Molecular Heterogeneous Catalysis, Wiley (2006), 352729662X

86 Chapter 3

N

i =	|cki |2 αk + 2	cki cliβkl	(3.6)
k=1		k<l

The first term here is the energy contribution due to the residence of an electron in a particular atomic orbital and the second term represents the interference of the atomic wavefunctions. Waves can annihilate or have positive or negative interference. For the 2 x 2 secular matrix equation of F2 the bonding and antibonding energies are given by the expression

	± =	αi ± βi	(3.7)
		1 ± Si
	i

where β, which is the overlap energy, is attractive and has a negative value. The positive sign (bonding) lowers the energy and the negative sign (antibonding) increases the energy contribution of the denominator. The corresponding molecular orbital expressions are

ψi± =	1		ϕ1(i) ± ϕ2(i)	(3.8)
	√
		2 ± 2Si

The sign in front of the second atomic orbital is negative for the antibonding orbitals. Returning to the orbitals in F2, we recognize σ3 and σ4 as bonding-antibonding pairs, σ5 and σ6 as bonding and antibonding pairs and the same for π3 and π4. When only bonding orbitals are occupied, the bond energy becomes (as is for instance the case in H2)

	∆Eb(ν+ = 2) = 2 + −2α			(3.9a)
	= 2∆(1 − S)			(3.9b)
	with
	∆ =	β − αS	∆ < 0	(3.9c)
		1 − S2

where 2∆ is the energy di erence + − − between the bonding and corresponding antibonding orbitals. The parameter that mainly controls ∆ is β.

We observe that the larger the value of ∆, the larger is the bond energy. This is an important result since ∆, the di erence in bonding and antibonding orbital energies, in principle can be measured spectroscopically and, hence, spectroscopic measurements can provide indirect information on bond energies.

The expression for the interaction energy is very di erent when two atomic orbitals are occupied, as is the case for the imaginary He2 molecule. Then:

∆Eb = (ν+ = 2, ν− = 2) = 2 + +2 − −4α = −4S · ∆

(3.10)

Now, within the tight-binding model, the interaction energy is repulsive. It is again approximately proportional to the square of the overlap energy as well as the atomic orbital overlap. As a general result, the expression for the total binding energy of a homopolar chemical bond is

Eb(total) =	+	−	+	· ∆i · (1 − Sj )	(3.11)
	− (nip	+ nip )Si · ∆i +	nj

ip

j

The Reactivity of Transition-Metal Surfaces 87

where ip sums the contribution to the energy of the pairs of occupied and the corresponding antibonding molecular orbitals and j sums the contribution to the bond energy of the occupied bonding orbitals. The contribution due to occupation of bonding as well as corresponding antibonding orbital pairs is repulsive. The occupation of the bonding orbitals is only attractive.

As an illustration of this, the di erence between the computed bond energies of F2, which is –260 kJ/mol, and N2, which is –1000 kJ/mol, is analyzed. In the F2 molecule both the bonding and antibonding σ(2s) and π(2px, 2py) orbital are occupied, thereby resulting in repulsive interactions. The only pair of molecular orbitals where electrons exclusively occupy only the bonding orbital is the σ5 orbital constructed from the 2pz atomic orbitals. This results in an overall attractive contribution to the chemical bond. The attractive orbital overlap contribution which is equal to 2∆(2pz ) = -9.1 eV is counteracted by the Pauli-repulsive interactions due the σ(2s) and π(2px,2py) orbital pairs.

The N2 molecule, on the other hand, has 4 electrons less. The N2 molecular orbitals, illustrated in Fig. 3.1b, are very similar to those of F2, but the relative energies are shifted. The σ5 energy is now higher than that of the π1 orbitals. The primary di erence between F2 and N2 is that for N2, the antibonding π2 orbitals are not occupied and, hence, the π systems changes from being repulsive in F2 to being attractive in N2. This explains the large di erences in bond energies between N2 and F2.

As a prelude to our discussions on chemisorption, we will now discuss orbital changes that occur when an additional bond to the dimer is formed. We will use as an example the hydrogen bond in HCN. The molecular orbitals for CN− and HCN along with their energies are shown in Figs. 3.2a and b, respectively. The CN− ion is iso-electronic with N2 and hence the two antibonding π2 type orbitals are unoccupied. The strong CN bond corresponds to three bonding orbitals being occupied. The bond order, therefore, is three. Figure 3.3b shows the electronic structure of HCN which contains the same number of electrons, but a bond is now formed between the C atom and the proton. The result is an overall downshift in energy of all the molecular orbitals and the generation of altered σ-type orbitals. The hydrogen atomic orbital is symmetric and interacts with the C 2s and C 2pz atomic orbitals.

