Chemistry 3211 Coordination Chemistry Part 3 Ligand Field and Molecular Orbital Theory

Chemistry 3211 Coordination Chemistry Part 3 Ligand Field and Molecular Orbital Theory Electronic Structure of Six and Four-Coordinate Complexes Using Crystal Field Theory, we can generate energy level diagrams describing the relative energies of the different metal-based d-orbitals in an octahedral crystal field. This assumes only electrostatic interactions and does not consider any covalent bonding (σ, π or δ) interaction or orbital overlap. This gives rise to two sets of orbital energy levels. The doubly degenerate e g set consists of the axial orbitals d x2-y2 and d z2 and is higher in energy than the triply degenerate t 2g set consisting of the interaxial d xy, d xz and d yz orbitals. The energy difference is Δ o. Distortions from the ideal octahedral environment cause variations in the orbital energy levels. For example, if we start pulling away one of the ligands along the z-axis, ultimately removing it to form a five-coordinate square pyramidal geometry, this partly removes an unfavourable (according to CF theory) interaction in the z-direction. All orbitals with a z-component (d z2, d xz and d yz ) fall in energy. The others go up in energy. This gives rise to the energy level splitting diagram shown below. C. M. Kozak Chemistry 3211 1

Removing the other ligand on the z-axis has the same effect, leading to the energy level diagram for a square planar complex. Note the large energy gap between the d xy and d x2-y2 orbitals. As a result, square planar complexes are almost exclusively those of d 8 metals (all metal orbitals are filled except the d x2- y2) and so have 16 electrons rather than 18. Figure 20-10 in Housecroft and Sharpe 2 nd Ed. illustrates the crystal field splitting parameters for common geometries. Four coordinate complexes are the second most abundant and the same kinds of arguments can be applied to these species, but we have to take into account the different order of the d-orbital energies. A tetrahedral geometry can be described by superposition within a cube. None of the metal d orbitals points exactly at the ligands, but the d xy, d xz and d yz orbitals approach the ligand location more closely than do the d z2 and d x2-y2 orbitals. Therefore, for a regular tetrahedron, the splitting of the d orbitals is inverted compared to that of an octahedron, and the crystal field splitting, Δ T, is smaller than Δ o (by a crude approximation, Δ T is generally 4/9 the magnitude of Δ o ). Z t 2 0.4Δ T Y X e Δ T 0.6Δ T Because there is no centre of inversion in a tetrahedron, the orbital sets are labelled t 2 for the triply degenerate set and e for the lower energy doubly degenerate set (the orbital designations do not include the parity label g or u). Ligand field stabilization energies for tetrahedral complexes can be calculate in exactly the same way as for octahedral complexes, the only differences being the order of occupation (e before t 2 ) and the contribution of each orbital to the total energy (-3/5 Δ T for an e electron and +2/5 Δ T for a t 2 electron). Tetragonal Distortions and the Jahn-Teller Effect As described above, distortion from the ideal octahedral geometry results in a new distribution of d orbital energy levels. These distortions may arise as a result of steric interactions among the ligands, or indeed from the nature of the metal ion itself. For example, copper(ii), which has nine d electrons, forms six-coordinate complexes that usually depart considerably from true O h symmetry and often show significant tetragonal distortions. Low-spin d 7 and high-spin d 4 six-coordinate complexes may show a similar distortion. Extension of the z-axis and compression of the remaining axes reduces the energy of the e g (d z2 ) orbital and increased the energy of the e g (d x2-y2 ) orbital. Therefore, if the e g set is occupied by one, two or three electrons (as in l.s. d 7, d 8, d 9 and h.s. d 4 complexes) a tetragonal distortion may be energetically advantageous. As a special case, the distortion of a h.s. d 8 complex may be large enough to encourage the pairing of two electrons in a d z2 orbital. Effectively, this may lead to the loss of two ligands on the z-axis and the formation of d 8 square planar complexes, such as those found for Rh(I), Ir(I), Pt(II), Pd(II) and Au(III). The common occurrence of square planar 4d 8 and 5d 8 complexes relates to the high value of the ligand field splitting parameter for these heavier transition metals, which gives rise to large ligand field stabilization by going to low spin square planar complexes. On the other hand, 3d 8 metal complexes, such as [NiX 4 ] 2- where X is a halogen are generally tetrahedral because the ligand field splitting is generally smaller for the first row transition metals. Only when coordinated to strong field ligands such as CO or CN- does a large enough ligand field splitting occur, resulting in the formation of a square planar complex, such as [Ni(CN) 4 ] 2-. C. M. Kozak Chemistry 3211 2

