21.5 Color and Paramagnetism of Complex Ions and Coordination Compounds
PRE-HEALTH PREP
Paramagnetic vs. Diamagnetic
Colored vs. Colorless: Predicting Complex Properties
General Chemistry 21.5
Coordination compounds appear colored when d-orbital crystal field splitting energies fall within the visible spectrum, enabling electronic transitions between lower and upper d-orbital sets. Complexes with d1 through d9 electron configurations are predicted to be colored, while d0 and d10 configurations produce colorless compounds. Magnetic behavior—paramagnetic vs diamagnetic—depends on unpaired electrons: paramagnetic substances contain at least one unpaired electron, and diamagnetic substances have all electrons paired. The same metal ion can display either property depending on whether the complex is high spin or low spin.
Why Coordination Compounds Are Colored
Complex ions and coordination compounds are frequently associated with strikingly vivid colors. Most transition metal coordination compounds display bright hues, and the explanation is rooted in how d electrons interact with visible light.
The origin of color in a coordination compound comes down to electronic transitions between d orbitals. When an electron occupies a lower-energy d orbital and a higher-energy d orbital sits empty above it, the compound can absorb light whose energy exactly matches the gap between those two orbitals. If the absorbed light falls within the visible spectrum (roughly 400–700 nm), the compound appears colored to our eyes.
Example: Why Oxygen Is Invisible
Consider the oxygen in the room around you—it is completely invisible. The energy gap between oxygen's highest occupied orbital and its lowest unoccupied orbital is enormous, corresponding to ultraviolet light. Since your eyes cannot detect ultraviolet radiation, oxygen appears colorless.
For a compound to appear colored, it must absorb light within the visible spectrum. This requires a much smaller energy gap than what exists in molecules like O2. The d-orbital splittings produced by crystal field theory in coordination compounds—whether octahedral, tetrahedral, or square planar—generate energy gaps that frequently correspond to visible light wavelengths. That is precisely why transition metal complexes tend to be so colorful.
Absorbed Color vs. Observed Color
Here is an important distinction: the color a compound absorbs is not the color it appears to your eyes. When a coordination compound absorbs a particular wavelength of visible light, it reflects everything else. The color you perceive is the complementary color—the color on the opposite side of the color wheel from the absorbed wavelength.
Example: Red Absorption → Green Appearance
If a complex absorbs red light, the remaining reflected wavelengths average out to produce a green appearance. Red and green sit on opposite sides of the color wheel, making them complementary colors.
Important Distinction: In general chemistry courses, we typically discuss the color of light absorbed rather than the color the compound appears to the eye. Keep this distinction clear—absorbed color and observed color are complementary, not identical.
Crystal Field Splitting and the Visible Spectrum
The size of the d-orbital crystal field splitting energy determines where in the visible spectrum a coordination compound absorbs light:
- Larger splitting energy → absorbs higher-energy light → shifted toward the blue-violet end of the spectrum
- Smaller splitting energy → absorbs lower-energy light → shifted toward the red end of the spectrum
You may encounter the terms blue-shifted and red-shifted to describe these tendencies. Strictly speaking, the high-energy end of the visible spectrum is violet (the order runs blue → indigo → violet), but it is common shorthand to refer to the "blue end" and the "red end."
Tip: You may not be able to predict the exact color a complex absorbs, but you can make comparative predictions. Given two complexes, the one with the larger crystal field splitting energy absorbs closer to the blue-violet end, while the one with the smaller splitting absorbs closer to the red end.
2 Requirements for a Colored Coordination Complex
For a coordination compound to appear colored through d-orbital transitions, 2 conditions must both be satisfied: there must be at least one electron in a lower-energy d orbital, and there must be at least one empty space in a higher-energy d orbital for that electron to be promoted into.
d1 Through d9: Expect Color
Any complex with one to nine d electrons satisfies both requirements. There are electrons available in the lower set and vacancies in the upper set, so visible light absorption is expected. The general rule: d1 through d9 coordination complexes are expected to be colored.
d0 and d10: Expect Colorless
At the 2 extremes of the d-electron count, the mechanism for color breaks down:
- d0 — No d electrons exist to be promoted, so no d-d transition can occur.
- d10 — All d orbitals are completely filled. Although electrons exist in the lower set, there are no empty spaces in the upper set. No promotion is possible.
Caveat: A d0 or d10 compound could still be colored for reasons unrelated to crystal field splitting (such as charge-transfer transitions or π-electron effects you may encounter in organic chemistry). However, within the scope of crystal field theory, we predict these configurations to be colorless.
