of H 2 on Pd(100)

Top view of the (210) surface Atomic adsorption energies Elbow plots Nonactivated adsorption

1 3 Position Coverage Theory Exp. On Pd(100), hydrogen dissociates sponta- 3 3 B 1 0.52 0.41 0.4 neously along reaction paths without any C 1 0.51 – 0.4 barrier. A 1 0.45 – Pd PES depends strongly on the lateral coor- A,B 2 0.40 0.33 Pd dinates and the orientation of the hydrogen H 2 2 A,B,C 3 0.26 0.23 H molecule: Pd(100) 1 0.50 2 0.0 PES highly corrugated and anisotropic 2 0.0 Pd(111) 1 0.50 0.0

(Å) 0.4 Far away from the surface: H 2 molecule z Adsorption energies for adsorption of an additional H atom 0.4 first attracted to the on-top site: 1 3 M. Lischka and A. Groß, PRB 65, Feb. 2002; A. Roudgar 1 1 corresponds to dihydride form of PdH 2 3Muschiol, Schmidt, Christmann, Surf. Sci 395 , 182 (1998) −0.5

−1.0 In general, chemisorbed molecular states

−0.5 not stable on metal surfaces, H 2 rather Preferential adsorption of hydrogen at low-coordinated step sites dissociates 0 0

1 2 3 1 2 r H-H (Å) dH-H (Å) S. Wilke and M. Scheffler, PRB 53, 4926 (1996). Coexistence of molecular and atomic adsorption: H/Pd(210) Dissociative adsorption of H 2/Si(100)

H2 molecular chemisorption state stabilized by atomic H adsorption On clean Si(100), dissociative adsorption of H 2 activated

P.K. Schmidt, K. Christmann, G. Kresse, J. Hafner, M. Lischka, A. Groß, Phys. Rev. Lett. 87, 096103 (2001)

Elbow plot Adsorption properties Charge density ( θH = 1 ) 3.0 3 Ead (H 2) [eV]

2.5 state theor. exp. 2 Å γ (θ = 1 ) 0, 29 0, 25 ¡ Å 2.0 1 H 1

γ2 (θH = 2 ) 0, 22 0, 16 Monohydrid phase: buckling of surface dimers lifted

¡ ¡ 1.5 γ (θ = 3 ) 0, 09 –

3 H 0 ⇒ Surface rearrangement upon adsorption leads to strong surface temperature effects in the

c B t B H2 vibrational frequency [eV]

1.0 sticking probability Surface distance z 1

gas phase 0.516

0.5 γ1 (θH = 1 ) 0, 42 0, 42 Surface distance z 2

0.0 3

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2 1 0 1 2 H H distance d Å x Å

Charge density difference plot

Role of steps in H 2 adsorption on silicon Modification of the surface reactivity by coadsorbates

Hydrogen dissociation on flat Si(100) hindered by sizable energy barrier but on steps Coadsorbates can significantly change the surface reactivity spontaneous dissociation possible The study of the influence of coadsorbates is – besides of its fundamental interest– of great

0.4 technological relevance for, e.g., the design of better catalysts

0.2 Coadsorbates that enhance the surface reactivity: promoters

1.1 1.1 0.0 Coadsorbates that reduce the surface reactivity: poisoners ¡

–0.2 lattice energy Energy (eV) Most prominent example for a poison process: optimal path 0.6 0.6 –0.4 poisoning of the three-way car exhaust catalyst by lead 0.0 0.2 3.5 3.7 3.9 –0.6 1.5 2.0 2.5 3.0 Sulfur also reduces the performance of car exhaust catalysts Distance from Step ( ) ⇒ sulfur-free gasoline will soon be required by law Hydrogen precoverage leads to equivalent electronic properties as on the steps

P. Kratzer et. al, PRL 81, 5596 (1998) Poisoning of hydrogen dissociation on Pd Electronic factors determining the poisoning

Elbow plots Details of the poisoning Factors: Population of the bonding σg and the antibonding σu∗ molecular states and of the bonding and antibonding surface-molecule states 3.0 4.0

Dissociative adsorption of H 2 still exother- ¡£¢ 2.5 3.5 mic, but adsorption activated due to the ¢¡¤£¥ presence of a sulfur (2 ×2) adlayer 2.0

