19.3 Spectroscopic and Magnetic Properties of Coordination Compounds

The behavior of coordination compounds cannot be adequately explained by the same theories used for main group element chemistry. The observed geometries of coordination complexes are not consistent with hybridized orbitals on the central metal overlapping with ligand orbitals, as would be predicted by valence bond theory. The observed colors indicate that the d orbitals often occur at different energy levels rather than all being degenerate, that is, of equal energy, as are the three p orbitals. To explain the stabilities, structures, colors, and magnetic properties of transition metal complexes, a different bonding model has been developed. Just as valence bond theory explains many aspects of bonding in main group chemistry, crystal field theory is useful in understanding and predicting the behavior of transition metal complexes.

Crystal Field Theory

To explain the observed behavior of transition metal complexes (such as how colors arise), 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 allows us 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. However, it tells the part that valence bond theory does not. 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. Let us 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 19.33. In an octahedral complex, the six ligands coordinate along the axes.

This figure includes diagrams of five d orbitals. Each diagram includes three axes. The z-axis is vertical and is denoted with an upward pointing arrow. It is labeled “z” in the first diagram. Arrows similarly identify the x-axis with an arrow pointing from the rear left to the right front, diagonally across the figure and the y-axis with an arrow pointing from the left front diagonally across the figure to the right rear of the diagram. These axes are similarly labeled as “x” and “y.” In this first diagram, four orange balloon-like shapes extend from a point at the origin out along the x- and y- axes in positive and negative directions covering just over half the length of the positive and negative x- and y- axes. Beneath the diagram is the label, “d subscript ( x superscript 2 minus y superscript 2 ).” The second diagram just right of the first is similar except the x, y, and z labels have been replaced in each instance with the letter L. Only a pair of the orange balloon-like shapes are present and extend from the origin above and below along the vertical axis. An orange toroidal or donut shape is positioned around the origin, oriented through the x- and y- axes. This shape extends out to about a third of the length of the positive and negative regions of the x- and y- axes. This diagram is labeled, “d subscript ( z superscript 2 ).” The third through fifth diagrams, similar to the first, show four orange balloon-like shapes. These diagrams differ however in the orientation of the shapes along the axes and the x-, y-, and z-axis labels have each been replaced with the letter L. Planes are added to the figures to help show the orientation differences with these diagrams. In the third diagram, a green plane is oriented vertically through the length of the x-axis and a blue plane is oriented horizontally through the length of the y-axis. The balloon shapes extend from the origin to the spaces between the positive z- and negative y- axes, positive z- and positive y- axes, negative z- and negative y- axes, and negative z- and positive y- axes. This diagram is labeled, “d subscript ( y z ).” In the fourth diagram, a green plane is oriented vertically through the x- and y- axes and a blue plane is oriented horizontally through the length of the x-axis. The balloon shapes extend from the origin to the spaces between the positive z- and negative x- axes, positive z- and positive x- axes, negative z- and negative x- axes, and negative z- and positive x- axes. This diagram is labeled “d subscript ( x z ).” In the fifth diagram, a pink plane is oriented vertically through the length of the y-axis and a green plane is oriented vertically through the length of the x-axis. The balloon shapes extend from the origin to the spaces between the positive x- and negative y- axes, positive x- and positive y- axes, negative x- and negative y- axes, and negative x- and positive y- axes. This diagram is labeled, “d subscript ( x y ).”

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. However, when ligands coordinate to a metal ion, the energies of the d orbitals are no longer the same.

In octahedral complexes, the lobes in two of the five d orbitals, the $d_{z^{2}}$ and $d_{x^{2} - y^{2}}$ orbitals, point toward the ligands (Figure 19.33). These two orbitals are called the e orbitals (the symbol actually refers to the symmetry of the orbitals, but we will use it as a convenient name for these two orbitals in an octahedral complex). The other three orbitals, the , , and orbitals, have lobes that point between the ligands and are called the (again, the symbol really 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 orbitals of the metal ion. However, the repulsions between the electrons in the orbitals (the and orbitals) and the ligands are greater than the repulsions between the electrons in the orbitals (the , , and orbitals) and the ligands. This is because the lobes of the orbitals point directly at the ligands, whereas the lobes of the orbitals point between them. Thus, electrons in the orbitals of the metal ion in an octahedral complex have higher potential energies than those of electrons in the orbitals. The difference in energy may be represented as shown in Figure 19.34.

