Bonding in Coordination Compounds: Crystal Field Theory

Crystal Field Theory

Crystal field theory states that d or f orbital degeneracy can be broken by the electric field produced by ligands, stabilizing the complex.

Learning Objectives

Discuss the relationships between ligand binding in a metal complex and the degeneracy of the d orbitals and between the geometry of a metal complex and the splitting of the d orbitals.

Key Takeaways

Key Points

  • When the ligands approach the central metal ion, d- or f-subshell degeneracy is broken due to the static electric field.
  • Because electrons repel each other, the d electrons closer to the ligands will have a higher energy than those further away, resulting in the d orbitals splitting.
  • The crystal field stabilization energy (CFSE) is the stability that results from ligand binding.

Key Terms

  • degenerate: Having the same quantum energy level.
  • ligand: An ion, molecule, or functional group that binds to another chemical entity to form a larger complex.

The Crystal Field Theory (CFT) is a model for the bonding interaction between transition metals and ligands. It describes the effect of the attraction between the positive charge of the metal cation and negative charge on the non-bonding electrons of the ligand. When the ligands approach the central metal ion, the degeneracy of electronic orbital states, usually d or f orbitals, are broken due to the static electric field produced by a surrounding charge distribution. CFT successfully accounts for some magnetic properties, colors, and hydration energies of transition metal complexes, but it does not attempt to describe bonding.

The electrons in the d orbitals of the central metal ion and those in the ligand repel each other due to repulsion between like charges. Therefore, the d electrons closer to the ligands will have a higher energy than those further away, which results in the d orbitals splitting in energy. This splitting is affected by:

  • the nature of the metal ion
  • the metal’s oxidation state (a higher oxidation state leads to a larger splitting)
  • the arrangement of the ligands around the metal ion
  • the nature of the ligands surrounding the metal ion

All of the d orbitals have four lobes of electron density, except for the dz2 orbital, which has two opposing lobes and a doughnut of electron density around the middle. The d orbitals can also be divided into two smaller sets. The dx2y2 and dz2 all point directly along the x, y, and z axes. They form an eg set. On the other hand, the lobes of the dxy, dxz, and dyz all line up in the quadrants, with no electron density on the axes. These three orbitals form the t2g set. In most cases, the d orbitals are degenerate, but sometimes they can split, with the eg and t2g subsets having different energy. The CFT accounts for this.

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d orbitals: This gives an overview of the d orbitals. The central model shows the combined d-orbitals on one set of axes.

The crystal field stabilization energy (CFSE) is the stability that results from placing a transition metal ion in the crystal field generated by a set of ligands. It arises due to the fact that when the d orbitals are split in a ligand field, some of them become lower in energy than before. For example, in the case of an octahedron, the t2g set becomes lower in energy. As a result, if there are any electrons occupying these orbitals, the metal ion is more stable in the ligand field by the amount known as the CFSE. Conversely, the eg orbitals are higher in energy. So, putting electrons in them reduces the amount of CFSE.

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Octahedral CFT splitting: Electron diagram for octahedral d shell splitting.

Crystal field stabilization is applicable to the transition-metal complexes of all geometries. The reason that many d8 complexes are square-planar is the very large amount of crystal field stabilization that this geometry produces with this number of electrons.

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Square planar CFT splitting: Electron diagram for square planer d subshell splitting.

Octahedral Complexes

Octahedral complexes have six ligands symmetrically arranged around a central atom, defining the vertices of an octahedron.

Learning Objectives

Discuss the degeneracy of the d orbitals in an octahedral metal complex.

Key Takeaways

Key Points

  • The term octahedral is used somewhat loosely by chemists, focusing on the geometry of the bonds to the central atom and not considering differences among the ligands themselves.
  • When two or more ligands are coordinated to an octahedral metal center, the complex can exist as isomers.
  • In an octahedral complex, the d-subshell degeneracy is lifted.

Key Terms

  • degeneracy: Having the same quantum energy level.
  • ligand: An ion, molecule, or functional group that binds to another chemical entity to form a larger complex.
  • vertex: The common point of the two rays of the angle, or its equivalent structure in polyhedra (meeting of edges) and higher order polytopes.

Octahedral molecular geometry describes the shape of compounds wherein six atoms or groups of atoms or ligands are symmetrically arranged around a central atom. The octahedron has eight faces, hence the prefix octa-. An example of an octahedral compound is molybdenum hexacarbonyl (Mo(CO)6).

