6.10: Factors Affecting Electronic Structure

Electronic Structures of Metal Complexes

 

According to the Aufbau principle, electrons are filled from lower to higher energy orbitals. For the octahedral case, this corresponds to filling the d_xy, d_xz, and d_yz orbitals first. Following Hund's rule, electrons are distributed into orbitals to give the highest number of unpaired electrons. For example, if one had a d³ complex, there would be three unpaired electrons.

Consider several examples of electronic configurations for octahedral complexes shown in Figure \(\PageIndex{1}\). The Ti³⁺ ion contains a single d electron, and additional configurations can be obtained as we proceed across the first row of the transition metals by adding a single electron at a time. Additional electrons are placed in the lowest-energy orbital available, while keeping their spins parallel as required by Hund’s rule. As shown in Figure \(\PageIndex{1}\), for d¹–d³ systems—such as [Ti(H₂O)₆]³⁺, [V(H₂O)₆]³⁺, and [Cr(H₂O)₆]³⁺, respectively—the electrons successively occupy the three degenerate t_2g orbitals with their spins parallel, giving one, two, and three unpaired electrons, respectively. We can summarize this for the complex [Cr(H₂O)₆]³⁺, for example, by saying that the chromium ion has a d³ electron configuration or, more succinctly, Cr³⁺ is a d³ ion.

Figure \(\PageIndex{1}\): The Possible Electron Configurations for Octahedral dⁿ Transition-Metal Complexes (n = 1–10). Two different configurations are possible for octahedral complexes of metals with d⁴, d⁵, d⁶, and d⁷ configurations; the magnitude of Δ_o determines which configuration is observed. (CC BY-SA-NC; anonymous by request)

When we reach the d⁴ configuration, there are two possible choices for the fourth electron: it can occupy one of the empty, higher-energy e_g orbitals (d_z² or d_x²-y²) or it can occupy one of the lower-energy, singly-occupied t_2g orbitals (d_xy, d_xz, or d_yz). Recall that placing an electron in an already occupied orbital results in electrostatic repulsions that increase the energy of the system; this increase in energy is called the spin-pairing energy (P). If Δ_o is less than P, then the lowest-energy arrangement places the fourth electron in one of the empty e_g orbitals. This configuration maximizes the spin multiplicity. Because this arrangement results in four unpaired electrons, it is called a high-spin configuration, and a complex with this electron configuration, such as the [Cr(H₂O)₆]²⁺ ion, is called a high-spin complex. Conversely, if Δ_o is greater than P, then the lowest-energy arrangement places the fourth electron in one of the occupied t_2g orbitals. Because this arrangement results in only two unpaired electrons, it is called a low-spin configuration, and a complex with this electron configuration, such as the [Mn(CN)₆]³⁻ ion, is called a low-spin complex. Similarly, metal ions with the d⁵, d⁶, or d⁷ electron configurations can be either high spin or low spin, depending on the magnitude of Δ_o.

In contrast, only one arrangement of d electrons is possible for metal ions with d⁸–d¹⁰ electron configurations. For example, the [Ni(H₂O)₆]²⁺ ion is d⁸ with two unpaired electrons, the [Cu(H₂O)₆]²⁺ ion is d⁹ with one unpaired electron, and the [Zn(H₂O)₆]²⁺ ion is d¹⁰ with no unpaired electrons.

If Δ_o is less than the spin-pairing energy, a high-spin configuration results. Conversely, if Δ_o is greater, a low-spin configuration forms.

A Note on units

The crystal field splitting energy, Δ_o, may be reported in units of J/mol or wave numbers (cm^-1). Typically, energies obtained by spectroscopic measurements are often given wave numbers; the wave number is the reciprocal of the wavelength of the corresponding electromagnetic radiation expressed in centimeters: 1 cm⁻¹ = 11.96 J/mol.

Factors That Affect the Magnitude of Δ_o

The magnitude of the crystal field splitting energy, Δ_o, dictates whether a complex with four, five, six, or seven d electrons is high spin or low spin, which affects its magnetic properties, structure, and reactivity. Large values of Δ_o (i.e., Δ_o > P) yield a low-spin complex, whereas small values of Δ_o (i.e., Δ_o < P) produce a high-spin complex. As we noted, the magnitude of Δ_o depends on three factors: the charge on the metal ion, the principal quantum number of the metal (and thus its location in the periodic table), and the nature of the ligand. Values of Δ_o for some representative transition-metal complexes are given in Table \(\PageIndex{1}\).