Square Planar d8 Complexes: Always Colored
Square planar complexes are a special case. They exist exclusively for d8 configurations. With eight electrons distributed across the square planar splitting pattern, there will always be electrons in the lower-energy orbitals and at least one vacancy in the highest-energy orbital. Therefore, every square planar d8 complex is expected to be colored.
| d-Electron Count | Electrons in Lower Set? | Empty Spaces in Upper Set? | Expected Color? |
|---|---|---|---|
| d0 | No | Yes | Colorless |
| d1–d9 | Yes | Yes | Colored |
| d10 | Yes | No | Colorless |
| d8 (square planar) | Yes | Yes | Always colored |
Paramagnetic vs Diamagnetic: Key Differences
Beyond color, another key property predictable from d-electron configurations is magnetic behavior. Understanding paramagnetic vs diamagnetic behavior is distinct from ferromagnetism, which is associated with materials like iron (where entire domains of aligned spins create permanent magnets).
Electrons possess an intrinsic property called spin, represented as either "spin up" or "spin down." These 2 spin states are equal in magnitude but opposite in direction. When 2 electrons are paired in the same orbital, their spins cancel completely, producing no net magnetic moment.
Paramagnetic: 1 or More Unpaired Electrons
A substance is paramagnetic when it contains one or more unpaired electrons. The unpaired spins produce a net magnetic moment, causing the substance to experience a slight attraction toward an external magnetic field. The more unpaired electrons present, the stronger the paramagnetic effect.
Diamagnetic: All Electrons Paired
A substance is diamagnetic when all electrons are paired. With no net spin, the substance experiences a very slight repulsion from an external magnetic field. This is a much weaker effect than paramagnetism.
4-Step Method to Determine Paramagnetic vs Diamagnetic: (1) Identify the number of d electrons. (2) Fill them into the appropriate splitting diagram (octahedral, tetrahedral, or square planar). (3) Account for high-spin vs. low-spin when applicable. (4) Count unpaired electrons. Any unpaired electrons → paramagnetic. All paired → diamagnetic.
| Property | Paramagnetic | Diamagnetic |
|---|---|---|
| Requirement | At least 1 unpaired electron | All electrons paired |
| Response to magnetic field | Slight attraction | Very slight repulsion |
| Net spin? | Yes | No |
7 Worked Examples: Predicting Color and Magnetic Properties
Example 1: Sc3+ (d0)
Predicting Properties of Sc3+
Start by determining the d-electron count. Scandium's electron configuration is [Ar] 4s2 3d1. Removing 3 electrons (the 2 4s electrons first, then the 1 3d electron) leaves just [Ar]—a noble gas configuration with zero d electrons (d0).
Color prediction: With d0, no electrons can be promoted between d-orbital sets. Expect colorless.
Magnetic prediction: The ion is isoelectronic with argon, meaning all electrons are paired. Expect diamagnetic.
Example 2: Cu+ (d10)
Predicting Properties of Cu+
Copper is one of the notable electron configuration exceptions: [Ar] 4s1 3d10 rather than [Ar] 4s2 3d9. Removing the single 4s electron for Cu+ gives [Ar] 3d10—a d10 configuration.
Color prediction: All d orbitals are completely filled regardless of geometry. No vacancies exist for electron promotion. Expect colorless.
Magnetic prediction: Every orbital is fully occupied with paired electrons. Expect diamagnetic.
Example 3: Fe2+ Octahedral Low-Spin (d6)
Fe2+ in an Octahedral Low-Spin Complex
Iron's configuration is [Ar] 4s2 3d6. Losing 2 electrons (both from 4s) produces Fe2+ with [Ar] 3d6—a d6 configuration. With 6 d electrons, the filling pattern differs dramatically between high spin and low spin.
Color prediction: As a d6 complex (between d1 and d9), electrons occupy the lower set with vacancies in the upper set. Expect colored.
Magnetic prediction (low spin): In a low-spin octahedral arrangement, the large crystal field splitting energy forces all 6 electrons to pair up in the lower t2g set before occupying the upper eg set. All electrons end up paired. Expect diamagnetic.
Example 4: Fe2+ Octahedral High-Spin (d6)
Fe2+ in an Octahedral High-Spin Complex
Same ion as above—Fe2+ is still d6. The electron count and color prediction remain unchanged.
Color prediction: Still d6, still between d1 and d9. Expect colored.
Magnetic prediction (high spin): In a high-spin arrangement, electrons occupy higher-energy orbitals before pairing in the lower set. Filling gives: 3 electrons singly occupying the t2g orbitals, then 2 electrons singly in the eg orbitals, and finally the 6th electron pairs in one of the t2g orbitals. This leaves 4 unpaired electrons—making the complex strongly paramagnetic.
Key Comparison — Paramagnetic vs Diamagnetic for the Same Ion: Fe2+ powerfully illustrates why spin state matters. The same ion in a low-spin octahedral complex is diamagnetic (all paired), while in a high-spin octahedral complex it is strongly paramagnetic (4 unpaired electrons). Ligand field strength completely changes the magnetic behavior.
