In the previous exercise a collection of ligands were placed in order from those producing the smallest to the largest d-orbital splitting in coordination compounds. This ordering of ligands is called a Spectrochemical Series. An expanded Spectrochemical Series is shown below.
Pyridine, , is represented by the abbreviation py. Two ligands, thiocyanate and nitrite, display linkage isomerism. Coordination to a metal occurs through the atom on the left.
Ligands that produce a small Δ are called weak-field ligands and lie at the left end of the series. Ligands that produce a large Δ are called strong-field ligands and lie at the right end of the series.
Recall that the Cr3+ ions in ruby and emerald are each surrounded by six oxide ions in an octahedral environment. The Cr-O distance is nearly identical for the two gems (1.913 Å in ruby and 1.906 Å in emerald). What differs between the two gems is the distribution of the other ions in the corunudum and beryl structures. The net result is that the beryl structure is a slightly weaker field ligand than the corunudum structure. Consequently, Δo is slightly smaller for emerald (16500 cm-1) than for ruby (17800 cm-1), as discussed in a previous exercise. It is this modest difference in Δo that makes the ruby red and the emerald green.
What factors determine the sequence of ligands in the Spectrochemical Series?
Before examining the specific factors determining the Spectrochemical Series, it should be noted that the Spectrochemical series in not an absolute ordering of ligands. The observed order in the series varies somewhat from one complex to another. The identity and oxidation state of the metal and the number and identities of the other ligands play a role in establishing the sequence for a particular class of complexes. The order of ligands shown above represents a general trend, but do not be surprised if you find another source presenting a Spectrochemical Series with a somewhat different sequence of ligands.
Sigma Bonding Interactions
The essential feature of a coordination compound is the donation of a pair of electrons by the ligand to form a coordinate covalent bond with the metal. This interaction is illustrated in the following energy diagram for an octahedral complex. (The six ligand donor orbitals are grouped into two sets, one of which has appropriate symmetry for interacting with the metal dz2 orbital and the other with appropriate symmetry for interacting with the metal dx2-y2 orbital. Thus two ligand orbitals are shown in the diagram. See the energy diagram for [Co(NH3)6]3+.)
Sigma Bonding in an Octahedral Complex
The Lewis acid-base reaction between the metal and the ligand results in a set of low energy, fully occupied (because the original ligand donor orbitals were fully occupied) σ bonding orbitals that are primarily localized on the ligand and a set of high energy σ* orbitals that are primarily localized on the metal. Three of the metal orbitals (dxy, dxz, and dyz) do not interact with the ligand orbitals and remain as nonbonding orbitals completely centered on the metal.
The d-orbital splitting, Δo, arises from the increase in energy of the σ* orbitals relative to the nonbonding orbitals. The stronger the bonding interaction, the higher the σ* energy and the greater Δo. A strong σ bonding interaction requires a good energy match between the metal and the ligand. Empirically, there is a correlation between Δo and the basicity of the ligand. A ligand that is a good Brønsted (or Lewis) base tends to form strong ? bonds with metals and thus produces a relatively large Δo.
The size of a ligand is significant, because the closer the ligand can approach the metal, the better the orbital overlap and consequently the larger Δo. Thus smaller ligands tend to have larger Δo than larger ligands. The trend in halide ligands reflects both of these effects:
I- < Br- < Cl- < F-
The Spectrochemical Series for the halides follows the trend in basicity (fluoride ion is the best base among the halides) and the reverse trend in size (fluoride ion is the smallest of the halides).
Pi Bonding Interactions
Some ligands are capable of π bonding interactions, either by acting as a π acceptor ([Cr(CO)], for example) or a π donor ([Cr(F)]2+, for example). The energy diagram shown below illustrates the behavior of a π donor ligand on Δo.
Pi-Donor Ligand in an Octahedral Complex
The π bonding behavior is similar to that for the σ bonding. The occupied ligand orbitals are lower in energy than the metal orbitals. Thus the new π orbitals, like the σ orbitals, are of low energy and are fully occupied. In addition, these orbitals are localized primarily on the ligand. The metal d orbitals that had been nonbonding in the σ-only case (vide supra) now become π* orbitals and are shifted to higher energy, which results in a decrease in the magnitude of Δo. (Note that the six π donor orbitals are grouped into three sets of orbitals that have correct symmetry to interact with the metal dxy, dxz, and dyz orbitals.)
