Ligand field theory

The crystal and ligand field theory are two different, but mutually complementary theories of complex compounds. The crystal field theory provides a qualitative understanding and the ligand field theory allows quantitative predictions of the properties of transition metal salts or complexes. Both theories explain the structure, color and magnetism of these substances.

A common feature of the crystal field and ligand field theory, the quantum- mechanical treatment of the complex center and the electrostatic description of the ligands.

What is different is the approach of both theories. The crystal field theory leads towards the quantum mechanical reality of the complexes, the ligand field theory is based on the quantum mechanical reality.

For a full understanding of the complex compounds other theories are needed. The most important are the valence bond ( VB theory ) and molecular orbital theory ( MO theory ). The VB theory provides an explanation for the complex geometry that is provided by the crystal field and ligand field theory. The MO theory allows a complete understanding of the covalent binding moiety in complexes.

• 3.1 Principle of the ligand field

• 4.1 Octahedral complexes
• 4.2 Tetrahedral complexes
• 4.3 Square - planar complexes
• 4.4 Other complex geometries

• 5.1 Color
• 5.2 Instrumentation of the orbitals to high-spin or low-spin complexes
• 5.3 magnetism
• 5.4 Thermodynamic stability
• 5.5 Kinetic inertness
• 5.6 Solid State Physics

• 7.1 Notes and references

Structure of the complex compounds

In contrast to the purely electrostatic ion binding, eg in the salt formation, which attract cations and anions electrostatically as point charges, go crystal field and ligand field theory from a partially quantum mechanical description of what is appropriate for most complex compounds. In the description, the crystal field and ligand field theory, the center of the complex is treated quantum mechanically, analogous to the quantum mechanical description of an atom, while the ligands surrounding the center of the complex, are described purely electrostatic. This has simply stated the following consequences:

• Between the central atom and the ligands is an electrostatic attraction.
• Between the central atom and a ligand as well as electrostatic repulsion, because the center of the complex having an electron system having a quantum- mechanical energy given shell structure. The electrons in the outer d orbitals practice because of its negative charge, a repulsion effect on the negatively charged ligand system.

The interaction of electrostatic potential ligands and quantum mechanical structure of the valence electrons of the central atom is essential for both the crystal field and for the ligand field theory.

What is different is the approach of both theories:

• The crystal field theory is based on the description of the ligand as a point-like charges and investigated the effect of so classic well-defined crystal field on the quantum mechanically determined electron system of the complex center ( with the ground state as the purest representatives ).
• The ligand field theory is based on the detailed quantum mechanical description of the complex center of ( ground state plus excited states ) in which the electrostatic ligand field is integrated. The ligand field is characterized here in detail by empirically determinable properties ( field strength), which allows an arbitrarily precise adaptation to the observable reality.

Crystal field theory

The crystal field theory, often abbreviated to CF theory, corresponding to the English term Crystal Field Theory, was from 1932 by John H. van Vleck - based on a work by Hans Bethe in 1929 - designed to explain the physical properties of transition metal salts that show unexpected magnetic and optical behavior.

It is a purely electrostatic model in which the anions or ligands can be regarded as a negative point charges affect the electric field, the crystal field, the electrons in the outer d orbitals of the cation. A crystal is not considered as a whole, but it is picked is a cation and examined only the effect of the nearest neighbor in the lattice.

Principle of the crystal field

The starting point is a classical description of the ligand system, where the ligands are considered as negative point charges, influences their electrostatic field, the crystal field, the electrons of the outer d- orbitals of the complex center. The term " crystal field " expresses that when the effect of the ligand on the complex, the center corresponding to the classic understanding of the crystal only, the influence of the nearest neighbors are examined.

Ligand field theory

The ligand field theory comes from Hermann Hartmann and FE Ilse and was published in 1951. It allows a very accurate interpretation of complex spectroscopic properties.

Principle of the ligand field

Starting point of the ligand field theory is the electrostatic potential ligands, which will be integrated from the beginning in the quantum mechanical description and characterized by empirical- experimental observables such as polarizability and field strength. Therefore, the ligand field theory is also called semi-empirical theory. However, the ligand field theory is no MO theory, because only the valence electrons of the complex center are treated quantum mechanically and not the electron system of the ligand.

Geometry -related energy level splittings

Outdoor center of the complex are the d orbitals degenerate, ie they have the same energy. Bring to an atom in a spherically symmetric ligand field, the degeneracy is preserved, but the energy content increases due to the repulsive interaction between d- electrons and ligands. In real complexes, the ligand system is not spherically symmetric, but has a dependent of the size ratios between the central atom and ligand specific geometry. As a result, some of the ligands destabilize d orbitals stronger than the other and there is a splitting of the energy seen states.

