Metal–Ligand Bonding

By Rob Janes, Elaine Moore

The Royal Society of Chemistry

Copyright © 2004 The Open University
All rights reserved.
ISBN: 978-0-85404-979-0

Contents

1 INTRODUCTION, 1,
1.1 What do d orbitals look like?, 2,
2 CRYSTAL-FIELD THEORY, 5,
2.1 Octahedral complexes, 5,
2.2 Ionic radii, 9,
2.3 Crystal-field stabilisation energy, 11,
3 ELECTRONIC SPECTRA OF OCTAHEDRAL COMPLEXES, 14,
4 SUBSTITUTED AND DISTORTED OCTAHEDRAL COMPLEXES, AND SQUARE-PLANAR COMPLEXES, 21,
5 TETRAHEDRAL COMPLEXES, 28,
5.1 The occurrence of tetrahedral and square-planar four-coordinate complexes, 31,
6 MAGNETISM AND THE MAGNETIC PROPERTIES OF TRANSITION-METAL COMPLEXES, 33,
7 SUMMARY OF CRYSTAL-FIELD THEORY, 40,
8 MOLECULAR ORBITAL THEORY OF TRANSITION-METAL COMPLEXES, 41,
9 BONDING IN OCTAHEDRAL COMPLEXES, 44,
9.1 σ-bonding, 44,
9.2 π-bonding in strong-field complexes, 47,
9.3 π-bonding in weak-field complexes, 52,
9.4 Summary of Section 9, 56,
10 BONDING IN COMPLEXES OF D4h SYMMETRY, 57,
10.1 Symmetry elements and symmetry point groups, 57,
10.2 Bonding in distorted octahedral complexes, 60,
10.2.1 Weak-field complexes, 60,
10.2.2 Strong-field complexes, 63,
10.3 Bonding in square-planar complexes, 64,
10.4 Summary of Section 10, 65,
11 BONDING IN TETRAHEDRAL COMPLEXES, 66,
11.1 Summary of Section 11, 69,
12 COMPLEXES OF OTHER SYMMETRY, 70,
13 COMPLEXES WITH TWO METAL ATOMS, 71,
13.1 Summary of Section 13, 74,
14.1 Ligand-to-metal charge-transfer bands, 76,
14.2 Metal-to-ligand charge-transfer bands, 80,
14.2 Metal-to-metal charge-transfer bands, 81,
14.4 Summary of Section 14, 82,
15 REVISION EXERCISE: COMPLEXES OF COBALT (II) AND COBALT (III), 83,
APPENDIX FLOW CHART FOR DETERMINING THE SYMMETRY POINT GROUP OF AN OBJECT, 84,
LEARNING OUTCOMES, 85,
ANSWERS TO QUESTIONS, 87,
ANSWERS TO REVISION EXERCISE QUESTIONS, 93,
ACKNOWLEDGEMENTS, 96,
INDEX, 97,

CHAPTER 1

INTRODUCTION

The attribute of transition-metal ions on which this book focuses is their possession of partially occupied d orbitals. Across the fourth row of the Periodic Table, an electron enters the 4s sub-shell at potassium, and a second fills it at calcium. Then, from scandium to zinc, the 3d sub-shell is progressively filled. For the neutral atoms, the energies of the 3d and 4s orbitals are very close, and it is the exchange energy stabilisation associated with half-filled and filled shells that gives rise to configuration irregularities at chromium and copper, respectively. This is shown in Table 1.1, where [Ar] represents the argon core electrons.

When transition-metal atoms form cations, the 4s electrons are lost first. On ionisation, the 3d orbitals are significantly more stabilised (that is, drop to lower energy) than the 4s would be. This stems from the fact that the 3d electrons are not shielded from the nucleus as well as the 4s electrons. Therefore, the +2 and +3 ions have electronic configurations of [Ar]3dn (or 1s22s22p63s23p63dn). The electronic configurations of the +2 and +3 ions, which we shall refer to frequently, are shown in Table 1.2.

One of the characteristic features of the chemistry of the transition elements is the formation of a vast number of complexes such as [Ti(H2O) 6]3+, Ni(CO)4 and [CoC1(NH3)4(H2O)]2+. These are molecules that consist of a central metal atom or ion, to which is bonded a number of molecules or ions by coordinate-covalent bonds. We refer to the latter as ligands, and the number of electron pairs donated to the metal is its coordination number.

* What is the coordination number of the metal in the following complexes?

(a) [FORMULA NOT REPRODUCIBLE IN ASCII].

(a) 6; (b) 4; (c) 6.