3.0 ¦¡¨§¢

¢¡ ©¢ ¢¡ £¥¡¨© Z 1.5 ⇒ Sulfur poisoning at low coverages ≤ 0.25

Z 2.5 ¢¡¨¦

¦¡¨¢

¡£¢¥§

¡£¢¥§

¡£¢¤

£¥¡¨©

¡£¢

¡£¢¨ ¦¡¨¢

¡£¢ © not dominated by site-blocking but by the

¢¡¨¦ ¡£¢¥

1.0 ¡£¢¥ ¡£¢

2.0 £¡¨ formation of barriers

¢¡¨¦

£¡

¡¦¢¥

¡£¢¥

¡ ¡£¢

¡£¢¥

¡¦¢ ©

¡£¢¥

£¡ £¡¤£

0.5 ¡£¢¥¤

£¡¨§

¥ ¥ H ¥ H H

¡¦¢ © x5 x5 x2

¡£¢¥¨ ¡¦¢¥§

¡£¢¥¤

1.5

£¥¡¨§ Barriers for hydrogen dissociation increase ¡¦¢¥¨

0.0

¡ ¡ dramatically in the vicinity of sulfur ¡ 1.0 DOS S DOS S DOS S 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.6 0.8 1.0 1.2 1.4 1.6 1.8 → strong repulsion between hydrogen and

dH-H dH-H

¢ ¢ sulfur ¢ bhb and hth PES of H /S(2 2)/Pd(100) surface Pd surface Pd surface Pd 2 ×

(C.M. Wei, A. Groß and M. Scheffler, PRB 57, 15572

£ £ £ ¤

(1998)). bulk Pd a) bulk Pd b) bulk Pd c)

0.0 0.0 0.0 -18.0 -8.0Ef 2.0 -18.0 -8.0Ef 2.0 -18.0 -8.0Ef 2.0

Energy E-E f (eV) Energy E-E f (eV) Energy E-E f (eV)

Influence of coadsorption on N 2 adsorption on Ru Influence of strain on reactivity Oxygen-covered strained Ru surface GGA-DFT calculations Reaction energies Coadsorption

0.2 Precoverages of N, O and H correspond to N at Ru(0001) 6,0 2 1/4, 1/2 and 3/4 of a monolayer 0.1 N2 at N a/Ru(0001) N 2 at O a/Ru(0001) N 2 at H a/Ru(0001) 4,0 Coadsorbates N, O, and H shift d-band 0.0 N dissociation barrier 2 center to lower energies as a function of

N the precoverage Surface protrusion created by argon implementation -0.1 O/Ru(0001) 2,0 2 chemisorption energy CO/Ru(0001)

Adsorption energy (eV) CO/Ru(0001) dissociation barrier

Reaction energy (eV) d band model: lower d band center corre- -0.2 CO/Pt(111) 0,0 Increasing precoverage spond to less reactivity -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 -3,5 -3,0 -2,5 -2,0 Lattice strain % Ru 4d-band center (eV) Ru: M. Mavrikakis et al. , PRL 81 , 2819 (1998). B. Hammer, PRB 63, 205423 (2001). Pt: A. Schlapka, M. Lischka et al. , PRL 91 , 016101 (2003). Surface reactivity increases with lattice ex- pansion, as rationalized by the d-band model Magnitude of reactivity change depends on STM image of oxygen adsorption on Ru(0001) the particular system: CO/Ru ↔ CO/Pt M.Gsell, P.Jakob, and D.Menzel, Science 280 , 717 (1998) Bimetallic surfaces Pseudomorphic Pt(111) films on Ru(001) Bimetallic systems: A. Schlapka, M. Lischka, A. Groß, U. K ¨asberger, and P. Jakob, PRL 91 , 016101 (2003). Possibility to tailor the reactivity by preparing specific surface compositions and structures STM image (800 ×800 A˚2) DFT calculations Pseudomorphic overlayer structure Effects • Electronic interaction of the overlayers with A the substrate B Pt fcc C • Geometric strain effects due to lattice A dPt Ru mismatch − B A Ru hcp Supported clusters • Coordination effects B A • Cluster-support interaction Lattice mismatch Pt/Ru: −2.5% • Strain and relaxation effects Stacking: first Pt layer hcp, then fcc