Before we continue further with the discussion of HCN, it is important to note the upward shift of the σ5 orbital in CN− (Fig. 3.2a) and N2 (Fig. 3.1b) with respect to the π orbital system, compared with its relatively low position in F2 (Fig. 3.1a). The background to this is the much smaller di erence in atomic orbital energies for the 2s and 2p states in N and C than in F. In fluorine, the [3σ, 5σ] subset of orbitals are in essence constructed of only 2s or 2pz atomic orbitals. This, however, is not true for N2 or CN−, where the 3σ and 5σ orbitals have the same symmetry and therefore have the

same general structure:
+
ψσ+ (1)	=	λ ϕ2s(1) + ϕ2s(2)	+ µ ϕ2pz (1) + ϕ2pz (2)		(3.12)
ψσ (2)	=	−µ ϕ2s(1) + ϕ2s(2) + λ ϕ2pz (1) + ϕ2pz (2)			(3.13)

Analogous expressions are valid for the antibonding 2s and 2pz combinations ψσ−(1) and ψσ−(2). Orbital σ5 is to be identified with ψσ+ (2), which explains its upwards shift in N2 compared to F2. In F2, the mixing of orbitals is virtually absent. The decrease in density between the N atoms indicates an increasing localization of electrons in positions to the left or right of N2. The mixing of the 2s and 2pz orbitals is seen to lead to hybridization

88 Chapter 3

Figure 3.2a. (a) Molecular orbital scheme and respective energies of the CN− ion. (b) Molecular orbital scheme and respective molecular orbital energies of the HCN molecule.

(for details on hybridization, see Addendum 3.11). The σ5 orbital can be considered as on the way to form lone pair orbitals on N2 directed away from the atoms. The antibonding orbitals σ4 and σ6 are identified with the ψσ−(1) and ψσ−(2) orbitals. Again one notes the decrease in density in the σ6 orbital between the two N atoms. The σ6 orbital in N2 can be considered an antibonding combination of N2 lone pair orbitals. The σ4 orbital is predominantly an antibonding N≡N orbital. In CN− the higher occupied molecular orbital now has a slightly increased density in the C lone-pair orbital. The corresponding σ3 molecular orbital has increased density on nitrogen.

We now return to HCN. By inspecting the σ-type orbitals we note significant changes. There are now 5 instead of the 4 σ-type orbitals in CN−. There is a small contribution of the hydrogen 1s orbital to σ3, the stronger inner σ bonding orbital in CN. The bonding interaction between H and C is clear in the σ4 orbital, which becomes antibonding between C and N. The antibonding C–H σ orbital can be recognized as the σ7 orbital, that is unoccupied. The σ5 orbital in HCN becomes the empty lone pair orbital on nitrogen, whereas in CN− it is primarily comprised of the lone pair orbital on carbon. This extensive analysis of the orbital nature changes in HCN on the addition of H+ to CN−, which illustrates the significant rehybridization that occurs in a molecule when strong new bonds

The Reactivity of Transition-Metal Surfaces 89

are formed. This is important to realize, since similar rehybridization is observed when molecules interact with surfaces, as will be seen for CO in subsequent sections.

3.3 Chemical Bonding to Transition-Metal Surfaces

In this section we introduce principles of the surface chemical bond. First principle ab initio computational results are analyzed using basic quantum-chemical concepts. In this section, we analyze the adsorption of molecules. In the following section, we analyze the adsorption of atoms. The adsorption of ammonia and CO is discussed first since they are known to interact predomenantly through donation and back-donation interactions, respectively. This will subsequently lead into the analysis of the stronger bonds that form between adatoms and a surface. We note the similarities in chemical bonding of these adsorbates to surfaces, clusters and organometallic complexes, and in addition describe some of the di erences.

Figure 3.3. R . ˚ . ◦

(a) Molecular orbital and energy scheme of NH3 . NH = 1 03A; Φ = 105 9 . (b) The electronic local density of states ρ(E) of an adsorbed free Rh atom and a Rh atom bound to NH3 on Rh(100) (1) and Rh(111) (2) respectively[2].