Possibly the most striking property of transition-metal complexes is the wide range of colours they exhibit. This tells us that part of the visible region of the electromagnetic spectrum is being absorbed by the molecule. But what energy changes are actually occurring at the molecular level? There are also intriguing variations in the magnetic behaviour of transition-metal complexes. For example, although they both contain central Fe2+ ions, [Fe(H2O)6]2+ is paramagnetic (it is attracted into a magnetic field), but [Fe(CN)6] 4- is diamagnetic (it is weakly repelled by a magnetic field). In this book, we shall look at some bonding theories to help us explain these, and other, observations.

Our starting point is crystal-field theory (Section 2). This is a delightfully simple approach, which, provides us with a remarkable insight into the chemical and physical properties of complexes of d-block metals. However, there are cases where this model is inadequate, and where molecular orbital theory is more appropriate. In developing a theory of bonding in transition-metal complexes, our starting point is a consideration of the properties of the d orbitals on the metal ion.

1.1 What do d orbitals look like?

There are five d orbitals, which, with reference to a set of mutually perpendicular axes, may be represented by their boundary surfaces, the contours inside which a d electron is found 95 per cent of the time. The orbitals shown in Figure 1.1 are strictly those for an electron in a hydrogen atom, but those for electrons in transition-metal ions will have the same shape. In Figure 1.2, the 3d orbitals are all presented from the same perspective, such that the xz plane is always the plane of the paper.

Four of these orbitals have the same shape but are orientated in different directions: the 3dxy, 3dyz and 3dxz orbitals have their lobes between the relevant coordinate axes, whereas the [FORMULA NOT REPRODUCIBLE IN ASCII] orbital has its lobes along the x and y axes. The fifth, [FORMULA NOT REPRODUCIBLE IN ASCII],looks different, but is, in fact, a combination of two orbitals [FORMULA NOT REPRODUCIBLE IN ASCII] and [FORMULA NOT REPRODUCIBLE IN ASCII], which are shaped like the other four (Figure 1.3).

The energies of electrons in the 3d orbitals in transition metals are larger than that of an electron in a 3d orbital in the hydrogen atom. (3d ionisation energies for the first transition series metals are in the range 12.8-17.6 x 10-9 as opposed to 2.4 x 10-19 J for hydrogen.) In addition, the energy of the 3d orbital changes when going from the free ion or atom to a complex. It is the changes in the energies of the d orbitals when we add ligands to a ‘naked’ transition-metal ion that concern us here. How does the energy of a 3d orbital change when a transition-metal ion is surrounded by ligands, and what are the consequences of this change?

CHAPTER 2

CRYSTAL-FIELD THEORY

We begin our consideration of bonding in transition-metal complexes by looking at crystal-field theory, which is relatively straightforward to apply, and allows us to rationalise, and make predictions about many properties of these molecules.

Crystal-field theory, developed by Hans Bethe and John Van Vleck in the 1930s, assumes that ligands behave as point negative charges, and that the metal–ligand interaction occurs on several levels. Overall, a complex will be stabilised relative to the free ion, due to the attraction between the negatively charged ligands and the positively charged metal ion. However, if we take a closer look at the electrons in the metal-ion d orbitals, we would expect their energy to increase due to repulsion by the ligands. In other words, the energy of the metal-ion d orbitals will rise. However, this is not the whole story. Given that we are considering an electrostatic interaction, whose magnitude will depend on the distance between the charge centres, we also need to look at how close the d electrons are to the ligands. This, in turn, will depend on which d orbital the electron occupies.

We shall start by looking at the application of crystal-field theory to octahedral complexes, since this geometry is one of the most common in transition-metal chemistry. Our emphasis is on complexes of the first transition series.

2.1 Octahedral complexes

We begin by assuming that the ligand negative charges are concentrated at six points representing six octahedrally arranged ligands, two on the x-axis, two on the y-axis and two on the z-axis (Figure 2.1). For a free ion, the d orbitals are energetically equivalent. We already know that the energies of all the d orbitals will increase, but the key question is: areallthe 3d orbitals equally affected by this charge?

To answer this question, let us look at the two d orbitals that are orientated in the xy-plane. Figure 2.2 shows the 3dxy and [FORMULA NOT REPRODUCIBLE IN ASCII] orbitals in the xy-plane, and the point charges on the x– and y-axes. By taking this bird’s-eye view down the z-axis, you can see that whereas the [FORMULA NOT REPRODUCIBLE IN ASCII] lobes are concentrated towards the point charges, those of the 3dxy orbital lie between the charges.