(see also M.T.M. Koper, Surf. Sci. 548 , 1 (2004)) Layer distance: ∆d Pt Ru /dPt Pt ≈ − 7% − − Four monolayers of Pt deposited on Ru(001) Cohesive energies: Alloys not considered here Courtesy of P. Jakob, University of Marburg Ru: 6.74 eV/atom Pt: 5.84 eV/atom Pt/Ru overlayers indeed pseudomorphic Simulations allow to disentangle these effects

CO adsorption on Pt n/Ru(0001) CO on Pt n/Ru(001): Comparison with the d band model

A. Schlapka, M. Lischka, A. Groß, U. K ¨asberger, and P. Jakob, PRL 91 , 016101 (2003). A. Schlapka, M. Lischka, A. Groß, U. K ¨asberger, and P. Jakob, PRL 91 , 016101 (2003).

Measured CO desorption temperatures Calculated CO adsorption energies Correlation with d band center Discussion

Pt overlayer on Ru compressed by 2.5 % 1.8 Pt H111 L 1.6 Compression leads to increased overlap of

D 1.6 d orbitals and downshift of d band center eV

@ 1.5

B 1.4 Strong interlayer bonding between first E

D nPt Ru H0001 L 1.2 1.4 Pt layer and the Ru substrate layer leads eV @ to a further downshift of the d band: 1.0 B 1.3  H L E 2Pt Ru 0001 0 2 4 ¼ ¥ Hypothesis: Pt layers on Ru H0001 L@ML D 1.2 Depositing a metal on a more reac- Desorption temperatures of CO from IR spectroscopy and TPD On-top CO binding energies on nPt/Ru(001), for strained Pt tive metal makes it less reactive Dashed line: Pure Pt(111) (Ru lattice constant) for a p(2 2) -CO (solid box) and a 1.1 × 1Pt Ru H0001 L (√3 √3)R30 ◦ CO overlayer ( ) × × Substrate-overlayer interaction operative up to the second layer Similar results for chemisorbed molecular O precursor state -2.6 -2.5 -2.4 -2.3 -2.2 2 Ε d @eV D Good agreement with d band model Both strain and substrate interaction effects lead to a reduction in the adsorption energies CO adsorption energies as a function of the d band center Dependence of electrochemical activity on the structure of H and CO on Pd n/Au

bimetallic electrodes A. Roudgar and A. Groß, Phys. Rev. B 67 , 033409 (2003); J. Electroanal. Chem. 548 , 121 (2003). Pd/Au structures Discussion H/Pd/Au(100) adsorption Bond length effects • Electrocatalytic acticivity can depend sensitively on the electrode structure H (a) (b) and composition H

d • Experimentally it is hard to resolve d’ Lattice structure (“ensemble”) versus composi- d Pd d’ tion (“ligand”) effects expansion

• Goal: Analyse the electrocatalytic ac- Pd Pd Pd Pd 1ML and 5 ML Pd on Au(111) (L.A. Kibler, M. Kleinert, R. Randler, tivity of Pd/Au overlayers and clusters D.M. Kolb, Surf. Sci. 443 (1999) 19) Lattice expansion Lattice expansion by electronic structure methods Relaxation of the adsorbate upon lattice expansion • Hydrogen and CO adsorption energies are used as a probe of the electrocata- H-Pd distance kept constant with ±0.01 A˚ lytic activity Exception: fourfold hollow site on Pd n/Au(100) • Unusual electrochemical stabibility of Pd cluster on Au(111) (G.E. Engelmann, J.C. Ziegler, D.M. Kolb, nanofabricated supported metal clusters Lattice constants: aAu = 4 .08 A,˚ aPd = 3 .89 A˚ J. Electrochem. Soc. 45 (1998) L 33.) ⇒ pseudomorphic Pd/Au films expanded by 5%

Adsorption energies of CO and H on Pd n/Au overlayers Adsorption on Pd n/Au overlayers and the d band model

A. Roudgar and A. Groß, Phys. Rev. B 67 , 033409 (2003); J. Electroanal. Chem. 548 , 121 (2003). A. Roudgar and A. Groß, Phys. Rev. B 67 , 033409 (2003); J. Electroanal. Chem. 548 , 121 (2003).