A diagram is shown with a vertical arrow pointing upward along the height of the diagram at its left side. This arrow is labeled, “E.” to the right of this arrow are two rows of squares outlined in yellow. The first row has three evenly spaced squares labeled left to right, “d subscript ( x y ),” “d subscript ( x z ),” and, “d subscript ( y z ).” The second row is positioned just above the first and includes two evenly spaced squares labeled, “d subscript ( z superscript 2 ),” and, “d subscript ( x superscript 2 minus y superscript 2 ).” At the right end of the diagram, a short horizontal line segment is drawn just right of the lower side of the rightmost square. A double sided arrow extends from this line segment to a second horizontal line segment directly above the first and right of the lower side of the squares in the second row. The arrow is labeled “ capital delta subscript oct.”. The lower horizontal line segment is similarly labeled “t subscript 2 g orbitals” and the upper line segment is labeled “e subscript g orbitals.” — Figure 19.34In octahedral complexes, the *e $_{g}$* orbitals are destabilized (higher in energy) compared to the t $_{2 g}$ orbitals because the ligands interact more strongly with the orbitals at which they are pointed directly.

The difference in energy between the e $_{g}$ and the t $_{2 g}$ orbitals is called the crystal field splitting and is symbolized by Δ $_{oc t}$ , where oct stands for octahedral.

The magnitude of Δ $_{oc t}$ 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:

a few ligands of the spectrochemical series, in order of increasing field strength of the ligand \to I^{-} < Br^{-} < Cl^{-} < F^{-} < H_{2} O < NH_{3} < e n < NO_{2}^{-} < CN^{-}

In this series, ligands on the left cause small crystal field splittings and are weak-field ligands, whereas those on the right cause larger splittings and are strong-field ligands. Thus, the Δ $_{oc t}$ value for an octahedral complex with iodide ligands (I⁻) is much smaller than the Δ $_{oc t}$ value for the same metal with cyanide ligands (CN⁻).

Electrons in the d orbitals follow the aufbau (“filling up”) principle, which says that the orbitals will be filled to give the lowest total energy, just as in main group chemistry. When two electrons occupy the same orbital, the like charges repel each other. The energy needed to pair up two electrons in a single orbital is called the pairing energy (P). Electrons will always singly occupy each orbital in a degenerate set before pairing. P is similar in magnitude to Δ $_{oc t}$ . When electrons fill the d orbitals, the relative magnitudes of Δ $_{oc t}$ and P determine which orbitals will be occupied.

In [Fe(CN)₆]⁴⁻, the strong field of six cyanide ligands produces a large Δ $_{oc t}$ . Under these conditions, the electrons require less energy to pair than they require to be excited to the e $_{g}$ orbitals (Δ $_{oc t}$ > P). The six 3d electrons of the Fe²⁺ ion pair in the three t $_{2 g}$ orbitals (Figure 19.35). Complexes in which the electrons are paired because of the large crystal field splitting are called because the number of unpaired electrons (spins) is minimized.

In [Fe(H₂O)₆]²⁺, on the other hand, the weak field of the water molecules produces only a small crystal field splitting (Δ $_{oc t}$ < P). Because it requires less energy for the electrons to occupy the e $_{g}$ orbitals than to pair together, there will be an electron in each of the five 3d orbitals before pairing occurs. For the six d electrons on the iron(II) center in [Fe(H₂O)₆]²⁺, there will be one pair of electrons and four unpaired electrons (Figure 19.35). Complexes such as the [Fe(H₂O)₆]²⁺ ion, in which the electrons are unpaired because the crystal field splitting is not large enough to cause them to pair, are called high-spin complexes because the number of unpaired electrons (spins) is maximized.

A similar line of reasoning shows why the [Fe(CN)₆]³⁻ ion is a low-spin complex with only one unpaired electron, whereas both the [Fe(H₂O)₆]³⁺ and [FeF₆]³⁻ ions are high-spin complexes with five unpaired electrons.

Example 19.7High- and Low-Spin Complexes

Predict the number of unpaired electrons.

(a) K₃[CrI₆]

(b) [Cu(en)₂(H₂O)₂]Cl₂

Solution

The complexes are octahedral.

(a) Cr³⁺ has a d³ configuration. These electrons will all be unpaired.

(b) Cu²⁺ is d⁹, so there will be one unpaired electron.

(c) Co³⁺ has d⁶ valence electrons, so the crystal field splitting will determine how many are paired. Nitrite is a strong-field ligand, so the complex will be low spin. Six electrons will go in the t $_{2 g}$ orbitals, leaving 0 unpaired.

Check Your Learning

The size of the crystal field splitting only influences the arrangement of electrons when there is a choice between pairing electrons and filling the higher-energy orbitals. For which d-electron configurations will there be a difference between high- and low-spin configurations in octahedral complexes?