* How do you think this will affect the energy of the two orbitals?

* An electron in a [FORMULA NOT REPRODUCIBLE IN ASCII] orbital comes closer to the point charges on average than does an electron in a 3dxy, orbital. Thus, the [FORMULA NOT REPRODUCIBLE IN ASCII] electron will be repelled more by the ligands, and hence the [FORMULA NOT REPRODUCIBLE IN ASCII] ITL orbital will be higher in energy than the 3d, orbital.

Similarly, if you look at the xz-plane, you will find that an electron in [FORMULA NOT REPRODUCIBLE IN ASCII] will experience a greater repulsion than one in the 3dxz orbital, and if you considered the yz-plane, you would find that an electron in [FORMULA NOT REPRODUCIBLE IN ASCII] would be repelled more than one in the 3dyz orbital.

To summarise: for a set of octahedrally arranged charges (an octahedral crystal field), the energy of the orbitals aligned along the axes ([FORMULA NOT REPRODUCIBLE IN ASCII] and [FORMULA NOT REPRODUCIBLE IN ASCII]) will be higher than those of the 3dxy, 3dxz and 3dyz orbitals, which are aligned between the axes (that is, further away from the ligands). This is represented in the form of an energy-level diagram in Figure 2.3. There are several points to note about this diagram. In both Figure 2.3a and b, the five d orbitals all have the same energy (they are referred to as being degenerate), and (b) simply represents the average energy of the orbitals in the complex, known as the barycentre. This level would correspond to a hypothetical situation in which the metal ion was surrounded by a sphere of negative charge. The splitting of the orbitals is shown in Figure 2.3c; they are ‘balanced’ about the barycentre. Furthermore, in an octahedral complex, the 3dxy 3dxz and 3dyz orbitals are energetically equivalent, as are the [FORMULA NOT REPRODUCIBLE IN ASCII] and [FORMULA NOT REPRODUCIBLE IN ASCII] orbitals. The symbol Δo (pronounced delta ‘oh’ for octahedral) denotes the energy separation between the two sets of orbitals, and is referred to as the crystal-field splitting energy. The 3dxy, 3dxz and 3dyz orbitals have an energy 2/5Δo less than the average energy of the orbitals, and the [FORMULA NOT REPRODUCIBLE IN ASCII] and [FORMULA NOT REPRODUCIBLE IN ASCII] orbitals are raised 3/5Δo higher than the average.

Note that the levels in Figure 2.3 are labelled t2g and eg. These are symmetry labels for a complex (or molecule) belonging to the symmetry point group of an octahedron, Oh.

We shall consider these symbols in more detail in Section 10 in the context of molecular orbital theory, but for the present you need only consider them as labels:

• t denotes a triply degenerate orbital. • e denotes a doubly degenerate orbital.

Later you will meet the symmetry labels ‘a’ and ‘b’, which are singly degenerate levels. The symbols ‘g’ and ‘u’ refer to the behaviour of an orbital under the operation of inversion (p. 57). They are only used for complexes that possess a centre of symmetry.

So we now have an energy-level diagram. But how can it be used to explain the properties of transition-metal complexes? The following steps will get us started:

(i) determine the oxidation state of the metal ion in the complex;

(ii) calculate the corresponding number of d electrons;

(iii) establish how these electrons occupy the energy-level diagram (bearing in mind that each energy level can hold a maximum of two electrons).

Firstly, let’s consider a complex of titanium in its +3 oxidation state, where there is one d electron (Ti3+, 3d11). This will enter the t2g level (Figure 2.4a). It does not matter whether we place the electron in the dxy, dyz or dxz orbital because they are degenerate. For complexes containing metal ions of configuration d2 (Ti2+ and V3+) or d3 (V2+ and Cr3+), the electrons enter the t2g level, but they occupy separate orbitals with parallel spins (Figure 2.4b and c).

The energy of an orbital is determined by the attraction of the nuclei in the complex for an electron in that orbital. Generally, when assigning electrons to orbitals, we ignore any interaction between the electrons. However, in this case, we need to consider the repulsion of the negatively charged electrons in more detail. Two electrons in one orbital will repel each other more than two electrons in different orbitals because, on average, they will be closer together. In addition, electrons with paired spins repel each other more than those with parallel spins. Consequently, electron repulsion is minimised if the electrons are in different orbitals with parallel spins. The energy required to force two electrons into the same orbital is the pairing energy, P.