For six-coordinate systems possessing an odd number of electrons in the e g orbitals, that is, for d 9, high spin d 4 and low spin d 7 electron configurations, these tetragonal distortions can be attributed electronically to the Jahn-Teller effect. It states that if the ground state electronic configuration of a non-linear complex is orbitally degenerate, the complex will distort so as to remove the degeneracy and achieve a lower energy. An octahedral d 9 complex has three electrons in its e g set of orbitals. The unpaired electron can occupy either of the d z2 or d x2-y2 orbital because they are energetically degenerate. Essentially, it resonates between the two orbitals and this destabilizes the complex. However, if the geometry is physically distorted and we allow one metal-ligand bond axis to lengthen, this will remove the degeneracy of the e g set and one orbital will become lower in energy than the other. Therefore, the paired electrons will preferentially occupy the lower energy orbital and the unpaired electron will populate the highest energy orbital. This results in a lowering of the overall ligand field stabilization energy for the complex. The distortion to give a square planar complex, where two of the ligands are removed entirely, is an extreme case of tetragonal distortion, but should not be confused with the Jahn- Teller distortion because d 8 electron configurations are not orbitally degenerate. The Jahn-Teller effect can only identify an unstable electron configuration; it does not predict the preferred distortion. d x2-y2 d x2-y2 d z2 d x2-y2 z-axis elongation d z2 Barycentre d z2 d x2-y2 z-axis elongation d z2 Barycentre d xy d yz d xz d xy d xy d yz d xz d xy d 9 d yz d xz l.s. d 7 d yz d xz d x2-y2 d z2 d x2-y2 z-axis elongation d z2 Barycentre d xy d yz d xz h.s. d 4 d yz d xy d xz Ligand Field Theory Although crystal field theory is useful in approximating energy levels in transition metal complexes, the fact that it ignores any possible covalent bonding interactions between the metal and its surrounding ligands is rubbish. We have already noted that the ligand field splitting parameters, Δ, are strongly dependant upon both the metal AND the ligand (thus the spectrochemical series of ligands). So then, why does the spectrochemical series arrange the ligands the way it does? What is common with the strong field ligands that allows them to increase Δ? Does the electron configuration in the atomic and molecular orbitals in these ligands have something to do with it? Of course it does! You are recommended to revise your understanding of basic Molecular Orbital theory for simple diatomic molecules (covered in Sections 2.8 and 2.9 of S & A 4Ed). Recall that in constructing molecular orbitals from atomic orbitals, the number of orbitals must remain constant (i.e. number of MOs equals the number of AOs). Typically, we place the more electronegative element on the right hand side and that its AOs are lower in energy. Remember also that for most heteronuclear diatomic C. M. Kozak Chemistry 3211 3

complexes, orbital mixing occurs (i.e. there is a hybridization of the atomic s and p orbitals because of similar energies). Below are molecular orbital diagrams for three simple diatomics, which will be useful in explaining various aspects of Ligand Field/Molecular Orbital theory for metal complexes. Note the difference in the arrangement of the σ 2p and π 2p orbitals between O 2 and N 2. Recall that for O 2 (and F 2 and Ne 2 ) the energy difference between the 2s and 2p orbitals is large and therefore no s-p orbital mixing is observed. The highest occupied molecular orbital (HOMO) in N 2 is of σ symmetry (a lone pair which can act as a Lewis base to form a coordinate covalent bond) whereas the HOMO in O 2 is of π* symmetry. The bonding modes exhibited by N 2 and O 2 should therefore be slightly different, and indeed they are, but more on that later! C. M. Kozak Chemistry 3211 4

Molecular Orbital Diagram for CO Carbon monoxide, or carbonyl, ligands are found throughout coordination chemistry and metal carbonyl compounds are particularly important as catalysts in organic synthesis. CO is isoelectronic with N 2 (C has one less electron than N, O has one more), therefore the MO diagram is very similar to that of N 2. It is diamagnetic, with a bond order of 3 (C O) and has a HOMO of σ 2p (weakly antibonding) symmetry and a lowest unoccupied molecular orbital (LUMO) of π* 2p (strongly antibonding) symmetry. Since O is far more electronegative than C, we would expect a large dipole moment with δ- on O. However, CO actually has only a small dipole moment (0.1 Debye) with the δ- charge on carbon. Usually electronegativities are a good indication of the direction and magnitude of the dipole on a molecule, but especially in molecules where orbitals with antibonding character are occupied, things are not so straightforward. As a result, CO ligands are good Lewis bases and are σ donors at the carbon atom. Also, the vacant π* orbital LUMO can act as an electron pair acceptor capable of forming metal ligand π bonds. These types of bonding in metal complexes are described by Ligand Field theory, which combines aspects of Crystal Field theory with the more rigorous treatment of bonding given by MO theory. It uses symmetry-adapted linear combinations (SALCs) of metal-ligand interactions and, as the name suggests, relies on some application of symmetry elements and group theory to produce a viable bonding model. Sigma (σ) Bonding Consider an octahedral complex in which each ligand has a single valence orbital directed toward the central metal atom. Each of these orbitals has local σ symmetry with respect to the M-L axis. Such ligands are termed sigma donor ligands and can be neutral, such as ammonia, NH 3, or charged, such as fluoride, F -. In a strictly octahedral environment, the metal orbitals divide by symmetry into four sets, which are given labels that describe their symmetry (subscripts g or u, 1 or 2), and their multiplicity (a or b, e, t). The resulting Symmetry Labels (also called Mulliken Symbols) are used to now describe sets of orbitals in a complex, rather than just the atomic orbital. Therefore, orbitals or groups of metal orbitals that are labelled by a particular Mulliken Symbol can only interact with a ligand set of orbitals that is described by the same label. C. M. Kozak Chemistry 3211 5