Answer

The other common geometry is square planar. It is possible to consider a square planar geometry as an octahedral structure with a pair of trans ligands removed. The removed ligands are assumed to be on the z-axis. This changes the distribution of the d orbitals, as orbitals on or near the z-axis become more stable, and those on or near the x- or y-axes become less stable. This results in the octahedral t $_{2 g}$ and the e $_{g}$ sets splitting and gives a more complicated pattern, as depicted below:

A diagram is shown with four rows of vertically oriented rectangles. The lower level has two rectangles with a space between them. The rectangle on the left is labeled, “d subscript x z,” below. The rectangle to its right is similarly labeled, “d subscript y z.” Just above, the second row contains only 1 rectangle above and between the lower two. This rectangle is labeled, “d subscript z squared.” Just above, the third row contains only 1 rectangle directly above. This rectangle is labeled, “d subscript x z.” Just above, the fourth row contains only 1 rectangle directly above. This rectangle is labeled, “d subscript x squared minus y squared.”

Magnetic Moments of Molecules and Ions

Experimental evidence of magnetic measurements supports the theory of high- and low-spin complexes. Remember that molecules such as O₂ that contain unpaired electrons are paramagnetic. Paramagnetic substances are attracted to magnetic fields. Many transition metal complexes have unpaired electrons and hence are paramagnetic. Molecules such as N₂ and ions such as Na⁺ and [Fe(CN)₆]⁴⁻ that contain no unpaired electrons are diamagnetic. Diamagnetic substances have a slight tendency to be repelled by magnetic fields.

When an electron in an atom or ion is unpaired, the magnetic moment due to its spin makes the entire atom or ion paramagnetic. The size of the magnetic moment of a system containing unpaired electrons is related directly to the number of such electrons: the greater the number of unpaired electrons, the larger the magnetic moment. Therefore, the observed magnetic moment is used to determine the number of unpaired electrons present. The measured magnetic moment of low-spin d⁶ [Fe(CN)₆]⁴⁻ confirms that iron is diamagnetic, whereas high-spin d⁶ [Fe(H₂O)₆]²⁺ has four unpaired electrons with a magnetic moment that confirms this arrangement.

Colors of Transition Metal Complexes

When atoms or molecules absorb light at the proper frequency, their electrons are excited to higher-energy orbitals. For many main group atoms and molecules, the absorbed photons are in the ultraviolet range of the electromagnetic spectrum, which cannot be detected by the human eye. For coordination compounds, the energy difference between the d orbitals often allows photons in the visible range to be absorbed.

The human eye perceives a mixture of all the colors, in the proportions present in sunlight, as white light. Complementary colors, those located across from each other on a color wheel, are also used in color vision. The eye perceives a mixture of two complementary colors, in the proper proportions, as white light. Likewise, when a color is missing from white light, the eye sees its complement. For example, when red photons are absorbed from white light, the eyes see the color green. When violet photons are removed from white light, the eyes see lemon yellow. The blue color of the [Cu(NH₃)₄]²⁺ ion results because this ion absorbs orange and red light, leaving the complementary colors of blue and green (Figure 19.37).

This figure includes three diagrams. In a, red, orange, yellow, green, blue, indigo, and violet incident arrows point from the upper left to the lower right toward one black, one white, and two yellow rectangular surfaces. No arrows are indicated leaving the black surface. On the white surface, arrows of all included colors extend from the surface of the rectangle extending from just right of the tips of the incident arrows that approach the rectangle to the upper right. For the first yellow surface, only a yellow arrow extends from a point just past the tip of the yellow incident arrow to the upper right. For the second yellow surface, all colors of arrows except indigo extend from points just past the tips of the incident arrows to the upper right. In b, a circle shaded in red at the upper left blends to orange, yellow, green, blue, indigo, and violet moving clockwise about the circle. The leftmost side of the red region has a radius that is labeled, “800 n m,” at the edge of the circle. A radius drawn to the top of the circle in the red-orange region is labeled, “620 n m.” A radius drawn to a point near the center of the first quadrant of the circle in the orange-yellow region is labeled, “580 n m.” A radius drawn to a point near the center of the second quadrant of the circle in the yellow-green region is labeled, “560 n m.” A radius drawn to the bottom of the circle in the blue region is labeled, “490 n m.” A radius drawn to a point near the center of the third quadrant of the circle in the indigo region is labeled, “430 n m.” An unlabeled radius is drawn to the leftmost point on the circle in the violet region. The violet region ends where the red region began on the circle. This radius is labeled, “400 n m,” just to the left and below the, “800 n m,” label associated with the red region. In c, a test tube containing a blue substance is shown. To the left of the test tube, incident colored arrows are shown pointing to the test tube. The colors of the arrows in order from bottom to top are red, orange, yellow, green, blue, indigo, and violet. Above these arrows is the label, “White light.” To the right of the test tube, yellow, green, blue, indigo, and violet arrows point right. These arrows are positioned at the same level on the test tube as their matching incident arrows on the left of the test tube. Above these arrows is the label, “Blue-appearing light.” — Figure 19.37(a) An object is black if it absorbs all colors of light. If it reflects all colors of light, it is white. An object has a color if it absorbs all colors except one, such as this yellow strip. The strip also appears yellow if it absorbs the complementary color from white light (in this case, indigo). (b) Complementary colors are located directly across from one another on the color wheel. (c) A solution of [Cu(NH₃)₄]²⁺ ions absorbs red and orange light, so the transmitted light appears as the complementary color, blue.

