Magnetic Properties of Transition Metal Complexes | OpenStax Chemistry 2e 19.3

The spin-only magnetic moment (μ) is calculated using the formula μ = √(n(n+2)) Bohr-Magnetons, where n is the number of unpaired electrons. For example, with 7 unpaired electrons: μ = √(7×9) = √63 ≈ 7.93 BM. This calculation involves multiplying the number of unpaired electrons by itself plus two, taking the square root of the product, and expressing the result in Bohr-Magnetons (BM).

The spin-only magnetic moment (μ) is calculated using the formula μ = √[n(n+2)] Bohr Magnetons, where n is the number of unpaired electrons. For n=1, μ = √3 ≈ 1.73 BM. When unpaired electrons = 1, the nearest integer value is 2 BM. This formula is used to determine magnetic properties of transition metal compounds.

The spin-only magnetic moment (μ) is calculated using the formula μ = √[n(n+2)] Bohr Magnetons, where n is the number of unpaired electrons. For example: 1 unpaired electron gives μ = 1.732 BM, 2 unpaired electrons give μ = 2.828 BM, 3 unpaired electrons give μ = 3.873 BM, 4 unpaired electrons give μ = 4.899 BM, and 5 unpaired electrons give μ = 5.916 BM.

The spin-only magnetic moment is calculated using the formula μ = √(n(n+2)) Bohr magnetons, where n is the number of unpaired electrons. Alternatively, using the spin quantum number s (where s = n/2), the formula is μ = √(4s(s+1)). For example, with one unpaired electron (s=1/2), μ = √(4×(1/2)(3/2)) = √3 ≈ 1.73 BM.

The spin-only magnetic moment is calculated using the formula: μ = √[n(n+2)] Bohr Magnetons, where n is the number of unpaired electrons. For example, Co²⁺ has 3 unpaired electrons, so μ = √[3(3+2)] = √15 Bohr Magnetons.

Ligands can be arranged in a spectrochemical series based on their ability to split d-orbitals. Weak field ligands (iodide, chloride, hydroxide, fluoride, ammonia) produce small splitting, while strong field ligands (carbon monoxide) produce large splitting. This classification determines whether complexes will be high spin or low spin. High spin complexes form with weak field ligands when electron pairing energy exceeds crystal field splitting energy, resulting in unpaired electrons and paramagnetism. Low spin complexes form with strong field ligands when large Δ₀ makes electron pairing energetically favorable, typically resulting in diamagnetism.

The spectrochemical series is an ordered list of ligands from weakest field (smallest crystal field splitting) to strongest field (largest crystal field splitting). This series helps predict whether a given metal-ligand complex will be high-spin or low-spin. Weak-field ligands like iodide, bromide, and chloride cause minimal splitting and typically produce high-spin complexes. Strong-field ligands like cyanide and carbon monoxide cause significant splitting and typically produce low-spin complexes. There is a gray area in the middle where ligands can lead to either high-spin or low-spin complexes depending on the specific metal center.

Ligands are classified as strong field or weak field based on the magnitude of Δ₀ relative to pairing energy P. Strong field ligands cause large splitting (Δ₀ > P), leading to low-spin complexes where electrons pair in t2g orbitals before occupying eg orbitals. Weak field ligands cause small splitting (Δ₀ < P), leading to high-spin complexes where electrons occupy eg orbitals before pairing in t2g orbitals. The spectrochemical series ranks ligands by field strength: I⁻ < Br⁻ < S²⁻ < SCN⁻ < Cl⁻ < NO₃⁻ < F⁻ < OH⁻ < C₂O₄²⁻ < H₂O < NCS⁻ < CH₃CN < NH₃ < en < bipy < phen < NO₂⁻ < PPh₃ < CN⁻ < CO.

The spectrochemical series ranks ligands by their ability to split the d-orbitals of a metal ion. Ligands at the left end (like I⁻, Br⁻, Cl⁻, SCN⁻) are weak field ligands that cause minimal splitting, while those at the right end (like CN⁻, CO, NO⁺) are strong field ligands that cause maximal splitting. This ranking determines whether a complex will be high-spin or low-spin. For example, [Fe(CN)6]⁴⁻ is low-spin because CN⁻ is a strong field ligand, whereas [FeF6]³⁻ is high-spin because F⁻ is a weak field ligand.

The spectrochemical series ranks ligands by field strength: I- < Br- < Cl- < F- < OH- < H2O < NH3 < en < CN- < CO. Strong field ligands cause large splitting (Δ > P), favoring low spin complexes. Weak field ligands cause small splitting (Δ < P), favoring high spin complexes. This series helps predict spin state and magnetic properties.

