Bonding and elementary steps in catalysis
4.1 INTRODUCTION
4.2.1 General Introduction
This introductory section intends to present the basic bonding concepts, necessary to understand chemical bonding to transition metal complexes, clusters and transition metal surfaces.
The valence electrons in transition metals are distributed over d(n - 1) and s(n) and p(n) electrons, n labeling the principle quantum-numbers.
The number of d electrons can vary between 0 and 10, distributed over five d-atomic orbitals. The maximum number of s electrons is 2 and p electrons is 6.
The latter are distributed over the three p atomic orbitals. Varying the position of the metal element from left to right through a row of the periodic systems shows an increase of the number of valence electrons.
The d-valence electron occupation reaches saturation for the elements Cu, Ag and Au.
Whereas the distribution of electrons over the d and s electrons is irregular for the transition metal atoms to the left of Cu, Ag and Au, this is much less the case for the transition metals in their solid state. Here the electron occupation of the s, p valence electronband is approximately constant and equal to one electron per atom, whereas the number of d-valence electrons steadily increases moving from the left to the right through a row of the periodic system.
The spatial extension of the s(n) and p(n) atomic orbitals is significantly larger than the more contracted d ( n - 1) atomic orbitals. Therefore the contribution to the chemical bond from the interaction with the s and p atomic orbitals is sometimes dominant and always substantial.
4.2.1.1 The Covalent Bond: Homonuclear Systems
For clarity we will limit the introductory discussion to chemical bonding to interacting atoms that only contribute an s-valence atomic orbital to the chemical bond.
To illustrate relevant aspects of the electronic factors that control the diff- erence in bonding to a single atom and bonding to several atoms, i.e. co- ordination changes, Fig. 4.1 gives the orbital energies that correspond to the two different situations. At the left side of the scheme (Fig. 4.1) for two atoms of equal energy, the energies of the bonding and antibonding orbitals are given, as computed within the Extended Htickel Approximation. In this method [1] the atomic orbital energies are denoted as (x, the overlap energy by ~' and non- orthogonality of orbitals is accounted for by the overlap S. [~' leads to bond formation and has a negative value. It is due to the attraction of an electron on one atom by the nuclear charge on the other atom. The overlap S, as we will see, is
4 ~ BONDING AND ELEMENTARY STEPS IN CATALYSIS 111
Fig. 4.1. I n t e r a c t i o n s c h e m e b e t w e e n t w o a t o m s a n d o n e a t o m i n a c l u s t e r .
responsible for the repulsive part of the potential energy curve. The bond energy follows by occupying the molecular orbitals with electrons, (maximum 2 per orbital), adding the orbital energies and subtracting the atom energies of the system before interaction.
In the interacting system one orbital energy is lower than that of the free atoms and it is called the bonding orbital. The other orbital is destabilized; the anti- bonding orbital. For finite overlap S (IS[ is always smaller than 1, the normal- ization constant), the stabilization of the bonding orbital is less than the destabilization of the antibonding orbital. One notes that the difference in the energies of the bonding and antibonding orbitals A ---2[3'. The exact expression
- 2 ( ~ ' - a S )
for A = 1 - S 2 . A is a measure of the covalent interaction strength.
When the system contains 2 electrons they will occupy the bonding orbital and the bond energy is equal to:
Eatb -- -A(1 - S) (4.1a)
--2[3' (S << 1) (4.1b)
When 4 electrons are present in the system, the bonding as well as antibonding orbitals become occupied. The bonding energy AEb n o w becomes:
E r -- - 2 A S b
(4.2a)
- - - 4~'S (S << 1) (4.2b)
112 4 - - BONDING AND ELEMENTARY STEPS IN CATALYSIS
Since [3' is a negative, attractive energy, it follows that the interaction is attractive when the total number of orbitals is half occupied, but is repulsive when all orbitals are doubly occupied.
The attractive interaction, approximately proportional to ~' is the covalent attractive contribution to the chemical bond energy. The repulsive part, approxi- mately proportional t o - ~ ' S depends explicitly on the overlap S. It can be understood as the Pauli repulsion, due to repulsive interaction of overlapping orbitals with electrons of equal spin.
As we will see later, orbital interactions between molecules with partially occupied orbitals will be predominantly attractive. However the interactions between the deeper doubly occupied orbitals are repulsive. The latter are re- sponsible for steric repulsive interactions.