Table \(\PageIndex{1}\): Crystal Field Splitting Energies for Some Octahedral (Δ_o) and Tetrahedral (Δ_t) Transition-Metal Complexes

Octahedral Complexes	Δo (cm^−1)	Octahedral Complexes	Δo (cm^−1)	Tetrahedral Complexes	Δt (cm^−1)
Source of data: Duward F. Shriver, Peter W. Atkins, and Cooper H. Langford, Inorganic Chemistry, 2nd ed. (New York: W. H. Freeman and Company, 1994).
[Ti(H2O)6]^3+	20,300	[Fe(CN)6]^4−	32,800	VCl4	9010
[V(H2O)6]^2+	12,600	[Fe(CN)6]^3−	35,000	[CoCl4]^2−	3300
[V(H2O)6]^3+	18,900	[CoF6]^3−	13,000	[CoBr4]^2−	2900
[CrCl6]^3−	13,000	[Co(H2O)6]^2+	9300	[CoI4]^2−	2700
[Cr(H2O)6]^2+	13,900	[Co(H2O)6]^3+	27,000
[Cr(H2O)6]^3+	17,400	[Co(NH3)6]^3+	22,900
[Cr(NH3)6]^3+	21,500	[Co(CN)6]^3−	34,800
[Cr(CN)6]^3−	26,600	[Ni(H2O)6]^2+	8500
Cr(CO)6	34,150	[Ni(NH3)6]^2+	10,800
[MnCl6]^4−	7500	[RhCl6]^3−	20,400
[Mn(H2O)6]^2+	8500	[Rh(H2O)6]^3+	27,000
[MnCl6]^3−	20,000	[Rh(NH3)6]^3+	34,000
[Mn(H2O)6]^3+	21,000	[Rh(CN)6]^3−	45,500
[Fe(H2O)6]^2+	10,400	[IrCl6]^3−	25,000
[Fe(H2O)6]^3+	14,300	[Ir(NH3)6]^3+	41,000

Factor 1: Charge on the Metal Ion

Increasing the charge on a metal ion has two effects: the radius of the metal ion decreases, and negatively charged ligands are more strongly attracted to it. Both effects decrease the metal–ligand distance, which in turn causes the negatively charged ligands to interact more strongly with the d-orbitals. Consequently, the magnitude of Δ_o increases as the charge on the metal ion increases. Typically, Δ_o for a +3 ion is about 50% greater than for the +2 ion of the same metal; for example, for [V(H₂O)₆]²⁺, Δ_o = 11,800 cm⁻¹; for [V(H₂O)₆]³⁺, Δ_o = 17,850 cm⁻¹.

Factor 2: Principal Quantum Number of the Metal

For a series of complexes of metals from the same group in the periodic table with the same charge and the same ligands, the magnitude of Δ_o increases with increasing principal quantum number: Δ_o (3d) < Δ_o (4d) < Δ_o (5d). The data for hexaammine complexes of the trivalent Group 9 metals illustrate this point:

[Co(NH₃)₆]³⁺: Δ_o = 22,900 cm⁻¹

[Rh(NH₃)₆]³⁺: Δ_o = 34,100 cm⁻¹

[Ir(NH₃)₆]³⁺: Δ_o = 40,000 cm⁻¹

The increase in Δ_o with increasing principal quantum number is due to the larger radius of valence orbitals down a column. In addition, repulsive ligand–ligand interactions are most important for smaller metal ions. Relatively speaking, this results in shorter M–L distances and stronger d orbital–ligand interactions.

Factor 3: The Nature of the Ligands

Figure \(\PageIndex{2}\): Low Spin, Strong Field (∆_o˃P) High Spin, Weak Field (∆_o˂P)Splitting for a \(d^4\) complex under a strong field (left) and a weak field (right). The strong field is a low spin complex, while the weak field is a high spin complex.