Pd n/Au(111) Pd n/Au(100) d band center Discussion -1.0 Both lattice expansion and overlayer- CO fcc hollow 0.6 CO hollow (eV) (a) 0.6 substrate interaction lead to a upshift of

H fcc hollow (eV) CO bridge (b) H hcp hollow -1.5 (111) H hollow ads 0.3 H bridge (100) the d band ads H bridge H on-top 0.3 H on-top 0.0 -2.0 0.0 Expansion of more open Pd(100) surface -0.3 -2.5 Surface (111) counterbalanced by inter-layer relaxation -0.3 Surface (100) -0.6 Subsurface (111) effects -3.0 Subsurface (100) -0.6 Depositing a reactive metal on an inert -2.1 -1.8 d-band center / eV -3.5 metal makes it even more reactive -2.4 -2.1 Adsorption energy E

0 1 2 3 Pd@Au Pd Adsorption energy E -4.0 0 1 2 3 Pd@Au Pd 0 1 2 3 Pd@Au Pd Position of d band centers does not pro- Number of Pd overlayers on Au Number of Pd overlayers on Au Number of Pd overlayers vide an explanation for maximum binding energies on two overlayers Both strain and substrate interaction effects lead to an increase of the adsorption energies Second layer effects responsible for maximum binding energies on two overlayers Maximum of binding energies for both H and CO at all sites on two overlayers Hydrogen adsorption on PdCu bimetallic surfaces Pd n cluster deposited on Au(111) Pseudomorphic Pd/Cu overlayer compressed by 8% Pd-Pd distances Distances H/PdCu(111) d-band center of surface layer NN bulk distances:

dAu = 2 .95 A,˚ dPd = 2 .80 A˚

Significant reduction of Pd-Pd distances in supported clusters

Pd-Pd distances in Pd n/Pd(111) cluster:

Pd 3: 2.69 A˚ Pd 7: 2.74 A˚

Pd-Pd distances in free Pd n cluster: Metallic adsorption energies: Pd/Cu(111): -3.011 eV, Pd/Pd(111): -2.766 eV Pd 3: 2.50 A˚ PdCu and CuPd overlayer systems show intermediate properties between pure Pd and Pd 7: 2.64 A˚ Cu surfaces due to the strong coupling of Pd and Cu d-electrons

Note: Pd/Cu rather forms surface alloys (see, e.g., A. Bach Aaen et al. , Surf. Sci. 408 , 43 (1998); A. de Siervo et al. , Surf. Sci. 504 , 215 (2002))

Electronic structure of Pd n/Au(111) cluster Pd n cluster deposited on Au(111)

Pd 3 Local density of states Electronic structure of Pd 3 H and CO adsorption energies d band positions

8

6 Pd /Au(111) Pd (d ) -1.0 3 xy -0.5 Free Pd cluster 4 3 Pd 3/Au(111): d orbitals confined within the cluster Pd 3/Pd(111) 2 (a) layer ( dxy and dx2 y2) exhibit discrete structure -0.6 -1.5 0 − 6 -0.7 Pd (d ) -2.0 yz H fcc 4 All other orbitals show a broad spectrum H hcp 1st layer, Corner 2 ⇒ strong coupling to the Au substrate -2.1 CO fcc -2.5 1st layer, Center 0 CO hcp 2nd layer, Corner 2nd layer, Center 6 -2.2 -3.0 Pd (d 3z^2-r^2 )

Unusual electrochemical stabibility of nanofabricated d-band position (eV) 4 -2.3

2 supported metal clusters has been explained by quan- Adsorption energy (eV) -3.5 -2.4 0 tum confinement effects Pd 3 Pd 7 overlayer Pd 10 overlayer 8 D.M. Kolb et al. , Angew. Chemie, Int. Ed. 39 , 1123 (2000) 3Pd 7Pd Overlayer 6 Pd (d xz ) 1 layer of Pd 2 layers of pd 4 2 This speculation is not supported by our calculations 0 Significant reduction of Pd-Pd distances in supported clusters LDOS projected on atomic orbitals 8