The pairing energy becomes important when we reach the 3d4 situation, as we are now faced with two choices. The fourth electron could either enter the t2g level and pair with an existing electron, or, it could avoid paying the price of the pairing energy by occupying the eg level. Which of these possibilities occurs depends on the relative magnitude of the crystal-field splitting and the pairing energy. The two options are:

(i) IfΔo<P, the fourth electron goes into the eg level, with a spin parallel to those of the t2g electrons. This is known as the weak-field or high-spin case, and is represented by the notation t2g3eg1.

(ii) If Δo >P, the energy required for an electron to occupy the upper level, eg, will outweigh the effect of electron-electron repulsion. The fourth electron then goes into a t2g orbital, where it has to be spin paired. This is represented by the notation t2g4eg0. and is known as the strong-field or low-spin case.

These two possibilities are considered in Figure 2.5, which also includes high- and low-spin arrangements for d5 and d6.

* Sketch orbital energy-level diagrams similar to Figure 2.5 showing the weak -field and strong-field configurations for a d7 complex.

* See Figure 2.6.

* Would we expect to see high-spin and low-spin complexes for d8 and d9 complexes in an octahedral crystal field?

No; there is only one possible arrangement of electrons in both cases, the size of Δo makes no difference to the occupation of the levels, [FORMULA NOT REPRODUCIBLE IN ASCII] and [FORMULA NOT REPRODUCIBLE IN ASCII] (see Figure 2.7)

You will notice that the different arrangements of electrons in the t2g and eg orbitals for d4–d7 ions can result in configurations where the d electrons are completely paired, or contain one or more unpaired electrons; that is, complexes containing these ions can be either diamagnetic or paramagnetic. The magnetic properties of transition-metal complexes are considered in more detail in Section 6, and at this stage we simply note the existence of these two possibilities.

We shall now use these d-electron configurations to explain the variations in an important property of transition-metal ions.

2.2 Ionic radii

A plot of the ionic radii of the dipositive ions for the first transition series shows an overall decrease with increasing atomic number, but with a double-bowl shaped profile. This is shown in Figure 2.8. As the nuclear charge increases, electrons enter the same sub-shell (3d); that is, the electrons are roughly the same distance from the nucleus. Electrons in the same shell do not screen the positive charge of the nucleus from each other very effectively. Hence the net nuclear charge experienced by the electrons increases as the atomic number increases. This increased charge causes the electrons to move closer to the nucleus, and hence the ionic radii of the first-row transition elements exhibit an overall decrease across the series.

If there were a spherical distribution of electric charge over the ions, we would expect a regular decrease in ionic radii (shown by the light green line in Figure 2.8), but clearly this is not the case. In fact, taking into account the regular distribution of the d orbitals, this situation would only be achieved for d0, d5 (high spin) and d10. Here crystal-field theory can help us. The radii in Figure 2.8 were obtained by measuring metal–fluorine distances in metal difluorides, and the crystal structures of these compounds are such that each metal ion is surrounded by an octahedron of fluoride ions. Hence, to a first approximation we are still dealing with octahedral complexes, so our d-orbital energy-level diagram derived in Section 2.1 (Figure 2.3) will apply.

Let us start with TiF2, which is actually unknown, but we can still use Figure 2.8 to estimate and discuss its notional internuclear distance. The Ti2+ ion has two 3d electrons, and in an octahedral crystal field they will occupy t2g orbitals with parallel spins. The electrons on the transition metal screen the fluoride ions (which we are regarding as point negative charges) from the charge of the metal nucleus. As the electrons are dividing their time between orbitals that are concentrated between the ligands, we would expect this screening to be less efficient than if the electrons were in eg orbitals. Since the fluoride ions are screened less than we would expect if the crystal field were spherical, they move closer to the metal nucleus, hence shortening the metal–fluorine distance. Thus, from crystal-field theory, we expect Ti2+ to have a smaller ionic radius than if it were a spherical ion.

* What variation from the spherical ion depiction does crystal-field theory predict for V2+ in VF2?

V2+ would have three electrons in the t2g level. So, like Ti2+, V2+ will have a smaller ionic radius than would be expected for a spherical ion; in fact, it has the largest deviation from the spherical ion prediction of all the elements in the first transition series.

For Cr2+, there are four d electrons, so we need to consider the possibility of high- and low-spin configurations. However, as we shall see later, fluoride ions are very weak -field ligands, so the complex will be high spin; that is, the fourth electron goes into the eg level.

(Continues…)Excerpted from Metal–Ligand Bonding by Rob Janes, Elaine Moore. Copyright © 2004 The Open University. Excerpted by permission of The Royal Society of Chemistry.
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