Name: octahedral d-orbital splitting in crystal fields
Uploaded: 2020-09-24T15:06:53.000Z
Duration: 2 min 58 s
Channel: JoVE

Crystal field theory describes the electronic structure of transition metal complexes based on electrostatic interactions between transition metal ions and ligand molecules. It has been used to explain certain properties of transition metal complexes such as magnetism and color.
The electrostatic interactions between the ligand molecules and the metal ion in a transition metal complex are modeled by approximating the ligands as negative point charges and calculating the net electrostatic field, or crystal field, due to these charges.
The electronic structure of the transition metal complex can then be described by examining the effect of the crystal field on the energies of the valence orbitals of the transition metal ion.
For example, when modeling the octahedral complex hexaamminecobalt(III), each amine ligand is replaced by a negative point charge, resulting in an octahedral crystal-field.
Under the influence of this field, the energies of the five d orbitals of the Co(III) ion are no longer the same.
Here, the dx2&#8722;y2 and dz2 orbitals have higher energy than the dxy, dyz, and dxz orbitals. This is attributed to the orientation of the d orbitals. The lobes of the dx2&#8722;y2 and dz&#178; orbitals point directly towards the ligands, accordingly, the electrons in these orbitals experience stronger repulsion from the ligand charges. 
The higher energy orbitals have eg symmetry, and are known as the eg set of orbitals, while the lower energy orbitals have t2g symmetry and constitute the t2g set of orbitals. The energy difference between the two sets is known as the crystal-field splitting energy, represented by the symbol &#916;oct.
The magnitude of &#916;oct depends on the net electrostatic interaction between the metal ion and the ligand molecules. Some ligands such as carbonyl create a strong crystal field, resulting in a large value of &#916;oct. Such ligands are called strong-field ligands.
In contrast, ligands such as iodide exhibit small values of &#916;oct and are known as weak-field ligands. The ability of ligands to cause increasing values of &#916;oct is listed in the spectrochemical series.
Increase in the charge on the metal ion also increases the net electrostatic interaction within the complex, thus resulting in a higher value of &#916;oct.