90 Chapter 3

The electronic structure of NH3 is shown in Fig. 3.3a. The angle between the NH bonds is 105.9◦. The N–H chemical bonds are very close in character to the 2p N atomic orbitals and the H atomic orbitals of which they are comprised. The N 2pz , 2s and symmetric combination of hydrogen atomic orbitals are σ symmetric with respect to the NH3 z-axis. The lower σ-type orbital is predominantly comprised of the 2s N orbital stabilized by a bonding interaction with the symmetric combination of three H s-atomic orbitals. The highest occupied molecular orbital (HOMO) for NH3 is predominantly non-bonding 2pz in character located on the N atom. The lowest unoccupied molecular orbital (LUMO) of NH3 is the antibonding analogue of the lower σ N–H bonding orbital.

The primary interaction between NH3 and a metal surface is predominantly a donative one which occurs via the transfer of electrons from the doubly occupied nonbonding 2pz lone-pair type orbital on N. The corresponding states on the metal depend upon the metal.

In a transition metal, the valence electrons available for bonding are of nd and (n + 1)s and (n + 1)p character. The metal-electron energies are continuously distributed in va- lence-electron bands, between upper and lower energy bounds as is shown schematically in Fig. 3.5b. The d-electrons form a narrow band of states with a bandwidth of a few electronvolts. The electronic structure of these states can be rather well described within the tight-binding formalism introduced in the previous section. The s and p electrons, on the other hand, behave more as free electrons. The interaction between adsorbate electrons and the sp electrons of the metal is usually bonding and does not vary much between di erent metals. The major variation in binding stems from the interaction between electrons of the adsorbate with the valence d-electrons of the metal. This is quite sensitive to d-valance electron occupation. The interaction between adsorbate orbitals and transition-metal states leads to the formation of bonding and antibonding surfaceadsorbate orbitals. The bond energy depends on the distribution of electrons over these orbitals, and the changes that occur in adsorbate and transition metal electronic structure.

Figure 3.3b illustrates the electron density distribution for NH3 adsorbed atop Rh(100) and Rh(111) surfaces. For symmetry reasons when NH3 adsorbs atop a surface atom, its NH3 2pz –type HOMO orbital interacts only with the Rh 4dz2 -atomic orbital of the metal d-atomic orbitals.

The electron distribution (Partial Density of States, PDOS) within the 4dz2 state on one of the surface atoms of the pristine Rh(100) surface is shown in Fig. 3.3b(1). The electron distribution within the 4dz2 state of the Rh(111) surface is shown in Fig. 3.3b(2). The coordination number of the surface atoms in the Rh(100) surface is 8 whereas that of the Rh(111) surface is 9. The width of the d-valence electron band is smaller for the Rh atom on the (100) surface, which has the smaller number of metal neighbors. In addition, the average energy of the valence band has been shifted slightly upwards. For an atom

with an s-valence-electron distribution, it can be shown that the valence bandwidth is

√

approximately proportional to Nn, Nn being the number of nearest-neighbor atoms. The

delocalization of the electrons increases with increase in the number of nearest-neighbor atoms[3].

The bandwidth is also a measure of the average di erence in energy between bonding

and antibonding orbitals. Hence the bonding contribution to the stability of surface atoms

√

also increases with Nn. This suggests that surface atoms with fewer neighbors are more reactive. This was briefly discussed this in Chapter 2. We show in this chapter that this is generally the case.

Valence electron band narrowing increases the average energy of the electrons, because

The Reactivity of Transition-Metal Surfaces 91

it increases the repulsive electron-electron energy. There appears to be a nearly linear relation between this increase in average d-valence electron energy and number of nearestneighbor electrons. Therefore, a nearly linear relation in average local d-valence electron energy and the adsorption energy is often found[4].

In the adsorption of ammonia on the surface, the NH3 2pz lone-pair molecular orbital interacts with a transition–metal surface atom to form bonding and antibonding orbital fragments. The resulting 4dz2 electron distributions are also shown in Fig. 3.3b.

The sharp peak at the bottom of Fig. 3.3b(1) at 9 eV represents the bonding orbital fragment between the Rh 4dz2 state and the NH3 σ-type orbital. There appears an upward shift of the average d-valence electron distribution in the antibonding regime. As a consequence of the upward shift above the Fermi level (the highest occupied metal orbital), the total electron occupation of the d–valence orbitals decreases. The antibonding orbital fragments between the Rh dz2 and NH3 σ-type orbital become less occupied and overall bonding becomes less repulsive or slightly bonding. A stronger interaction between Rh dz2 and its metal neighbor atoms results in a weaker interaction between the Rh dz2 state with the ammonia σ orbital. The average position of the dz2 orbital energy on Rh(111) is lower than that on the Rh(100) surface. The average upwards shift is less, so that less empty dz2 orbital density now appears above the Fermi level. Since the Fermi level refers to the highest occupied molecular orbital energy in the bulk, it is the same for the (111) or (100) surface. Therefore, the repulsive interactions of NH3 with the Rh dz2 orbital on the Rh(111) surface are larger.

