Topic 2: Inorganic Chemistry II - The Origin of Color & Magnetism

Origin of Color

• When an object appears colored, it means that only a portion of the light striking it is absorbed, and the remaining light is reflected

• The absorbed light provides energy to excite electrons into higher energy (excited) orbitals

• The color perceived is the complementary color to the one absorbed (visualized using a color wheel)

  • Example: If a compound absorbs green light (around 510 nm), it will appear red-violet or pink

Origin of Color - In Transition Metal Complexes

• In transition metal complexes, the color typically arises from electronic transitions between the split d-orbitals, known as d-d transitions

• If the energy gap (Δₒ) matches the energy (E) of an incoming photon → the photon is absorbed → an electron in a lower t_2g orbital can be excited to the higher e_g orbital

Energy-Wavelength Relationship

λ = hc/E

Where:

• λ (lambda) → wavelength of light (usually in meters, m)

• h → Planck’s constant (6.626 × 10⁻³⁴ J·s)

• c → speed of light (3.00 × 10⁸ m/s)

• E → energy of one photon (in joules, J)

Δₒ in Transition Metal Complexes

Often falls within the visible spectrum (400–700 nm), causing them to appear colored

Colored Compounds

Transition metals with d¹ through d⁹ configurations usually display d-d transitions (and are colored)

Colorless Compounds

Transition metals with d⁰ or d¹⁰ configurations absorb photons outside the visible spectrum

• d⁰ lacks electrons in t_2g orbitals

• d¹⁰ has t_2g and e_g orbitals completely filled

Ligand Field Strength Effect on Δₒ

• Strong-field ligands → greater Δₒ → higher energy (shorter wavelength) absorbed

• Weak-field ligands → smaller Δₒ → lower energy (longer wavelength) absorbed

Spectrochemical Series

CO > CN⁻ > NO₂⁻ > en > NH₃ > H₂O > C₂O₄²⁻ > OH⁻ > F⁻ > Cl⁻ > Br⁻ > I⁻

Exceptions - Charge Transfer and Color

d⁰ or d¹⁰ complexes can be colored due to charge transfer!

Ligand to Metal Charge Transfer (LMCT)

• Electron transfers from ligand orbital to metal orbital

• Common in high oxidation states (e.g., MnO₄⁻)

Metal to Ligand Charge Transfer (MLCT)

• Electron transfers from metal to ligand orbital

• Common in low oxidation states (e.g., [Ru(bipy)₃]²⁺)

Beer-Lambert Law

A = log₁₀(I₀/I) = ε·c·L

Molar absorption coefficient (ε), concentration (c), and path length (L)

Calibration Curve

Plotting absorbance vs. concentration gives a straight line to intrapolate the unknown concentration

Diamagnetic

• All electrons paired

• Weakly repelled by magnetic fields

Paramagnetic

• One or more unpaired electrons

• Strongly attracted to magnetic fields

Molar Magnetic Susceptibility (χₘ)

Quantitative measure of magnetic property

Measurement Method

1. Suspending a sample of a material between the poles of a magnet

2. Switching the magnet on attracts a paramagnetic material and weakly repels a diamagnetic material

3. Causes a change in weight detected by a Guoy balance

Effective Magnetic Moment (μ_eff) - General Formula

• Reported in Bohr magnetons (μB)

• Relates to χₘ and T: μ_eff = 2.828√(χₘ×T)

  • Where χ_m = molar magnetic susceptibility, T = temperature

Effective Magnetic Moment (μ_eff) - Spin-only formula

• Reported in Bohr magnetons (μB)

• μ_eff = √(n(n+2))

  • Where n = number of unpaired electrons

• Approximation: μ_eff ≈ n + 1 (rough estimate)

High-Spin Complexes

Weak-field ligands (small Δₒ), more unpaired electrons, large μ_eff

Low-Spin Complexes

Strong-field ligands (large Δₒ), fewer unpaired electrons, may be diamagnetic, smaller μ_eff

Spin-Crossover (SCO)

Compounds that switch between high-spin and low-spin states under heat, light, or pressure

Single Molecule Magnets (SMM)

Retain spin orientation even without magnetic field (e.g., [Mn₁₂O₁₂(Ac)₁₆(H₂O)₄])