By contrast, a ligand with π-acceptor properties has unoccupied orbitals at energies well above the metal dxy, dxz, and dyz orbitals with which mixing occurs to form π and π* orbitals. In this case, the π* orbitals are localized on the ligand (not the metal). The former nonbonding d orbitals now become π orbitals and are shifted to lower energies, thus increasing Δo.
Pi-Acceptor Ligand in an Octahedral Complex
The net effect, as regards the Spectrochemical Series, is that π-acceptor ligands produce large values for Δo and are typically strong-field ligands, whereas π-donor ligands produce small values for Δo are are typically weak-field ligands.
Note that carbon monoxide is a very poor Brønsted base, but it lies at the strong-field extreme of the Spectrochemical Series on account of its very strong π-acceptor properties. Use π-bonding interactions to explain the relative positions in the Spectrochemical Series for the following pairs of ligands. (It may be helpful to draw Lewis structures for each ligand.)
Explain how the polarizability of the coordination site atom affects the position of a ligand in the Spectrochemical Series.
Ligand donor orbitals, whether σ or π in nature, are usually fully occupied, and consequently the associated metal-ligand σ and π orbitals are filled. In the case of a π-acceptor ligand, the acceptor orbitals are unoccupied (which is why the ligand can serve as an acceptor), and the resulting π* orbitals are also unoccupied.
A critical aspect of the electron configuration is the occupancy of the metal d orbitals, which may be σ*, π*, π, or n in character. For a transition metal, the number of valence electrons in the free atom is given by the atom's group. Iron is a Group 8 transition metal and thus has eight valence electrons (3d6 4s2). Silver is a Group 11 transition metal and thus has 11 valence electrons (4d10 5s1). Subtract the atom's oxidation state from the number of valence electrons to obtain the number of d electrons. For Fe2+, there are 8 - 2 = 6 d electrons, thus Fe2+ is a d6 metal ion. Similarly, Ag+ is a d10 metal ion (11 - 1 = 10). While the Aufbau Principle places electrons in the (n+1)s orbital before the nd orbital, in a cation the nd orbital is always lower in energy than the (n+1)s orbital, and therefore ionization of an atom always removes electrons from the orbital with the highest principal quantum number.
The d electrons reside in the former metal d orbitals, which are now split by the interaction with the ligands. Consider a d4 atom in an octahedral complex. There are two different ways to distribute the electrons.
In the configuration at the left, all electrons reside in the three low-lying orbitals. Hund's Rule requires the first three electrons be placed spin up (+1/2) in separate orbitals and the fourth electron be placed spin down (-1/2) in one orbital. While this keeps all four electrons in the lowest energy orbitals, it requires two electrons be paired. The price (in energy) to be paid for pairing electrons is called the Pairing Energy, P. The alternative, shown at the right, is to place one electron (spin up) in the σ* set of orbitals. This configuration avoids pairing electrons, but an energy Δo is required to promote an electron to the σ* orbital.
The electron configuration on the left is called low spin (total spin = 1/2 + 1/2 + 1/2 - 1/2 = 1), while the configuration on the right is called high spin (total spin = 1/2 + 1/2 + 1/2 + 1/2 = 2).
Whether a complex is low spin or high spin depends upon the relative sizes of the pairing energy and the splitting energy. If P > Δo, the complex will be high spin, because promotion of an electron to a σ* orbital requires less energy than pairing an electron. If P < Δo, the complex will be low spin.
The Fe2+ ion is d6 and has a pairing energy of approximately 17000 cm-1 (this is 2.1 eV or 200 kJ mol-1). (The pairing energy varies somewhat with the coordination environment.) For [Fe(H2O)6]2+, Δo = 10000 cm-1. Because P > Δo, [Fe(H2O)6]2+ is a high-spin complex. The electron configuration is (π*)4 (σ*)2 and the total spin is 2. (Note that water is a weak π-donor ligand.) On the other hand, for [Fe(CN)6]4- Δo = 33800 cm-1, and this complex is low-spin (P < Δo). All six d electrons reside in the low lying (π) orbitals (cyanide is an excellent π-acceptor ligand), leading to a total spin of zero.
As one moves down a group, the pairing energy decreases and Δo increases. For this reason, almost all second- and third-row transition metal complexes are low spin. First-row transition metals may be either low spin or high spin. Because tetrahedral complexes have much smaller splitting (Δt) than octahedral complexes (Δo), almost all tetrahedral first-row transition metal complexes are high spin. For octahedral complexes, the nature of the ligand plays a major role in determining whether the complex is low spin or high spin. Weak-field ligands give rise to small Δo and thus are high spin. Strong-field ligands give rise to large Δo and are low spin.
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