Ammonia adsorption is stronger to the (100) surface (–91 kJ/mol) than (111) surface (–82 kJ/mol). Ammonia prefers atop adsorption over twoor three-fold adsorption on both surfaces. Adsorption at these higher-fold coordination sites is less favored on the (111) surface [Eads (two-fold) (111) surface = –13 kJ/mol; (100) surface = –36 kJ/mol]. This is due to the much larger repulsive interaction of the doubly occupied ammonia lone pair orbital when ammonia is adsorbed to more surface atoms on the Rh(111) surface.

Calculations for NH3 chemisorbed to Cu clusters which simulate the Cu (100) surface illustrate the change in bonding character of the adsorbate bond with the metal surface nicely. Figure 3.4 shows the orbital interaction of the NH3, lone pair orbital with Cu(4s), Cu(4p) and Cu(3d2z ) orbitals. Both the OPDOS (the Overlap Population Densities of States) and Local Density of States (LDOS) are shown.

The OPDOS πij (Ek) is defined as
π	ij	(E	) = ck ck S	ij	(3.14)
		k	i j

where πij (Ek) is proportional to the interference term in the interaction part of the orbital energy. Hence, when πij (Ek) is positive the orbital interaction is attractive when πij (Ek) is negative this interaction is repulsive. The LDOS are the electron densities in the interacting fragment orbitals which are proportional to (cki )2.

The OPDOS curves, Figs. 3.4a and b, show that the interaction of the NH3 σ2pz orbital with the metal d-orbitals changes from attractive (positive) to repulsive (negative) in comparing the values for πij at increasing orbital energies. The Bond Order Overlap Population (BOOP) between fragment orbitals i and j is defined as

occ

occ

Pij = 2	πij (Ek) = 2 ck ck Sij	(3.15)
	i j
k	k

The BOOP provides a measure for the strenght of bonding. The BOOP Pij for an adsorbate with the Cu d-atomic orbitals at the atop adsorption site is –0.005, while that for

92 Chapter 3

Figure 3.4. LDOS of NH3 σ and copper orbitals and the OPDOS between both NH3 and Cu(9,4,5), and Cu(8,6,2), respectively, for one-fold and two-fold NH3 adsorption. Central copper orbitals: (a, b) 3d; (c, d) 4s; (e, f) 4p; NH3 position; (a, c, e) one-fold, (b, d, f) two-fold. Each graph shows - - - - - - LDOS of NH3 σ orbital, -.-.-.-. LDOS of central copper orbitals, and —— OPDOS[5].

The Reactivity of Transition-Metal Surfaces 93

the adsorbate at the two–fold site is –0.157. This larger repulsive interaction at two-fold position is the result of the larger repulsive interaction when two Cu atoms with doubly occupied d-atomic surface orbitals interact with the doubly occupied NH3 σ-orbital. The computed NH3 interaction energies at the two-fold sites on the (111) and (100) surfaces are Eads (two-fold)= –13 and –36 kJ/mol, respectively.

For s-type orbitals the Pauli repulsion energy increases linear with the number of neighbors:

EPauli ≈ ZS2

(3.16)

where Z is the coordination number of the adsorbate orbital with surface atoms. The

√

attractive contribution to the bond energy, as mentioned earlier, is proportional to Z. The attractive interaction between NH3 and the Cu surface arises from the interaction with the free electron-type Cu(4s) and Cu(4p) orbitals. These metal orbitals contain one

electron per metal atom.

Figure 3.5. R . ˚

(a) DFT-computed molecular orbitals and energies of molecular CO. CO = 1 14A; Ebonding = −11.9 eV. (b) Left-handside: orbital energy-level diagram for metal chemisorption system of adsorbed CO; σ5 to be identified with 5σ and σ4 to be identified with 4σ; π2 to be identified with 2π and π1 to be identified with 1π. Right-hand side: schematic representation of the electronic structure of the transition metal.