6 Pd (d ) x^2-y^2 Pd 3/Pd(111): All d orbitals broadened 4 ⇒ Even stronger coupling between Pd 3 and Pd(111) Effects of lower coordination in the clusters counterbalanced by compression 2

0 -4 -3 -2 -1 0 1 Energy E - E F (eV) H and CO adsorption on Pd 10 /Au(111) clusters Hydrogen evolution on Pd n/Au(111) clusters

J. Meier, K.A. Friedrich, U. Stimming, Faraday Discuss. 121 , 365 (2002)

STM images of tip-induced palladium particles on Au

Highest hydrogen evolution rate found for smallest Pd cluster on Au

H and CO adsorption energies on Pd 10 /Au(111) (free Pd 10 ) clusters Kinetic modelling (M. Eikerling,J. Meier, and U. Stimming, Z. Phys. Chem., accept.): Adsorption energies on supported 3D cluster even smaller than on planar clusters Low hydrogen desorption rate on Pd nanoparticle required → Hydrogen spillover to Au substrate from where they are released

Smaller reactivity of supported 3D cluster due to reduced distances and substrate Our calculations ⇒ Experiment has probed properties of locally pseudomorphic Pd interaction nano-islands on Au(111) rather than 3D supported nano-clusters

H adsorption in the presence of a water overlayer CO adsorption in the presence of a water overlayer

Water structures on Pd/Au(111) H adsorption energies CO/water structures on Pd/Au(111) CO adsorption energies

H2O H fcc H hcp θH2O Eads Eads Eads 1/4 -0.308 -0.634 -0.592 CO CO CO site Eads Eads Eads 1/3 -0.295 -0.606 -0.610 H-down H-up clean 1/2 -0.419 -0.582 -0.602 fcc -1.831 -1.894 -2.023 1 +3.135 – – hcp -1.866 -1.923 -2.043 3/4 -0.465 -0.561 – bridge — — -1.827 2/3 (b) -0.528 -0.633 -0.596 on-top -1.243 — -1.413 2/3(c) -0.499 – – 2/3(d) -0.327 – – CO adsorption energies ( θCO = 1 /3) in eV/molecule on H2O/Pd/Au(111) 0 – -0.690 -0.655 CO/H 2O structures (H-down): a) CO in fcc hollow, b) CO on-top

H2O adsorption energies in eV/H 2O and H adsorption energies ( θH = 1 /3) in eV/atom on Pd/Au(111) Both H 2O and CO are polar molecules. Still the dipole-dipole interaction between CO H2O structure: a) monomer and dimer, b) H-down bilayer (ice Ih), and H 2O in the ice-Ih structure on Pd/Au(111) only < 50 meV c) H-up bilayer, d) half-dissociated bilayer ∼

H adsorption energies only slightly changed by the presence of water

(see also S.K. Desai, V. Pallassana, and M. Neurock, J. Phys. Chem. B 105 , 9171 (2001)) Electric field effect on the H 2O-Pd/Au distance Water orientation as a function of the electric field

A. Roudgar and A. Groß, Chem. Phys. Lett. 409 , 157 (2005) Water structure under the influence of an external electric field Change of the total energy of the H-down and H-up water bilayers as a function of an external electric field 2.66

2.65 0.0 H-down 2.64 -0.1 H-up -0.2 2.63 (A) -0.3 Pd-O 2.62 d -0.4 d 2.61 Pd−O -0.5

2.60 Total energy (eV) -0.6 2.59 -0.4 -0.2 0.0 0.2 0.4 -0.7 -0.8 -0.6 -0.4 -0.2 0 E (eV/A) external External electric field E (V/Å)

H O/Pd/Au structure and H O-Pd/Au distance as a function of an external electric field 2 2 Electric field induces rotation of water bilayer External electric field introduced via a dipole layer in the vacuum region Field-induced water reorientation confirmed by experiment for H 2O/Ag(111) Small changes in water-electrode distance for relatively weak electric fields K. Morgenstern and R. Nieminen, J. Chem. Phys. 120 , 10786 (2004)