The term octahedral is used somewhat loosely by chemists, focusing on the geometry of the bonds to the central atom and not considering differences among the ligands themselves. For example, [Co(NH3)6]3+, which is not octahedral in the mathematical sense due to the orientation of the N-H bonds, is referred to as octahedral.

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Hexamminecobalt(III) chloride: Example of an octahedral coordination complex.

When two or more types of ligands are coordinated to an octahedral metal center, the complex can exist as isomers. The number of possible isomers can reach 30 for an octahedral complex with six different ligands (in contrast, only two stereoisomers are possible for a tetrahedral complex with four different ligands).

For a free ion, such as gaseous Ni2+ or Mo, the d orbitals are degenerate. In an octahedral complex, this degeneracy is lifted. The dz2 and dx2−y2 (the so-called eg set), which are aimed directly at the ligands, are destabilized. On the other hand, the dxz, dxy, and dyz orbitals (the so-called t2g set) see a decrease in energy.

Given that such a variety of octahedral complexes exist, it is not surprising that a wide variety of reactions have been described. These reactions can be classified as follows:

  • Ligand substitution reactions (via a variety of mechanisms)
  • Ligand addition reactions, including protonation (among many others)
  • Redox reactions (in which electrons are gained or lost)
  • Rearrangements where the relative stereochemistry of the ligands change within the coordination sphere

Many reactions of octahedral transition metal complexes occur in water. For example, [Co(NH3)5Cl]2+ slowly aquates to give [Co(NH3)5(H2O)]3+ in water, especially in the presence of acid or base.

Tetrahedral and Square Planar Complexes

Both tetrahedral and square planar complexes have a central atom with four substituents.

Learning Objectives

Discuss the d-orbital degeneracy of square planar and tetrahedral metal complexes.

Key Takeaways

Key Points

  • In tetrahedral molecular geometry, a central atom is located at the center of four substituents, which form the corners of a tetrahedron.
  • Tetrahedral geometry is common for complexes where the metal has d0 or d10 electron configuration.
  • The CFT diagram for tetrahedral complexes has dx2−y2 and dz2 orbitals equally low in energy because they are between the ligand axis and experience little repulsion.
  • In square planar molecular geometry, a central atom is surrounded by constituent atoms, which form the corners of a square on the same plane.
  • The square planar geometry is prevalent for transition metal complexes with d8 configuration.
  • The CFT diagram for square planar complexes can be derived from octahedral complexes yet the dx2-y2 level is the most destabilized and is left unfilled.

Key Terms

  • substituents: Any atom, group, or radical substituted for another, or entering a molecule in place of some other part which is removed.
  • degeneracy: Having the same quantum energy level.
  • ligand: An ion, molecule, or functional group that binds to another chemical entity to form a larger complex.
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Tetrakis(triphenylphosphine)palladium: 3-dimensional representation of tetrahedral Tetrakis(triphenylphosphine)palladium

Tetrahedral Complexes

In tetrahedral molecular geometry, a central atom is located at the center of four substituent atoms, which form the corners of a tetrahedron. The bond angles are approximately 109.5° when all four substituents are the same. This geometry is widespread, particularly for complexes where the metal has d0 or d10 electron configuration.

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Nickel carbonyl: 2-dimensional representation of tetrahedral nickel carbonyl.

For example, tetrakis(triphenylphosphine)palladium(0), a popular catalyst, and nickel carbonyl, an intermediate in nickel purification, are tetrahedral. Many complexes with incompletely filled d-subshells are tetrahedral as well—for example, the tetrahalides of iron(II), cobalt(II), and nickel(II).

Tetrahedral complexes have ligands in all of the places that an octahedral complex does not. Therefore, the crystal field splitting diagram for tetrahedral complexes is the opposite of an octahedral diagram. The dx2−dy2 and dz2 orbitals should be equally low in energy because they exist between the ligand axis, allowing them to experience little repulsion. In contrast, the dxy,dyz, and dxz axes lie directly on top of where the ligands go. This maximizes repulsion and raises energy levels.

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Tetrahedral CFT splitting: Notice the energy splitting in the tetrahedral arrangement is the opposite for the splitting in octahedral arrangements.

Square Planar Complexes

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Carboplatin: 2- and 3-dimensional representations of the anti-cancer drug carboplatin

In square planar molecular geometry, a central atom is surrounded by constituent atoms, which form the corners of a square on the same plane. The geometry is prevalent for transition metal complexes with d8 configuration. This includes Rh(I), Ir(I), Pd(II), Pt(II), and Au(III). Notable examples include the anticancer drugs cisplatin [PtCl2(NH3)2] and carboplatin.