94 Chapter 3

The interaction of CO and a metal is very di erent to that for ammonia, since the CO has lower antibonding energy π states that are unoccupied and can accept electrons from the metal, i.e. back-donation. The electronic structure of CO is shown in Fig. 3.5a. The hybridization of 2s and 2pz atomic orbitals in CO is clearly noted in its highest occupied 5σ lone-pair orbital, that is mainly localized on carbon. The 5σ-orbital is antibonding with respect to the C–O bond, and predominantly comprised of C 2s, 2pz and O 2pz s character (see also Fig. 4.19). In between the occupied 4σ- and 5σ-orbitals there are the two occupied 1π-orbitals. These four occupied orbitals will strongly interact with the transition metal surface and, similarly as in the case of the lone-pair orbital of NH3, are expected to have a repulsive interaction with the occupied transition metal d–orbitals. The lowest unoccupied 2π -orbitals have a much lower energy than the antibonding unoccupied orbitals in NH3. Therefore, in CO the interaction between the CO 2π -orbitals and surface states becomes important. The frontier orbital scheme for the interaction of CO with the transition–metal surface is illustrated in Fig. 3.5b. In this elementary scheme only the interactions of the HOMO and LUMO of CO with transition-metal electrons are considered. The interaction of the frontier 5σ and 2π orbitals creates bonding as well as antibonding orbital fragments. The antibonding orbital fragments of the 5σ orbital are partially occupied, which leads to a repulsive interaction. Only bonding orbital fragments of the 2π and surface d-orbitals are occupied, thus resulting in an attractive contribution.

Compared this elementary bonding scheme, OPDOS calculations of CO adsorbed atop or three-fold to an Ru19 cluster simulating the Ru(0001) surface modify this bonding picture in an essential way (see Fig. 3.6). The binding energies for CO adsorbed atop and three-fold are –192 and –116 kJ/mol, respectively. The orbital pictures as well as the overlap population density of states (OPDOS) between the C-atomic orbital CO and the nearest-neighbor metal d-states are shown for CO at atop and three-fold hollow sites of the Ru in Fig. 3.6. The corresponding LDOS are shown in Fig. 3.7. The comparison of Figs. 3.6 and 3.7 allows for an assignment of the LDOS peaks.

We will first consider the interaction of the metal states with the CO σ-orbitals. We recognize in Fig. 3.6a the 4σ orbital and the 5σ orbitals of CO at –14 and –11 eV, respectively. The features above –10.2 eV correspond to the antibonding 4σ–d interactions. In addition to the elementary Blyholder picture[6] that considers only the 5σ CO lone pair interactions, we now note that the interaction with the 4σ orbital is also important and that this interaction is also repulsive. A comparison between the orbitals for adsorbed CO and those for the free CO indicate that there is a rehybridization between 4σ and 5σ orbitals, with a shift of electron density towards the oxygen atom. Hybridization e ects have been confirmed recently by XPS measurements[7] . Figure 3.8a illustrates that mixing of the two σ-CO orbitals with a metal-surface atom leads to bonding, nonbonding and antibonding orbital interactions. The nonbonding interaction is distinguished by strong localization of density on the oxygen atom.

If one compares the σ-type interaction at the atop and three-fold adsorption sites in Fig. 3.6, one notes a much greater interaction for CO at the three-fold site, especially for that of the 4σ CO orbital with the transition-metal surface, thus leading to much stronger repulsive interactions than in the atop adsorption mode.

Let us now analyze the π-type interactions. In Fig. 3.6a we note at –10.6 eV a strong bonding interaction between CO-1π and surface dxz and π orbitals. A nonbonding π-type orbital is present at –9.2 eV which is localized on oxygen. The bonding interactions with the 2π orbital of CO are apparent around –6 eV (–1.5 eV below the Fermi level) and

The Reactivity of Transition-Metal Surfaces 95

Figure 3.6. OPDOS of the carbon atomic orbital adsorbed on a Ru surface with Ru d-valence electrons. Also the orbitals with maximum density are shown. (a) CO adsorbed atop; (b) CO adsorbed three-fold. —, σ-Symmetric orbital interactions; ..., π-symmetric orbital interactions. The Fermi level is at –4.8 eV.

antibonding interactions around –2 eV (2.5 eV above the Fermi level). The shift of the electron density towards the oxygen atom occurs in the rehybridization regime of 1π and 2π orbitals (–10 to –6 eV). This agrees very well with Scheme 3.8b. The interaction of the molecules 1π, metal d, molecules 2π states leads to a bonding, nonbonding and antibonding fragment orbitals. The nonbonding orbital mainly has electron density located on the oxygen atom. For CO bound at the three-fold sites, the corresponding positions