Experimentally, it is found that the Δ_o observed for a series of complexes of the same metal ion depends strongly on the nature of the ligands. Ligands that cause a transition metal to have a small crystal field splitting, which leads to a high-spin configuration, are called weak-field ligands. Ligands that produce a large crystal field splitting, which leads to a low-spin configuration, are called strong field ligands (Figure \(\PageIndex{2}\)).

For a series of chemically similar ligands, the magnitude of Δ_o decreases as the size of the donor atom increases. For example, Δ_o values for halide complexes generally decrease in the order F⁻ > Cl⁻ > Br⁻ > I− because smaller, more localized charges, such as we see for F⁻, interact more strongly with the d orbitals of the metal ion.

In addition, a small neutral ligand with a highly localized lone pair, such as NH₃, results in significantly larger Δ_o values than might be expected. Because the lone pair points directly at the metal ion, the electron density along the M–L axis is greater than for a spherical anion such as F⁻.

The experimentally observed order of the crystal field splitting energies produced by different ligands is called the spectrochemical series. It is shown here in order of increasing Δ_o:

\[ \underset{\textrm{weak-field ligands}}{I^- < Br^- < Cl^-} < \underline{S}CN^- < CH_3COO^- < F^- < OH^- < ox^{2-} < \underset{\textrm{intermediate-field ligands}}{ONO^- < H_2O < SC\underline{N}^-} < EDTA^{4-} <NH_3 < en < NO_2^- < \underset{\textrm{strong-field ligands}}{ CN^- \approx CO} \nonumber\]

Note that SCN^- and NO₂- ligands are represented twice in the above spectrochemical series since there are two different Lewis base sites (e.g., free electron pairs to share) on each ligand (e.g., for the SCN^- ligand, the electron pair on the sulfur or the nitrogen can form the coordinate covalent bond to a metal). The specific atom that binds in such ligands is underlined.

The largest Δ_o splittings are found in complexes of metal ions from the third row of the transition metals with charges of at least +3 and ligands with localized lone pairs of electrons.

Factor 4: Molecular Geometry

In addition to octahedral complexes, two common geometries observed are that of tetrahedral and square planar. These complexes differ from the octahedral complexes in that the orbital levels are raised in energy due to the interference with electrons from ligands. For the tetrahedral complex, the d_xy, d_xz, and d_yz orbitals are raised in energy while the d_z², d_x²-y² orbitals are lowered. For the square planar complexes, there is greatest interaction with the d_x²-y² orbital and therefore it has higher energy. The next orbital with the greatest interaction is d_xy, followed below by d_z². The orbitals with the lowest energy are the d_xz and d_yz orbitals. There is a large energy separation between the d_z² orbital and the d_xz and d_yz orbitals, meaning that the crystal field splitting energy is large. We find that the square planar complexes have the greatest crystal field splitting energy compared to all the other complexes. This means that most square planar complexes are low spin, strong field ligands.

The splitting energy (from highest orbital to lowest orbital) is \(\Delta_{sp}\) and tends to be larger then \(\Delta_{o}\)

\[\Delta_{sp} = 1.74\,\Delta_o \label{2} \]

Moreover, \(\Delta_{sp}\) is also larger than the pairing energy, so the square planar complexes are usually low spin complexes.

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Example \(\PageIndex{1}\)

For the complex, predict its structure, whether it is high spin or low spin, and the number of unpaired electrons present:

[CoF₆]³⁻

Solution

With six ligands, we expect this complex to be octahedral.

The fluoride ion is a small anion with a concentrated negative charge, but compared with ligands with localized lone pairs of electrons, it is weak field. The charge on the metal ion is +3, giving a d⁶ electron configuration.

Because of the weak-field ligands, we expect a relatively small Δ_o, making the compound high spin.

In a high-spin octahedral d⁶ complex, the first five electrons are placed individually in each of the d orbitals with their spins parallel, and the sixth electron is paired in one of the t_2g orbitals, giving four unpaired electrons.

Example \(\PageIndex{2}\)

For the complex, predict its structure, whether it is high spin or low spin, and the number of unpaired electrons present:

[Rh(CO)₂Cl₂]⁻

Solution

This complex has four ligands, so it is either square planar or tetrahedral.