The type of decomposition is determined by the geometry of the ligand system. The crystal field theory provides qualitative assessments in the form of energy-level diagrams. The results are often to be found graphical representations of the state division by the geometry of the ligand system.

The ligand field theory allows one to calculate the magnitude of the splitting very accurately and quantitatively. The magnitude of the splitting depends on the "strength" of the central atom and the "strength" of the ligands. The field strength parameters of the complex components are empirically determined relative to each other and held in Spectrochemical series.

Octahedral complexes

Six point charges arrange themselves in the form of an octahedron around the central atom to. Thus, the orbitals are dz2 and dx2 - y2 raised energy, the orbitals dxy, dyz and dxz lowered in energy. This results in a 2-3 splitting.

A transition metal central atom can potentially 3 × 2 = 6 electrons in three orbitals cheap place, but it has to be expended energy, so that two electrons can be in an orbital. Whether the favorable orbitals are fully occupied, depends on whether this more energy is gained or lost, so how big is the energy difference between the orbitals.

Thus one finds in weak ligand high spin -configured central atoms, in which it has not energetically worthwhile to fully occupy the orbitals achievable, and low spin -configured complex centers with all members present at a relatively strong ligand. The two electron arrangements " high spin " and " low spin " is the octahedral crystal field only for d4, d5, d6, d7.

In an octahedral complex energy levels are degenerate, ie that can not be found, in which orbital an electron is, enters a geometric distortion, while being lifted by this degeneracy. This is called the Jahn -Teller effect.

An example, the valence electron is D1: This electron has to be attributed to one of the three t2g orbitals in an octahedral array. Since it is not determinable, in which it is actually placed, there is a distortion that leads on the one hand, that now can be told exactly in which orbital the electron is on the other hand enters an energy minimization for this electron.

In this example, (d1 ), the Jahn -Teller distortion causes a compression in the z- direction. This results in a further splitting of the t2g and eg orbitals: The orbitals with z -component ( dxz, dyz, dz2 ) could be undermined by the approach of those ligands which are located on the z- axis, whereas those without z- share ( dx2 - y2, dxy ) be further stabilized. In this new energy orbital sequence can be the dxy orbital attributed to an electron, which is now the most stable ( lowest- energy ) orbital represents. Since the amount of stabilization and destabilization is the same, this dxy orbital is now deeper than previously in the " composite " of the degenerate t2g set, which means for the electron that in the distorted (here compressed ) undergoes a greater stabilization octahedron.

As an extension along the z- axis is possible in other cases, whereby the ligands are further away from this axis, the central atom. This goes hand in hand with stabilization of all orbitals z-component and therefore destabilization of all orbitals without z- component.

Jahn -Teller stable complexes, ie those that are not subject to Jahn -Teller distortion: d3, d5 high-spin, low-spin d6, d8 and d10. In these, the electronic states are not degenerate.

Tetrahedral complexes

Four point charges can be arranged in the form of a tetrahedron around the central transition metal. With this geometry, the orbitals dxy, dyz and dxz disadvantage and favors dz2 and dx2 - y2. This gives a splitting 3-2 (t2 and e).

In d3, d4, d5, d6 both configurations " low spin " and expect to "high spin" would be - because of the low -field splitting, however, exist only "high spin" complexes (An exception is, for example, tetrakis (1- norbornyl ) cobalt (IV ) that the norbornyl ligands cause a sufficient splitting ).

The ligand field splitting in the tetrahedral crystal field corresponds to 4/9 of the Oktaederaufspaltung.

Square - planar complexes

Another possibility for four point charges is the square. The resulting splitting is more complicated: dx2 - y2 is a great disadvantage, is slightly disadvantaged dxy, dyz below it on the same level and dxz, dz2 is the deepest ( 1-1-2-1 splitting ). ( Depending on the metal, the order of the two lowest levels can, however, turn around and the dz2 dyz and dxz is above the, eg Ni2 )

This geometry is often found at d8 configurations (or 16 electron complexes ) with a large ligand field splitting. The dx2 - y2 orbital, the energy is very high due to electrostatic repulsion to all ligands, it remains unoccupied.

Typical is this splitting of palladium, platinum and gold cations, since it usually comes to the typical large ligand field splitting with them. All of the complexes formed by these ions are diamagnetic low-spin complexes.

Other complex geometries

The crystal and ligand field theories have also been successfully applied to the interpretation of the effect of many other complex geometries.