Metal Orbital Symmetry Label Degeneracy s p x, p y, p z d xy, d yx, d xz d x2-y2, d z2 a 1g t 1u t 2g e g 1 3 3 2 Six symmetry-adapted linear combinations of the six ligand σ symmetry orbitals can also be formed. These combinations are shown below, where we are only considering ligand s orbitals to keep things simple. Bear in mind that these are not specifically s or p atomic orbitals any more, but only the orbitals, atomic or molecular, which exhibit σ symmetry with respect to the metal-ligand bond axis. We are now treating all six ligands as a group. Among the metal orbitals, only the t 2g set (d xy, d xz, d yz ) does not possess suitable symmetry to undergo σ-bonding interactions with the ligand SALCs. However, it does possess π symmetry, which will be discussed later. Molecular orbitals for the resulting complex are formed by combining SALCs and metal orbitals of the same symmetry type. Since we have six metal orbitals that can be broken down into three groups according to their symmetry (a 1g, t iu and e g ) and six ligand SALCs, these combine to form 6 bonding and 6 antibonding MOs. The metal t 2g set remains non-bonding in this scenario. The resulting MO diagram can now be populated with electrons according to the Aufbau process, Pauli principle and Hund s rule. For the resulting energy levels, the greatest contribution to the molecular orbital of lowest energy is from atomic orbitals of lowest energy. For most ligands, particularly those of period 2 and 3 (n quantum number 3) in the main group, the ligand σ orbitals are derived from AOs with energies much lower than those of the metal d-orbitals. Thus, the six bonding MOs of the complex are mostly ligand-orbital in character. These six bonding orbitals can accommodate the 12 electrons provided by the six ligand lone pairs. Therefore, the electrons provided by the ligands are largely confined to the ligands in the complex. However, this is not to say that there is no metal character in these MOs, or that there is no ligand electron density present near the central metal atom. C. M. Kozak Chemistry 3211 6

The d electrons of the metal centre, if any, occupy the lower energy, non-bonding metal t 2g set and the higher energy, antibonding e g set. Therefore, the metal based d electrons tend to reside largely on the metal atom. In summary, the frontier orbitals of the complex are the non-bonding, entirely metal based t 2g orbitals and the antibonding e g orbitals, which are mainly metal in character anyway. Therefore, because most bonding (and therefore chemistry ) occurs in the valence (or frontier ) orbitals of a compound, most reactions of metal complexes occur at the metal centre. The octahedral ligand field splitting parameter, Δ o, in this approach is called the HOMO-LUMO separation, or HOMO-LUMO gap. It is approximately the splitting of the metal d orbitals caused by the ligands, whereas in CFT Δ o is purely a metal d orbital separation. The diagram below shows how the SALCs of the ligand orbital sets combine with the metal orbitals to produce molecular orbital energy levels (the MO diagram) of an octahedral ML 6 complex. The t 2g and e g * (which is now of antibonding symmetry with respect to the M-L bond) are empty in this diagram, suggesting the metal ion, M, has a d 0 electron configuration. LFT explains very well the problem that Werner faced regarding the ability of a metal to bind numerous ligands (secondary valence). With several d orbitals (as well as s and p orbitals) available in the valence shell, enough delocalized MOs C. M. Kozak Chemistry 3211 7

can be constructed to accommodate all the electrons needed to bind the ligands. Also, since lanthanides have f orbitals as well, they can accommodate even more ligand electrons and, therefore, can easily have coordination numbers higher than 6. C. M. Kozak Chemistry 3211 8