In principle, square planar geometry can be achieved by flattening a tetrahedron. As such, the interconversion of tetrahedral and square planar geometries provides a pathway for the isomerization of tetrahedral compounds. For example, tetrahedral nickel(II) complexes such as NiBr2(PPh3)2 undergo this change reversibly..

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CFT energy diagram for square planar complexes: Notice how the dx2 – y2 orbital is unfilled.

The removal of a pair of ligands from the z-axis of an octahedron leaves four ligands in the x-y plane. Therefore, the crystal field splitting diagram for square planar geometry can be derived from the octahedral diagram. The removal of the two ligands stabilizes the dz2 level, leaving the dx2-y2 level as the most destabilized. Consequently, the dx2-y2 remains unoccupied in complexes of metals with the d8 configuration. These compounds typically have sixteen valence electrons (eight from ligands, eight from the metal)

Color

Transition metal complexes are often colored due to either d-d or change band electron transitions induced by the absorption of light.

Learning Objectives

Discuss the process which provides color in coordination complexes.

Key Takeaways

Key Points

  • The colors in metal complexes come from the d orbitals because they are not involved in bonding.
  • d-d electron transitions are allowed in complexes if the center of symmetry is disrupted, resulting in a vibronic transition.
  • In Metal-to- Ligand Charge Transfer (MLCT), electrons can be promoted from a metal-based orbital into an empty ligand-based orbital.
  • An electron may jump from a predominantly ligand orbital to a predominantly metal orbital (Ligand-to-Metal Charge Transfer or LMCT).
  • Coordination complex color results from the absorption of complimentary colors.

Key Terms

  • ligand: An ion, molecule, or functional group that binds to another chemical entity to form a larger complex.
  • band theory: In a solid, those ranges of energy that an electron is allowed to have.
  • centrosymmetric: Having a center of symmetry.
  • orbital: A specification of the energy and probability density of an electron at any point in an atom or molecule.

Color in Coordination Compounds

Metal complexes often have spectacular colors caused by electronic transitions induced by the absorption of light. For this reason, they are often applied as pigments. We know that light can be emitted corresponding to the difference in energy levels. We could expect them to come from the d-orbitals. This is because they are not involved in bonding, since they do not overlap with the s and p orbitals of the ligands. Most transitions that are related to colored metal complexes are either d–d transitions or charge band transfer.

d-d Transitions

In a d–d transition, an electron in a d orbital on the metal is excited by a photon to another d orbital of higher energy. In complexes of the transition metals, the d orbitals do not all have the same energy. In centrosymmetric complexes, d-d transitions are forbidden by the Laporte rule. The Laporte rule states that, if a molecule is centrosymmetric, transitions within a given set of p or d orbitals are forbidden. However, forbidden transitions are allowed if the center of symmetry is disrupted. Transitions that occur as a result of an asymmetrical vibration of a molecule are called vibronic transitions. Through such asymmetric vibrations, transitions that would theoretically be forbidden, such as a d-d transition, are weakly allowed.

An example occurs in octahedral complexes such as in complexes of manganese(II). It has a d5 configuration in which all five electrons have parallel spins. The color of such complexes is much weaker than in complexes with spin-allowed transitions. In fact, many compounds of manganese(II), like manganese(II) chloride, appear almost colorless. Tetrahedral complexes have somewhat more intense color. This is because mixing d and p orbitals is possible when there is no center of symmetry. Therefore, transitions are not pure d-d transitions.

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Example of weaker color due to d-d transition: Sample of manganese(II) chloride.

Change Band Transfer

Electrons can also be transferred between the orbitals of the metal and the ligands. In Metal-to-Ligand Charge Transfer (MLCT), electrons can be promoted from a metal-based orbital into an empty ligand-based orbital. These are most likely to occur when the metal is in a low oxidation state and the ligand is easily reduced. Ligands that are easily reduced include 2,2′-bipyridine (bipy), 1,10-phenanthroline (phen), CO, CN-, and SCN-. An example of color due to MLCT is tris(2,2′-bipyridyl)ruthenium(II), which is a versatile photochemical redox reagent.

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Example of color due to MLCT transition: Sample of tris(bipyridine)ruthenium(II)-chloride

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Examples of color due to LCMT transitions: Samples of (from top to bottom) potassium chromate, potassium dichromate, and potassium permanganate.