crystal field theory - octahedral complexes

Crystal Field Theory - Octahedral Complexes

<h3>Crystal Field Theory</h3>
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on the nonbonding electrons on the central metal ion in coordination complexes not on the metal-ligand bonds. Like valence bond theory, CFT tells only part of the story of the behavior of complexes. In its pure form, CFT ignores any covalent bonding between ligands and metal ions. Both the ligand and the metal are treated as infinitesimally small point charges.
All electrons are negative, so the electrons donated from the ligands will repel the electrons of the central metal. Consider the behavior of the electrons in the unhybridized d orbitals in an octahedral complex. The five d orbitals consist of lobe-shaped regions and are arranged in space, as shown in Figure 1. In an octahedral complex, the six ligands coordinate along the axes.
<img alt="Atomic orbital shapes diagram; d-orbitals visualization; educational chemistry concept." src="/files/ftp_upload/11461/11461_Image_1.png" style="text-align: center; height: 200px;" data-altupdatedat="1754904545000" data-alt="&#60;p&#62;Atomic orbital shapes diagram; d-orbital orientations in 3D coordinate planes.&#60;/p&#62;" />
Figure 1. The directional characteristics of the five d orbitals are shown here. The shaded portions indicate the phase of the orbitals. The ligands (L) coordinate along the axes in octahedral complexes. For clarity, the ligands have been omitted from the dx2&#8722;y2 orbital so that the axis labels could be shown.
In an uncomplexed metal ion in the gas phase, the electrons are distributed among the five d orbitals in accord with Hund's rule because the orbitals all have the same energy. In transition metal complexes, the energies of the d orbitals of transition metal atoms are affected by the type of ligands and the molecular geometry. If the ligand molecules are uniformly arranged around the metal ion, a spherical crystal field is created. This spherical crystal field raises the energies of the d orbitals of the metal ion by an equal amount (Figure 2). When the ligands coordinate to a metal ion in an octahedral geometry, the energies of the d orbitals are no longer the same.
<img alt="Octahedral crystal field splitting diagram, metal ion orbitals &#916;oct, eg, t2g levels shown." src="/files/ftp_upload/11461/11461_Image_2.png" style="text-align: center; height: 350px;" data-altupdatedat="1754904545000" data-alt="Crystal field splitting diagram; &#916;oct symbols; octahedral, spherical fields; d-orbitals." />
Figure 2. The d orbitals of the metal ion in a spherical crystal field are destabilized (higher in energy) in comparison to the d orbitals of the uncomplexed free metal ion. In octahedral complexes, the eg orbitals are further destabilized (higher in energy) compared to the t2g orbitals because the ligands interact more strongly with the d orbitals at which they are pointed directly.
In octahedral complexes, the lobes in two of the five d orbitals, the dx2&#8722;y2 and dz2 orbitals, point toward the ligands (Figure 1). These two orbitals are called the eg orbitals (the symbol refers to the symmetry of the orbitals). The other three orbitals, the dxy, dxz, and dyz orbitals, have lobes that point between the ligands and are called the t2g orbitals (again, the symbol refers to the symmetry of the orbitals). As six ligands approach the metal ion along the axes of the octahedron, their point charges repel the electrons in the d orbitals of the metal ion. However, the repulsions between the electrons in the eg orbitals (the dx2-y2 orbitals) and the ligands are greater than the repulsions between the electrons in the t2g orbitals (the dxy, dxz, and dyz orbitals) and the ligands. This is because the lobes of the eg orbitals point directly at the ligands, whereas the lobes of the t2g orbitals point between them. Thus, electrons in the eg orbitals of the metal ion in an octahedral complex have higher potential energies than those of electrons in the t2g orbitals. The difference in energy may be represented as shown in Figure 2.
The difference in energy between the eg and the t2g orbitals is called the crystal field splitting and is symbolized by &#916;oct, where oct stands for octahedral. The magnitude of &#916;oct depends on many factors, including the nature of the six ligands located around the central metal ion, the charge on the metal, and whether the metal is using 3d, 4d, or 5d orbitals. Different ligands produce different crystal field splittings. The increasing crystal field splitting produced by ligands is expressed in the spectrochemical series, a short version of which is given here:
<img alt="Ligand field strength series diagram with ligands I&#60;sup&#62;-&#60;/sup&#62; to CO, demonstrating ligand field theory." src="/files/ftp_upload/11461/11461_Image_3.png" style="text-align: center; height: 100px;" data-altupdatedat="1754904545000" data-alt="Ligand field strength order, spectrochemical series, diagram, chemistry, ligand binding strength." />
This text is adapted from <a href="https://openstax.org/books/chemistry-2e/pages/19-3-spectroscopic-and-magnetic-properties-of-coordination-compounds">Openstax, Chemistry 2e, Section:19.3: </a><a href="https://openstax.org/books/chemistry-2e/pages/19-3-spectroscopic-and-magnetic-properties-of-coordination-compounds">S</a><a href="https://openstax.org/books/chemistry-2e/pages/19-3-spectroscopic-and-magnetic-properties-of-coordination-compounds">pectroscopic and Magnetic Properties of Coordination Compounds</a>.

Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between ...

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Transition Metals and Coordination Complexes

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octahedral d-orbital splitting in crystal fields

Crystal field theory explains how ligands affect the d orbitals in transition metal complexes. This electrostatic model helps predict the colors, magnetic behavior, and some structures of coordination compounds. It focuses on the nonbonding electrons on the central metal ion, not on the metal-ligand bonds.

In crystal field theory, the metal ion and ligands are treated as very small point charges. Because electrons are negative, electrons donated by the ligands repel the electrons in the metal’s unhybridized d orbitals. In its pure form, this model ignores covalent bonding between ligands and metal ions, so it gives only part of the full picture.

The five d orbitals have different shapes and directions in space. In an octahedral complex, six ligands approach the metal ion along the axes. In a free metal ion in the gas phase, the d orbitals have the same energy, so electrons fill them according to Hund’s rule.

When ligands are arranged evenly around a metal ion, they create a spherical crystal field. This field raises the energy of all the d orbitals by the same amount. The picture changes in an octahedral geometry, where the d orbitals no longer all stay at the same energy.

In an octahedral complex, the d x2-y2 and d z2 orbitals point directly toward the ligands. These are called the e g orbitals. The d xy, d xz, and d yz orbitals point between the ligands, and these are called the t 2g orbitals. Because the e g orbitals face the ligands more directly, they feel stronger repulsion and have higher energy than the t 2g orbitals.

The energy gap between the e g and t 2g orbitals is called crystal field splitting and is written as Δ oct. The size of Δ oct depends on the ligands around the metal ion, the charge on the metal, and whether the metal uses 3 d, 4 d, or 5 d orbitals. Different ligands produce different splitting values, which are organized in the spectrochemical series.