Adsorption at non-zero temperatures and pressures Thermodynamical considerations

K. Reuter and M. Scheffler, Appl. Phys. A 78 , 793 (2004) Appropriate thermodynamical potential: Gibbs free energy G(T, p, N i) Heterogeneous catalysis: Reactions occur under non-zero temperatures and pressures gas phase (T,p) Practical approach: divide whole system in three contributions:

gas phase (T,p) G = Gbulk + Ggas + ∆ Gsurface . (161)

For bulk and gas, take values for the homogeneous system substrate

Connection between the Gibbs free energy and the total energy calculations: Helmholtz free energy F (T, V, N i) substrate tot conf vib F (T, V, N i) = E (V, N ) + T S + F (T, V, N i) , (162)

Schematic representation of a substrate in contact with a surrounding gas phase at G(T, p, N i) = F (T, V, N i) + pV (T, p, N i) . (163) temperature T and pressure p. Gibbs free energy of adsorption Example: Self-assembled Monolayers (SAM)

NM substrate atoms in the surface region per unit cell for the clean surface and MM Self-assembled monolayers of organics molecules on anorganic substrates substrate atoms and Nads adsorbate atoms after adsorption: Gibbs free energy of adsorption Example: Mercaptopyridine on Au(111)

ad ∆G (T, p ) = G(T, p, M M, N ads ) G(T, p, N M, 0) − (MM NM)µM(T, p ) Nads µgas (T, p ) , (164) − − −

µM = gbulk and µgas = ggas : Gibbs free energies of the substrate and gas atoms, respectively. Neglect terms from the configurational entropy, the vibrations and the work term pV (Note that we are concerned with free energy differences ):

ad tot tot ∆G (T, p ) E (MM, N ads ) E (NM, 0) ≈ − tot (MM NM)E Nads µgas (T, p ) . (165) − − M − Etot : total energy. Structure with lowest free energy is stable in a certain range of the chemical potential

J. Kucera and A.Groß, in preparation.

Example: surface oxides Chemical potential and adsorption energy Recently, surface oxide of great interest, in particular in oxidation catalysis Chemical potential of oxygen: Surface oxides: thin oxide layer on a substrate 1 1 tot µO(T, p ) = µO2(T, p ) = EO + ∆ µO(T, p ) Example (√5 √5) R27 ◦ PdO surface oxide structure on Pd(100) 2 2 2 × 1 tot 0 1 p = E + ∆ µO(T, p ) + kBT ln . (166) 2 O2 2 p0

Definition of the adsorption energy:

1 tot tot O Eads = E (MM, N ads ) E (NM, 0) N  − Pd O O Pd Pd tot 1 total (MM NM)EM EO , (167) Pd − − − 2 2 

Gibbs free energy of adsorption per surface area A: a) b) ⇒

∆γ(T, p ) = γ(T, p, M M, N ads ) γclean (T, p, N M, 0) − M. Todorova et al. Surf. Sci. 541 , 101 (2003). 1 ad NO = ∆G (T, p ) = (Eads ∆µO(T, p )) . (168) A A − Surface phase diagram of the PdO/Pd(100) system Surface phase diagram of the CO +O+Pd(100) system Free energy of adsorption together with pressure and temperature dependence of the Surface phase diagrams important to understand structures in heterogeneous catalysis chemical potential: Surface phase diagram

−20 −10 0 10 10 10 10 10 T = 600K p (atm) O2 −40 −20 0 10 10 10 T = 300K 0 100 10 2 bulk bulk oxide −1 oxide 10 50 −2 10

clean −3 (atm) 2

∆ γ 10

0 O p(2x2) −4 10 c(2x2) surface oxide −50 −5 (√5 √5) 10 x R27 adlayer −6 10 Pressure p −100 metal −7 metal 10 adlayer surface oxide o −8 Adsorption energy−150 (meV/Å ) 10 −2.0 −1.5 −1.0 −0.5 0.0 600 700 800 900 a) Chemical potential ∆µ O (eV) Temperature T(K) b) J.Rogal K. Reuter, and M. Scheffler, CO oxidation at Pd(100): A first-principles constrained thermodynamics study, Phys. Rev. B 75 , 205433 (2007). K. Reuter, C. Stampfl, and M. Scheffler, Ab initio atomistic thermodynamics and statistical mechanics of surface properties and functions, in Handbook of Materials Modeling , edited by S. Yip, volume 1, page 149, Springer, Berlin, 2005.