Small changes in the relative energies of the orbitals that electrons are transitioning between can lead to drastic shifts in the color of light absorbed. Therefore, the colors of coordination compounds depend on many factors. As shown in Figure 19.38, different aqueous metal ions can have different colors. In addition, different oxidation states of one metal can produce different colors, as shown for the vanadium complexes in the link below.

This figure shows three containers filled with liquids of different colors. The first appears to be purple, the second, orange, and the third red. — Figure 19.38The partially filled d orbitals of the stable ions Cr³⁺(aq), Fe³⁺(aq), and Co²⁺(aq) (left, center and right, respectively) give rise to various colors. (credit: Sahar Atwa)

The specific ligands coordinated to the metal center also influence the color of coordination complexes. For example, the iron(II) complex [Fe(H₂O)₆]SO₄ appears blue-green because the high-spin complex absorbs photons in the red wavelengths (Figure 19.39). In contrast, the low-spin iron(II) complex K₄[Fe(CN)₆] appears pale yellow because it absorbs higher-energy violet photons.

Two photos are shown. Photo a on the left shows a small mound of a white crystalline powder with a very faint yellow tint on a watch glass. Photo b shows a small mound of a yellow-tan crystalline powder. — Figure 19.39Both (a) hexaaquairon(II) sulfate and (b) potassium hexacyanoferrate(II) contain d⁶ iron(II) octahedral metal centers, but they absorb photons in different ranges of the visible spectrum.

In general, strong-field ligands cause a large split in the energies of d orbitals of the central metal atom (large Δ $_{oc t}$ ). Transition metal coordination compounds with these ligands are yellow, orange, or red because they absorb higher-energy violet or blue light. On the other hand, coordination compounds of transition metals with weak-field ligands are often blue-green, blue, or indigo because they absorb lower-energy yellow, orange, or red light.

A coordination compound of the Cu⁺ ion has a d¹⁰ configuration, and all the e $_{g}$ orbitals are filled. To excite an electron to a higher level, such as the 4p orbital, photons of very high energy are necessary. This energy corresponds to very short wavelengths in the ultraviolet region of the spectrum. No visible light is absorbed, so the eye sees no change, and the compound appears white or colorless. A solution containing [Cu(CN)₂]⁻, for example, is colorless. On the other hand, octahedral Cu²⁺ complexes have a vacancy in the e $_{g}$ orbitals, and electrons can be excited to this level. The wavelength (energy) of the light absorbed corresponds to the visible part of the spectrum, and Cu²⁺ complexes are almost always colored—blue, blue-green violet, or yellow (Figure 19.40). Although CFT successfully describes many properties of coordination complexes, molecular orbital explanations (beyond the introductory scope provided here) are required to understand fully the behavior of coordination complexes.

Two photos are shown. Photo a on the left shows a small mound of a white crystalline powder on a watch glass. Photo b shows a small mound of a bright blue crystalline powder. — Figure 19.40(a) Copper(I) complexes with d¹⁰ configurations such as CuI tend to be colorless, whereas (b) d⁹ copper(II) complexes such as Cu(NO₃)₂·5H₂O are brightly colored.

Key Concepts and Summary

Crystal field theory treats interactions between the electrons on the metal and the ligands as a simple electrostatic effect. The presence of the ligands near the metal ion changes the energies of the metal d orbitals relative to their energies in the free ion. Both the color and the magnetic properties of a complex can be attributed to this crystal field splitting. The magnitude of the splitting (Δ $_{oc t}$ ) depends on the nature of the ligands bonded to the metal. Strong-field ligands produce large splitting and favor low-spin complexes, in which the t $_{2 g}$ orbitals are completely filled before any electrons occupy the e $_{g}$ orbitals. Weak-field ligands favor formation of high-spin complexes. The and the orbitals are singly occupied before any are doubly occupied.