Octahedral d-Orbital Splitting in Crystal Fields

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properties of transition metals

Transition Metals in the Periodic Table

Transition metals are the d-block elements and the inner transition metals in the f-block. They are defined by partially filled d orbitals. In the periodic table, the transition elements are in groups 3 through 11, and the inner transition metals appear in the two rows below the main body of the table. The d-block is often grouped into transition series. The first transition series runs from Sc through Cu. The second series runs from Y through Ag. The third series includes La and Hf through...

coordination compounds and nomenclature

How Transition Metal Complexes Are Named

Transition metal complexes are named by following rules for ligands, metal ions, and oxidation state. These compounds form when a central metal ion or atom, often a transition metal or inner transition metal, accepts electron pairs from ligands. A ligand is a Lewis base that can be an atom, molecule, or ion with one or more lone pairs to donate. In these complexes, the bond is a coordinate covalent bond. That means both electrons in the bond come from the donor, such as ammonia, and are...

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Coordination Complexes and Chelation

Coordination complexes form when a metal ion bonds to ligands. These compounds appear in familiar examples such as hemoglobin in blood, chlorophyll in green plants, vitamin B-12, and the catalyst used to make polyethylene. Transition metal ions are especially likely to form these complexes. In a coordination complex, the metal acts as a Lewis acid. The ligand acts as a Lewis base and donates both electrons in the coordinate covalent bond. A ligand can be an atom, molecule, or ion, as long as...

coordination number and geometry

Transition Metal Shapes from Coordination Number

Transition metal complexes are often identified by their coordination number and the shape around the metal ion. The coordination number is the number of donor atoms bonded to the central metal. In many complexes, the most common shapes are octahedral, tetrahedral, and square planar. Coordination number and molecular geometry are linked in a clear pattern. A coordination number of 2 gives a linear shape, as in [Ag(NH3)2]+. A coordination number of 3 gives a trigonal planar shape, as in...

structural isomerism

Linkage and Ionization Isomers

Isomers are different chemical species that share the same chemical formula. In coordination compounds, structural isomerism includes linkage isomers and coordination-sphere isomers. These two forms show how the same atoms can be arranged in different ways around a metal center. Linkage isomers form when a ligand can attach to a transition metal through two different atoms. The cyanide ligand, CN−, can bind through carbon or nitrogen. The thiocyanate ligand, SCN−, can bind through sulfur or...

stereoisomerism

Isomer Shapes in Coordination Complexes

Isomer shapes in coordination complexes can change a compound’s properties even when the chemical formula stays the same. Isomers are different chemical species with the same formula. In transition metal complexes, the atoms stay connected through the same types of bonds, but their arrangement in space can differ. One common form is geometric isomerism. In these complexes, ligands (the ions or molecules attached to the metal) can sit in cis or trans positions. The octahedral [Co(NH3)4Cl2]+ ion...

valence bond theory

Metal Ligand Bonds in Coordination Complexes

Coordination complexes form metal-ligand bonds through valence bond theory. In this model, Linus Pauling explained bonding with hybridization and overlap of atomic orbitals. The central metal atom or ion acts as a Lewis acid. It uses empty orbitals of suitable energy to accept electron pairs from ligands, which act as Lewis bases. These coordinate covalent bonds help explain the color, geometry, and magnetic behavior seen in coordination compounds. The type of hybridization helps determine the...

Crystal field theory explains how ligands affect the d orbitals in transition metal complexes. This electrostatic model helps predict the colors, magnetic behavior, and some structures of coordination compounds. It focuses on the nonbonding electrons on the central metal ion, not on the metal-ligand bonds. In crystal field theory, the metal ion and ligands are treated as very small point charges. Because electrons are negative, electrons donated by the ligands repel the electrons in the...

crystal field theory - tetrahedral and square planar complexes

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Crystal Field Splitting in Non-Octahedral Shapes

Crystal field theory also explains d orbital splitting in tetrahedral and square planar complexes. These shapes do not follow the same pattern as an octahedral complex, so the d orbitals respond to ligand placement in different ways. In tetrahedral complexes, the four ligands sit between the axes. None of the d orbitals points directly at the ligands, but the d x2−y2 and d z2 orbitals lie along the Cartesian axes and overlap less with the ligands than the d xy, d xz, and d yz orbitals. The d...

colors and magnetism

Color and Spin in Coordination Complexes

Color in coordination complexes comes from how metal electrons absorb light. When atoms or molecules absorb light at the right frequency, electrons move to higher-energy orbitals. For many main-group atoms and molecules, the absorbed light is ultraviolet and cannot be seen. In coordination compounds, the energy gap between d orbitals often matches visible light, so the compound can absorb and emit colors that the human eye detects. Small changes in orbital energy can cause large shifts in the...

key terms and concepts

Learn how octahedral ligands split d orbitals into e g and t 2g levels, and how crystal field splitting affects color, magnetism, and structure.

Octahedral d-Orbital Splitting in Crystal Fields | JoVE K12

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Octahedral d-Orbital Splitting in Crystal Fields

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