Example 5: Cr3+ Octahedral (d3)
Predicting Properties of Cr3+
Chromium is another electron configuration exception: [Ar] 4s1 3d5 rather than [Ar] 4s2 3d4. Removing 3 electrons (1 from 4s, then 2 from 3d) produces Cr3+ with a d3 configuration.
With only 3 d electrons, the filling pattern is identical regardless of spin state—each electron occupies one of the 3 t2g orbitals singly. The distinction between low and high spin only matters for d4 through d7 in octahedral complexes.
Color prediction: As d3, electrons are present in the lower set with vacancies in the upper set. Expect colored.
Magnetic prediction: 3 unpaired electrons. Expect paramagnetic.
Example 6: [FeF6]3− Weak-Field Ligand (d5 High Spin)
Predicting Properties of [FeF6]3−
Step 1 — Identify geometry: 6 monodentate fluoride ligands give a coordination number of 6, which means octahedral geometry.
Step 2 — Determine oxidation state: Each F− contributes −1, totaling −6. The overall complex charge is −3, so iron must be in the +3 oxidation state.
Step 3 — Find d-electron count: Iron is [Ar] 4s2 3d6. Removing 3 electrons (2 from 4s, 1 from 3d) gives Fe3+ with a d5 configuration.
Step 4 — Determine spin state: F− is a weak-field ligand, which corresponds to a small crystal field splitting energy, meaning high spin. All 5 electrons occupy separate orbitals before any pairing occurs.
Color prediction: As d5, this falls within the d1–d9 range. Expect colored.
Magnetic prediction: 5 unpaired electrons make this complex highly paramagnetic.
Spectrochemical Series Rule: Weak-field ligand → small crystal field splitting → high spin. Strong-field ligand → large crystal field splitting → low spin. This relationship is critical for predicting paramagnetic vs diamagnetic behavior from the spectrochemical series.
Example 7: Ni2+ Square Planar (d8)
Predicting Properties of Ni2+ in a Square Planar Complex
Nickel's configuration is [Ar] 4s2 3d8. Removing 2 electrons gives Ni2+ with [Ar] 3d8—a d8 configuration. Square planar geometry exists exclusively for d8 complexes.
Color prediction: Every square planar d8 complex has electrons in the lower-energy orbitals and at least 1 vacancy at the top of the splitting pattern. Expect colored.
Magnetic prediction: When 8 electrons fill the square planar splitting pattern, all electrons pair up completely. Expect diamagnetic.
Comparing Complexes: Which Absorbs Blue Light?
Consider 2 complexes: [Fe(CN)6]4− and [Fe(H2O)6]2+. Both contain Fe2+ (verify: cyanide is −1 each, 6 gives −6, so iron is +2 to make the overall charge −4; water is neutral, so the +2 charge comes entirely from iron). Since both complexes feature the same metal ion, the difference in their light absorption comes entirely from the ligands.
To answer which complex absorbs blue light, you need the spectrochemical series—the ranking of ligands by the crystal field splitting energy they produce. Cyanide (CN−) sits at the top of the spectrochemical series, producing the largest crystal field splitting. Water (H2O) sits lower, producing a smaller splitting energy.
Example: Comparing Light Absorption Using the Spectrochemical Series
[Fe(CN)6]4− — large crystal field splitting → absorbs higher-energy light → closer to the blue-violet end of the spectrum.
[Fe(H2O)6]2+ — smaller crystal field splitting → absorbs lower-energy light → closer to the red end of the spectrum.
Therefore, the cyanide complex is more likely to absorb blue light.
Note: Whether these complexes are high spin or low spin is irrelevant for this comparison. The energy of light absorbed corresponds to the crystal field splitting energy regardless of electron filling order. What matters here is solely the size of the splitting, which is determined by the ligand's position in the spectrochemical series.
8 Key Takeaways
- Coordination compounds appear colored because d-orbital crystal field splitting energies often correspond to visible light wavelengths, enabling electron promotion between d-orbital sets.
- Absorbed color does not equal observed color. A compound's visible color is the complement of the absorbed wavelength, as described by the color wheel.
- d1 through d9 complexes are expected to be colored (electrons available for promotion and vacancies to receive them), while d0 and d10 complexes are expected to be colorless.
- Square planar d8 complexes are always expected to be colored.
- Paramagnetic substances have 1 or more unpaired electrons and are slightly attracted to a magnetic field; diamagnetic substances have all electrons paired and experience a very slight repulsion.
- Spin state determines paramagnetic vs diamagnetic behavior: the same ion (e.g., Fe2+) can be diamagnetic in a low-spin complex or paramagnetic in a high-spin complex.
- Weak-field ligands produce high-spin complexes (small crystal field splitting); strong-field ligands produce low-spin complexes (large splitting).
- Larger crystal field splitting shifts light absorption toward the blue-violet end of the spectrum; smaller splitting shifts it toward the red end. The spectrochemical series ranks ligands by their splitting strength.