Pi (π) Bonding The above diagram ignores any potential π bonding that may be present (the t 2g set is non-bonding). If the ligands in a complex have orbitals with local π symmetry with respect to the M-L axis (a t 2g ligand SALC), then they may form π MOs with the t 2g set of metal orbitals. These ligand π orbitals may be populated or vacant and, therefore, may act as electron donors or acceptors as shown in the diagram below. The effect of this bonding on Δ o depends on where the electron density is going. For π-acceptor ligands, the bonding is SYNERGIC: σ-donation to the metal strengthens π-backbonding to the ligand, and π-donation from the metal to the ligand strengthens the σ-donor component of bonding. This is because σ-donation leads to increased electron density on the metal, which allows increased π- backdonation. Conversely, π-backdonation reduces the amount of electron density on the metal, which allows more σ-donation from the ligand to the metal. C. M. Kozak Chemistry 3211 9

A π donor ligand has filled orbitals that have π symmetry around the M-L axis. The energies of these orbitals are similar to those of the metal d orbitals and the ligand has no vacant low energy π orbitals (strictly speaking these are of π* symmetry). Examples of π donor ligands include Cl -, OH -, NR 2 - and H 2 O. These all turn out to be low in the spectrochemical series (weak field ligands) that lower Δ o. The full π orbitals of the π donor ligands lie lower in energy than the partially filled d orbitals of the metal. This means that when they form molecular orbitals with the metal t 2g orbitals, the bonding combination lies lower than the ligand orbitals and the antibonding combination lies above the energy of the d orbitals of the free metal (figure below on the left). The result is that ligand electrons occupy the bonding t 2g MO, while the metal electrons now occupy the antibonding t 2g MO set, which has been raised in energy. Ligands that are π donors decrease Δ o. Ligands that are π acceptors increase Δ o. A π-acceptor ligand is a ligand that has filled π orbitals, which are much lower in energy than the metal t 2g orbitals. It also has empty π orbitals which are close enough in energy to the metal d orbitals to allow population. Examples of ligands that possess orbitals of this appropriate energy are CO and N 2, which their MO diagrams we have described previously. The bonding π orbital of MO is populated and is largely localized on the O atom because O is more electronegative than C, hence the lower energy π bonding orbital is mostly O in character. The antibonding π* orbital of CO has its largest amplitude on C and has appropriate symmetry and energy to overlap the t 2g orbitals of the metal. Because of the resulting energy correlation, the π donor ability of CO is very small, and its bonding to metals is dominated by its π acceptor character along with its σ donor ability (see diagram below). Because these π acceptor ligands are typically of antibonding character with respect to the ligand atoms, they lie higher in energy than the metal d orbitals, they form molecular orbitals of t 2g symmetry which are largely of metal d orbital in nature. These bonding combinations lie slightly lower in energy than the metal d orbitals themselves. As a result, Δ o is increased due to the pushing down in energy of the bonding t 2g symmetry molecular orbitals. C. M. Kozak Chemistry 3211 10

The spectrochemical series can now be put in perspective on account of the σ and π binding ability of the ligands. Strong σ donors, like H - and CH 3 -, are high in the series. When π bonding is taken into consideration, strong π acceptors are high in the series due to their ability to increase Δ o. Strong π donors are low in the spectrochemical series due to their lowering effect on Δ o. Below is the resulting molecular orbital (MO) diagram for an octahedral complex with strong π- acceptor ligands (e.g. Cr(CO) 6 ). The Cr 0 centre is a 3d 6 configuration. The 6 CO ligands each donate two electrons to the metal centre via σ bonding. The π bonding symmetry orbitals of the ligands are also populated, but cannot effectively act as π donors to the metal centre, partially because of their energies being much lower than the appropriate symmetry metal t 2g set, but also because the metal d 6 centre has its t2g set populated by metal based electrons; electron-electron repulsion further hinders any π donor ability from the CO ligand. C. M. Kozak Chemistry 3211 11

The antibonding π* orbitals of the CO ligand are vacant and are low enough in energy to undergo orbital overlap with the populated metal t 2g set. Therefore, the metal back-donates this electron density into the CO π* orbitals. In total, this complex has 18 electrons that participate in bonding. In transition metal complexes, this 18 electron rule is similar to the octet rule used in main group chemistry. Complexes possessing 18 bonding electrons are particularly stable. Werner studied Co 3+ ammine complexes because of their stability. The Co3+ ion has a 3d 6 configuration. Each ammine ligand is a two electron donor, hence [Co(NH 3 ) 6 ] 3+ possess 6 + (6 2) = 18 electrons. Although a large number of exceptions to this rule are found in classical coordination chemistry, the stability of organometallic compounds (those possessing metal-carbon bonds) is strongly attributed to this effect. C. M. Kozak Chemistry 3211 12