Surface Physics: Lecture 2

9.4 Introduction to Bonding & Reactivity of Metal Surfaces

Considerations for Surface calculations: slabs vs. clusters

vs.Cluster geometries:

+ computationally cheap for small clusters (local basis sets)+ good for local aspects (defects etc.) − slow (possibly oscillatory) convergence with cluster size (embedding etc.)

Supercell geometries:

+ proper surface electronic structure (band structure)+ good convergence with slab thickness (“semi-infinite”)+ suitable for plane wave basis sets− artificial lateral periodicity in 3D: “ordered arrays”− inherently expensive (large systems); plne waves ‘wasted’ on vacuum

Electronic structure methods for Surface calculations

- Tight-binding- Density-functional theory- Quantum chemical methods (> HF)- (Quantum Monte Carlo)

- Total energy- Forces (relaxation, vibrations, diffusion, reaction pathways, MD…)- Electronic structure (DOS, band structures, atomic ‘populations’, spin (magnetic) effects)

But: manageable system sizes ~ 1000 electrons (DFT: n3)known inaccuracies due to Vxc

Figure courtesy of S. Yamagashi, S.J. Jenkins and D.A. King.

Considerations for Surface calculations: slabs vs. clusters

The following issues (in no particular order) can be important when aiming for accurate adsorption structures and adsorption energies:1. Number of substrate layers (relaxation or not?) …usually the more the better (oscillations between odd and even numbers of layers are sometimes observed) 2. Amount of vacuum between slabs3. Adsorbates on one or both sides of the slab. If on one side then a dipole correction in the vacuum may be needed4. Adsorbate-adsorbate interaction between adjacent cells – effectively determines the adsorbate coverage5. k-point sampling: especially if have metals and especially if have noble metals (Cu, Ag, Au) or free electron metals (Al)…the more the better.6. Other issues such as kinetic energy cut-off, pseudopotential, etc…

Physisorption• Balance between van der Waals attraction and Pauli repulsion

- + + -zr’ z

metal

r

• Remember chapter on cohesion ~-Ar-6 attractive term

Physisorption• Case Study: Xe adsorption

From DFT:

J. L.F. Da Silva, C. Stampfl, and M. Scheffler, Phys. Rev. Lett. 90, 066104 (2003).

Chemisorption Theory I: Frontier Orbital Theory

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1-2

Chemisorption Theory I: Frontier Orbital Theory

Case study I: THE famous example - CO adsorption (Blyholder, 1964)

3σ

4σ

1π5σ

2π*

2π

CO Molecular Orbitals (gas phase)

CO gas CO gas

CO gasCO gas CO gas

• Originally refers to model for bonding of CO at metal surfaces, but has been applied to other systems

• Coupling of frontier orbitals (i.e. HOMO and LUMO) with metal states ⇒ donation of electrons from 5s HOMO and back-donation of electrons into 2p* LUMO

Case study I: THE famous example - CO adsorption (Blyholder, 1964)

• Relative strength of the interactions depends on the adsorption site: 2π-metal mixing favoured at higher coordination sites; 5σ-metal favoured at atop sites…seen in vibrational frequencies

Chemisorption & Frontier Orbital Theory

Case Study IIWater adsorption (‘4 electron attraction’)

Water adsorption

Partial DOSPartial DOSDensity DifferenceDensity Difference

Green = -

Blue = +

ρρ(H(H22O/Ru) O/Ru) –– ρρ(Ru) (Ru) –– ρρ(H(H22O)O)

J. Am. Chem. Soc. 125, 2746 (2003)

Case Study III: CH3 adsorption

“Agostic” H-metal bond

Surf. Sci. 437 (1999) 362

•For molecular adsorption the orientation of the molecule can be an issue. For CH3 adsorbed at a 3-fold site on Ni(111) there is a ~0.2 eV preference to have the CH bonds directed at underling Ni atoms (A) as opposed to an alternative structure (B). •This is a result of mixing of an (occupied) CH bonding orbital with Ni 3d states, leading to an ‘agostic’ bond.

Case Study III: CH3 adsorption

• We know that the CO stretch frequency depends strongly upon the adsorption site, being ‘softer’ at higher coordination sites. • The C-H symmetric stretch of some hydrocarbon molecules exhibits analogous behaviour. In CH3, for example, the CH stretch is softened by about 100-200 cm-1 for CH3 at a three-fold compared to CH3 adsorbed at an atop site. • The reason for the softening is different here – for CO it was due to occupation of the 2π* antibonding states; here it is because of the ‘agostic’ C-H-metal interaction. • As with CO these different chemical interactions can be observed in experiment through vibrational spectroscopy.

J. Chem. Phys. 114, 2523 (2001)

Chemisorption & Frontier Orbital Theory

• Interaction of molecular orbitals with surface dipole leads to changes in energy levels

• HOMO raised above Fermi level ⇒ electrons flow to surface• LUMO lowered below Fermi level ⇒ electrons flow to adsorbate

HOMO

LUMO

HOMO

LUMO

• A single molecular orbital may interact with many different surface orbitals; in extreme cases leads to “metallic” bonding

• More than one molecular orbital may contribute to the same adsorbate-surface orbital, particularly if the adsorbate is a radical (i.e. rehybridisation)

Some light relief from STM:

Theory of adsorption II: Newns-Anderson model

s-band

d-band

EF

free atom clean surface

s-band

d-band

EF

interaction with d-band:splitting in bonding and

anti-bonding peaks

interaction with s-band:renormalization and

broadening

≈ a generalization of molecular orbital (MO) schemes to finite bands

D.M. Newns, Phys. Rev. 178, 1123 (1969);P.W. Anderson, Phys. Rev. 124, 41 (1961)

Theory of adsorption II: Newns-Anderson model

Theory of adsorption II: Newns-Anderson model cont’d

Filling of d-band occupies antibonding O-M states

Sc Ti V CrMnFe Co Ni CuZn

Y ZrNbMoTcRuRhPdAgCd

La HfTa W ReOs Ir Pt AuHg

Ru Rh Pd Ag

O 2p O 2p O 2p O 2p

EF

Achievements:- qualitative electronic structure at the surface- correct trend in adsorption strength over TM series- reactivity patterns → d-band center (Hammer/Nørskov)

Failures:- no adsorbate induced reconstructions- no site specificity (→ reactivity theory, HSAB, covalent/ionic)- no lateral interactions

Sc Ti V CrMnFe Co Ni CuZn

Y ZrNbMoTcRuRhPdAgCd

La HfTa W ReOs Ir Pt AuHg

Theory of adsorption II: Newns-Anderson model cont’d

M. Todorova et al., Phys. Rev. Lett. 89, 096103 (2002)