Conversely, an electron may jump from a predominantly ligand orbital to a predominantly metal orbital (Ligand-to-Metal Charge Transfer or LMCT). These can most easily occur when the metal is in a high oxidation state. For example, the color of chromate, dichromate, and permanganate ions is due to LMCT transitions.

“Seeing” Color

We can perceive colors for two reasons: either we see it because that color is the only color not absorbed or because all colors of visible light are absorbed except for a particular color known as its complimentary color.

Large energy differences should correspond to smaller wavelengths and purple colors, while small energy differences should result in large wavelengths and colors closer to red. For example, you might expect to see red for a complex with a small energy gap and large wavelength. Green is the compliment of red, so complexes with a small energy gap will actually appear green.

The color we see for coordination complexes is a result of absorption of complimentary colors. A decrease in the wavelength of the complimentary color indicates the energy gap is increasing and can be used to make general rankings in the strengths of electric fields given off by ligands. These phenomena can be observed with the aid of electronic spectroscopy (also known as UV-Vis).

Magnetic Properties

Metal complexes that have unpaired electrons are magnetic.

Learning Objectives

Discuss the correlation between the electronic structure of a coordination complex and its magnetic properties.

Key Takeaways

Key Points

  • Unpaired electrons exist when the complex has an odd number of electrons or because electron pairing is destabilized.
  • The more unpaired electrons, the stronger the magnetic property.
  • Tetrahedral complexes have weaker splitting because none of the ligands lie within the plane of the orbitals.
  • Square planar compounds are always low-spin and therefore are weakly magnetic.
  • In bi- and polymetallic complexes, the electrons may couple through the ligands, resulting in a weak magnet, or they may enhance each other.

Key Terms

  • diamagnetic: Exhibiting diamagnetism; repelled by a magnet.
  • ligand: An ion, molecule, or functional group that binds to another chemical entity to form larger complex.
  • paramagnetic: Exhibiting paramagnetism (the tendency of magnetic dipoles to align with an external magnetic field).

Magnetic Properties of Coordination Compounds

An interesting characteristic of transition metals is their ability to form magnets. Metal complexes that have unpaired electrons are magnetic. Since the last electrons reside in the d orbitals, this magnetism must be due to having unpaired d electrons. Considering only monometallic complexes, unpaired electrons arise because the complex has an odd number of electrons or because electron pairing is destabilized.

For example, monomeric Ti(III) species have one d electron and must be (para)magnetic, regardless of the geometry or the nature of the ligands. Ti(II), with two d electrons, forms some complexes that have two unpaired electrons and others with none.

As an example, Fe prefers to exist as Fe3+ and is known to have a coordination number of six. Since the configuration of Fe3+ has five d electrons, we would expect to see five unpaired spins in complexes with Fe. This is true for [FeF6]3-; however, [Fe(CN)6]3- only has one unpaired electron, making it a weaker magnet. This trend can be explained based on the properties of the ligands. We expect CN to have a stronger electric field than that of F, so the energy differences in the d orbitals should be greater for the cyanide complex.

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Crystal field theory splitting diagram: Example of influence of ligand electronic properties on d orbital splitting. This shows the comparison of low-spin versus high-spin electrons.

In order for this to make sense, there must be some sort of energy benefit to having paired spins for our cyanide complex. That is, the energy level difference must be more than the repulsive energy of pairing electrons together. Since systems strive to achieve the lowest energy possible, the electrons will pair up before they will move to the higher orbitals. This is referred to as low spin, and an electron moving up before pairing is known as high spin.

Tetrahedral complexes have naturally weaker splitting because none of the ligands lie within the plane of the orbitals. As a result, they have either have too many or too few d electrons to warrant worrying about high or low spin. Square planar compounds, on the other hand, stem solely from transition metals with eight d electrons. [Ni(CN)4]2-, [Pt(NH3)3Cl]+, and [PtCl4]2- are all diamagnetic.

Since this encompasses the full spectrum of ligand strength, we can conclude that square planar compounds are always low spin and therefore are weakly magnetic. In bi- and polymetallic complexes, in which the individual centers have an odd number of electrons or electrons are high-spin, the situation is more complicated.

If there is interaction between the two (or more) metal centers, the electrons may couple, resulting in a weak magnet, or they may enhance each other. When there is no interaction, the two (or more) individual metal centers behave as if in two separate molecules.