The right part of Fig. 4.1 gives the changes in electronic structure when an atom interacts with n neighboring atoms. Again the free atom energies are assumed equal. The n cluster atoms are assumed not to interact. The conse- quences of this interaction will be discussed later in this section.
The most important change when co-ordination number n changes is the value of A(n), the difference between bonding and antibonding orbital energy values:
A(n) = -2~J-n(~'--~S)
1 - n S 2 (4.3a)
= ~ A ( 1 ) (r/S 2 < < 1) ( 4 . 3 b )
The attractive interaction when the atomic orbitals are half filled becomes:
at at
E b (n)= ~ E b (1) (4.4)
The repulsive Pauli interaction, that one finds for the system with all orbitals doubly occupied becomes:
E ~ (n) = 2n A(1)S (4.5)
Comparison of expression (4.5) with (4.1) shows that the attractive interaction becomes approximately proportional to the square of the number of coordina- ting atoms, but the Pauli-repulsion term is linear in the number of coordinating atoms.
As we will see later this difference in the dependence of the attractive and repulsive interaction on co-ordination number will lead to a preference for low coordination numbers for systems that have significant Pauli-repulsive inter- actions.
4 -- BONDING AND ELEMENTARY STEPS IN CATALYSIS 1 1 3
4.2.1.2 The Covalent Bond; Heteronuclear System: The Lewis Acid--Lewis Base Interaction
Aspects of bonding between non-equal atoms are illustrated by Fig. 4.2, which gives the orbital energy levels for a two atom system with free atom energies (z0 and (Xl. Again bonding (eb) and antibonding (Ea) levels are formed.
When the energy difference I % - (xl [ >> [[Y], their respective energies are:
~ # 2 1 1S
E b = E b -- (% 1 = - - ~ + - - a
(4.6a)
(x0 -(Xl 2
~ , 2 1
g a - E a - (X 0 -" + ~ + - - a ~ (4.6b)
(x0 - c ~ 2
Two terms contribute to the shifted orbital energies. The first terms represent the stabilization and destabilization of the initially non-interacting orbitals due to covalent bonding. Their form, proportional to the square of the overlap energy and inverse to the energy difference, is the usual one from Frontier Orbital Theory. The second term is the Pauli-repulsion. The expressions for A ~ and A ~ are slightly different from A.
i (~'_--a_oS) (4.7a)
A 1 - 2 \ 1 - 8 2
A ~ ([Y-~ 1 S / 1 - - 8 2 (4.7b) One notes that if the two orbitals become doubly occupied the two fragments have a repulsive interaction equal to:
orbital scheme
E
a ; \
~8~.
I ;
' I
I I
I I
l l
I !
I I
ib
( I 0
asymmetric
Fig. 4.2. O r b i t a l s c h e m e f o r t w o a t o m s .
114 4 ~ BONDING AND ELEMENTARY STEPS IN CATALYSIS
E rep = ( A 1 + A 0 ) S (4.8)
When each of the two atoms has initially one electron, the bond energy becomes:
E coy = 2[3' 2
b - - ~ + A I S +(C~1 - a 0 ) (4.9)
0~0 - 0 ~ i
The third term arises from electron transport from atom (0) to atom (1). (a0-al) is equal to the Ionization Potential(I.P.) of atom (0) minus the Electron Affinity (E.A.) of atom (1). This electron transfer results in a positive charge on atom (0) and a negative charge on atom 1.
Therefore the total bond energy is equal to:
E b(tOtal) =E c~ b 4" E electrostatic (4.10) To the covalent contribution an electrostatic term has to be added.
!q].2
Eelectr~ =
-Ir0 -rll
(4.11a)with
I t
[3' 21
q = + 1 -
l J
(4.11b)
= +{1-Ae} (4.11c)
The charge q is reduced due to backdonation of electrons from the doubly occupied orbital on atom (1) by an amount Ae. Backdonation reduces the electron density on atom 1, but enhances the electron density on atom 0. The correspond- ing energy contribution equals:
2 ~ ' 2
E backdonation -" -- ~ ( 4 . 1 2 a )
0~0 -0~i
= -(cz0 -cz 1).Ae (4.12b) Expressions (4.12) can be considered the interaction-energy between a Lewis acid (empty orbital, %) and Lewis base (doubly filled orbital, al).