Because rhodium is a second-row transition metal ion with a d⁸ electron configuration and CO is a strong-field ligand, the complex is likely to be square planar with a large Δ_o, making it low spin. Because the strongest d-orbital interactions are along the x and y axes, the orbital energies increase in the order d_z²d_yz, and d_xz (these are degenerate); d_xy; and d_x²−y².

The eight electrons occupy the first four of these orbitals, leaving the d_x²−y². orbital empty. Thus there are no unpaired electrons.

Problems

Exercise \(\PageIndex{1}\)

For the complex, predict its structure, whether it is high spin or low spin, and the number of unpaired electrons present.

[Mn(H₂O)₆]²⁺

Answer

octahedral; high spin; five

Exercise \(\PageIndex{2}\)

For the complex, predict its structure, whether it is high spin or low spin, and the number of unpaired electrons present.

[PtCl₄]²⁻

Answer

square planar; low spin; no unpaired electrons

Exercise \(\PageIndex{3}\)

For the complex ion [Fe(Cl)₆]^3- determine the number of d electrons for Fe, sketch the d-orbital energy levels and the distribution of d electrons among them, list the number of lone electrons, and label whether the complex is paramagnetic or diamagnetic.

Answer

Step 1: Determine the oxidation state of Fe. Here it is Fe³⁺. Based on its electron configuration, Fe³⁺ has 5 d-electrons. Step 2: Determine the geometry of the ion. Here it is an octahedral which means the energy splitting should look like:

Step 3: Determine whether the ligand induces is a strong or weak field spin by looking at the spectrochemical series. Cl^- is a weak field ligand (i.e., it induces high spin complexes). Therefore, electrons fill all orbitals before being paired.

Step four: Count the number of lone electrons. Here, there are 5 electrons. Step five: The five unpaired electrons means this complex ion is paramagnetic (and strongly so).

 

Exercise \(\PageIndex{4}\)

For each of the following, sketch the d-orbital energy levels and the distribution of d electrons among them, state the geometry, list the number of d-electrons, list the number of lone electrons, and label whether they are paramagnetic or dimagnetic:

1. [Ti(H₂O)₆]²⁺
2. [NiCl₄]^2-
3. [CoF₆]^3- (also state whether this is low or high spin)
4. [Co(NH₃)₆]³⁺ (also state whether this is low or high spin)
5. True or False: Square Planer complex compounds are usually low spin.

Answer a

octahedral, 2, 2, paramagnetic

 

Answer b

tetrahedral, 8, 2, paramagnetic (see Octahedral vs. Tetrahedral Geometries)

 

Answer c

octahedral, 6, 4, paramagnetic, high spin

 

Answer d

octahedral, 6, 0, diamagnetic, low spin

 

Answer e

True

Summary

Crystal field theory, which assumes that metal–ligand interactions are only electrostatic in nature, explains many important properties of transition-metal complexes, including their colors, magnetism, structures, stability, and reactivity. Crystal field theory (CFT) is a bonding model that explains many properties of transition metals that cannot be explained using valence bond theory. In CFT, complex formation is assumed to be due to electrostatic interactions between a central metal ion and a set of negatively charged ligands or ligand dipoles arranged around the metal ion. Depending on the arrangement of the ligands, the d orbitals split into sets of orbitals with different energies. The difference between the energy levels in an octahedral complex is called the crystal field splitting energy (Δ_o), whose magnitude depends on the charge on the metal ion, the position of the metal in the periodic table, and the nature of the ligands. The spin-pairing energy (P) is the increase in energy that occurs when an electron is added to an already occupied orbital. A high-spin configuration occurs when the Δ_o is less than P, which produces complexes with the maximum number of unpaired electrons possible. Conversely, a low-spin configuration occurs when the Δ_o is greater than P, which produces complexes with the minimum number of unpaired electrons possible. Strong-field ligands interact strongly with the d orbitals of the metal ions and give a large Δ_o, whereas weak-field ligands interact more weakly and give a smaller Δ_o. The colors of transition-metal complexes depend on the environment of the metal ion and can be explained by CFT.

Contributors and Attributions

• Asadullah Awan (UCD), Hong Truong (UCD)

• Prof. Robert J. Lancashire (The Department of Chemistry, University of the West Indies)