Metallocenes: metallocenes have split 2-1-2. Orbitals in the xy plane ( dxy and dx2 - y2) hardly occur in the interaction with ligands and are therefore favored. DZ2 occurs only with a part in the interaction and located in the center. Be destabilized Stark dxz and dyz, the show completely to the rings.

Consequences of the energy splitting

Color

The colors of transition metal salts come about by the described splitting of the d orbitals. Electrons in the beneficiary orbitals can be excited with light in the disadvantaged orbitals. There is only light of a specific wavelength absorbed, which corresponds exactly to the energy difference between advantaged and disadvantaged orbital. Because the gaps are small, is an absorption in the visible region.

Occupation of the orbitals to high-spin or low-spin complexes

There are two ways to occupy d orbitals:

• Is the splitting low, so one can consider the orbitals as approximately degenerate. The cast is then carried out according to Hund's rule, ie first of each singly occupied orbital and the unpaired electrons have parallel spin all. More electrons must receive a negative spin. The complex therefore has a high net spin and is called high-spin complex.

• Is splitting large, the construction principle applies and there are first the lower-energy orbitals doubly occupied. This results in lower total spin of the low-spin complexes.

If an orbital with two electrons to be filled, a spin-pairing energy must be expended. Exceeds the ligand field splitting of the spin-pairing energy, it can come to the " low-spin complex." That lower-lying d orbitals are initially filled with two electrons before higher -lying d orbitals are filled.

Strong ligands promote the ligand-field splitting and thus the formation of low- spin complexes (see Spectrochemical series ). Central atoms of the 5th and 6th period tend thanks to larger ligand field splitting for low-spin complexes. The higher the oxidation number of the central atoms, the stronger ligand -field splitting and hence the preference for low-spin complexes.

Magnetism

The more unpaired electrons are present on the cation, the paramagnetic it is. Based on the statements on the reshuffle of the d orbitals, the magnetic properties of many transition metal salts could be clarified, especially the formulation of high spin and low spin -configured cations explains the high paramagnetism of iron or cobalt salts with weak anion / ligand and the comparatively low paramagnetism in strong anion / ligand. Are all electrons paired, then the ion is diamagnetic.

Thermodynamic stability

A compound is thermodynamically stable if it itself is energetically favorable and a possible product of this compound is energetically less favorable. With the crystal field theory can be estimated on the basis of the d- orbital splitting, if a connection is favorable or unfavorable as their product and how big the difference in energy between. This allows you to predict whether a reaction is thermodynamically possible. Take these predictions to the bulk of the ionic and classical complexes.

Kinetic inertness

A compound is kinetically inert, when the reaction product to a possible, but very slowly, that is, when the activation energy for the reaction product is very high. The crystal field theory allows the calculation of a substantial proportion of the activation energies for the reactions of transition metal complexes by considering how the possible transition states or intermediates could look at the reaction and how the d- orbital splitting and electron distribution changes with formation of these transition states / intermediates on the cation. Are the possible transition states energetically very unfavorable compared to the initial state, the activation energy is very high. Accordingly, the reaction almost never runs out. The statements of the crystal field theory for the kinetics of ligand substitution on complexes are very reliable even for non-classical complexes.

Solid State Physics

The ligand field theory is also used in solid state physics for the description of deep impurities in semiconductor crystals.

Valid ranges of the crystal field and ligand field theory

The crystal field theory is semi- classical and the ligand field theory semi- empirically. In spite of the restrictive conditions, the contribution of the crystal field theory for the qualitative understanding and the contribution of the ligand field theory for the quantitative derivation of complex properties is large. The reason for this is the quantum- mechanical treatment of the complex in the center two theories.

Although the purely quantum mechanical molecular orbital theory provides a more accurate picture of the complex structure because the ligands are treated quantum mechanically, but the resulting splitting pattern the same as in the crystal field and ligand field theory. What describes the crystal field or ligand field theory as a stronger electrostatic repulsion, is in the MO theory larger splitting and increase the antibonding orbitals ( the bonding be occupied by the electrons of the ligands). Only the MO theory provides an understanding of the covalent binding moiety in complexes with π - back-bonding, as occurs in the carbonyl complexes, for example.

The valence -bond (VB ) theory of Linus Pauling provides an explanation for the prerequisite of the crystal field and ligand field complex geometry.

For a full understanding of the complex compounds several theories are required.

The systematic connection between all complex theories, in particular the complementarity of crystal field and ligand field theory, suggests the existence of a unified field molecular behavior, which is closely linked to the spatial structure.