Since the disturbance of the original orbitals with energies ax and o~ is small, the orbital q ~ becomes mainly part of the bonding orbital ~b and atomic orbital q~a0becomes mainly part of the antibonding orbital ~a. The admixture of the
4 ~ B O N D I N G A N D E L E M E N T A R Y STEPS IN CATALYSIS 115 respective other atomic orbitals in the bonding and antibonding molecular orbitals gives electron transfer Ae.
4.2.1.3 The Embedded System
Figure 4.3 schematically illustrates electronic structure changes w h e n a cluster becomes embedded in a surface. The first scheme (Fig. 4.3a) is similar to scheme 4.1b. When an atom interacts with n neighbours (that have no interaction between themselves) the covalent interaction is ~ ~fn 13'.
Figure 4.3b shows the electron distribution p(E) as a function of electron energy E for a surface cluster of (z + 1) atoms embedded in the surface of a metal atom interacting with overlap energy [3. Because the bulk system terminated with a surface is semi-infinite, the energies of an infinite number of metal orbitals are continuously distributed between an u p p e r and lower energy value determined by lattice topology and interaction energy parameter 13. At the surface the width of energy-density on the surface atoms is proportional to ~ [1] (z is the number of nearest neighbour metal atoms of a surface atom, 13 the overlap energy of the metal atoms).
Fig. 4.3. Electronic structure changes when a cluster is embedded in a surface.
116 4 ~ BONDING AND ELEMENTARY STEPS IN CATALYSIS
The attractive contribution to the bond energy of the surface metal atoms has the same co-ordination dependence.
Electron density at the bottom of the metal electron energy belongs to bonding-orbitals between the metal atoms, electron density at the top of this band belongs to antibonding orbitals.
Figures 4.3c, d and e illustrate changes in electronic structure of cluster 3a when the cluster atoms become part of a surface. Three physically different situations have to be distinguished: surface molecule limit, intermediate ad- sorption and weak adsorption. Figure 4.3c schematically presents the electronic structure in the surface molecule limit. Then the interaction between adatom and surface atoms [3' is significantly larger than [3:
- ~ >> 1 (4.13)
Whereas in the free adatom-cluster the difference between bonding and antibonding orbitals is A, this splitting decreases for the embedded cluster.
Embedding delocalizes the cluster atom electrons and the effective interaction between adatom and cluster-atoms decreases. This is reflected in the smaller bond splitting A' compared to A. The decrease in bandsplitting is proportional to
~fz~, the localization energy of the surface electrons.
The adsorption energy can be approximately written as the sum of three terms:
Eads = Esurface tool + Eloc + Eemb (4.14a)
= ( 2 ~ ' - n ~ ' S) - 2~]z~ 4 Z ~ 2 (4.14b)
The first term is the interaction energy within the free cluster; the second term the localization (or decoupling) energy of the surface cluster electrons, the third term the interaction due to the restoration of bonding between cluster (now in inter- action with adsorbate) and surface. Remember that the overlap energies are negative.
In the surface molecule limit, the first term dominates and the last term is small compared to the localization-energy.
Hence in the surface molecule limit the interaction-energy between adsorbate and surface decreases when the number of surface neighbour atoms (z) of the interacting surface atom increases.
This is a result often found in chemisorption. The chemisorption strength to a dense surface (surface atoms have high co-ordination, the coordination number
4 ~ BONDING AND ELEMENTARY STEPS IN CATALYSIS 117 is proportional to the number of nearest-neighbour atoms) is small compared to the adsorption energy to an open surface (surface atoms have low co-ordination).
Note that the adsorption energy dependence on surface atom co-ordination relates to the weakening of the bond energies between the surface atoms (due to electron localization, only partially being restored by Eemb).
When intermediate surface bonding (~fd[3 = ~/z~) occurs the adatom bonding and antibonding orbitals are not any more separate, but then overlap as broaden- ed bands in the surface electron density regime (Fig. 4.3d).
In the weak interaction limit (Fig. 4.3e) the orbitals collapse. The localization energy cannot be overcome and the surface electron structure is only weakly disturbed.
The band width of the electron distribution on the surface atoms (the analogue of A) has now become very small and equal to:
__ 2 , f ~ , ~ '
A 2nl~'l = 2 "(4rnl i) (4.15a)
<< ~/-dl [3' [ (4.15b)
The covalent contribution to the bond energy has now become very much less than the free cluster value ~Fn 113' i. The bond energy decreases ~(~/~)-1 when the surface co-ordination of surface atoms increases.