Color arises from d-orbital splitting. Electrons absorb specific wavelengths to jump between split orbitals. The observed color is complementary to absorbed wavelength. Larger Δ means shorter absorbed wavelength (violet/blue). Smaller Δ means longer absorbed wavelength (red/orange). For [Co(NH3)6]^3+, absorbs violet (~400 nm), appears yellow. For [Co(H2O)6]^3+, absorbs orange (~600 nm), appears blue.

Metal complexes consist of a central metal atom or ion surrounded by ligands. Three major electronic transitions occur in UV-Visible spectroscopy: (1) Intraligand transitions within organic ligands (π to π*, σ to σ*, non-bonding to antibonding) appear in UV region (200-400 nm); (2) d-d transitions involve electron movement between split d-orbitals of the central metal, appearing in visible region (400-800 nm); (3) Charge transfer transitions (MLCT/LMCT) involve electron movement between metal and ligand orbitals. Ligand approach causes d-orbital splitting: octahedral environments split d-orbitals into lower-energy (3 orbitals) and higher-energy (2 orbitals) sets, while tetrahedral environments split into lower-energy (2 orbitals) and higher-energy (3 orbitals) sets. The color of metal complexes is determined by the complementary color to the absorbed light.

Copper(II) sulfate pentahydrate is blue while anhydrous copper sulfate is white. The blue color arises because water ligands create specific d-orbital splitting that absorbs orange light (600-650 nm). The transmitted blue light is observed. When water is removed, the splitting changes and the complex becomes white as it no longer absorbs visible light. This demonstrates how ligand identity and hydration state directly determine complex color through their effects on d-orbital energy separation.

Many colored inorganic compounds are coordination complexes of transition metals. In solution, metal cations are surrounded by ligands forming coordination complexes. In crystal field theory, ligands are treated as point charges creating an electric field. In octahedral fields, the five degenerate d-orbitals split into two energy levels: higher energy eg orbitals (dz2, dx2-y2) pointing directly at ligands, and lower energy t2g orbitals (dxy, dxz, dyz) pointing between ligands. The energy difference (Δ) corresponds to light energy absorbed in the visible region, producing characteristic colors. The color depends on the magnitude of d-orbital splitting, determined by the metal ion and ligands. Different metals with the same ligands produce different colors because splitting depends on metal identity. Different ligands with the same metal produce different colors because ligands have different field strengths. The spectrochemical series ranks ligands: I- < Br- < Cl- < F- < OH- < H2O < NH3 < en < CN- < CO. In addition to d-d transitions, coordination complexes exhibit charge transfer transitions (LMCT and MLCT) producing very intense bands (ε > 10,000) responsible for intense colors.

Crystal Field Theory explains the special properties of transition metals by considering how negative point charge ligands around a metal ion repel and split the d-orbital energy levels into two sets (t2g and eg), with the magnitude of splitting determined by ligand strength (spectrochemical series). This splitting determines whether complexes are high-spin (weak field, more unpaired electrons, paramagnetic) or low-spin (strong field, fewer unpaired electrons, diamagnetic), and directly influences the color of transition metal complexes through electronic transitions between split energy levels.

Coordination complexes are chemical species formed from a central metal ion (typically from the d-block or f-block of the periodic table) surrounded by ligands, which are molecules or ions that donate electron pairs to form coordinate bonds; these complexes exhibit distinctive properties such as intense coloration and magnetic behavior, and have important applications in homogeneous catalysis and medical imaging (like MRI contrast agents using gadolinium complexes), with their structure and naming following specific conventions where ligands are listed alphabetically with numerical prefixes, followed by the metal name and oxidation state, enclosed in brackets with the overall charge indicated.

Coordination chemistry enables powerful medical applications. Cisplatin, a square planar d⁸ platinum(II) complex, treats testicular cancer by binding to DNA at guanine N7 positions, creating intrastrand cross-links that kink DNA and prevent transcription/translation, triggering apoptosis. The cis isomer's adjacent chloride ligands enable DNA binding; trans isomer lacks this property. Beyond DNA, cisplatin binds sulfur-containing amino acids (cysteine, methionine), causing side effects. Analogous drugs like carboplatin and oxaliplatin contain bidentate chelating ligands that increase complex stability and reduce reactivity, minimizing side effects through the chelate effect. Gadolinium contrast agents enhance MRI by shortening proton relaxation times. Gadolinium(III) has seven unpaired electrons in its 4f sublevel, creating a large magnetic moment that accelerates neighboring proton relaxation. Effective agents require: high aqueous solubility for IV administration, open coordination sites for water binding, high relaxivity, and fast water exchange rates. Since gadolinium is toxic and can substitute for essential metals like calcium, all clinical agents are chelated with multidentate ligands (often 8-dentate) to ensure stability and prevent toxicity while maximizing contrast enhancement.

Coordination chemistry enables medical applications. Gadolinium and technetium complexes with high Kf are safe for MRI contrast despite metal toxicity. Cisplatin, a square planar Pt complex, coordinates to DNA nitrogen atoms, preventing replication and treating cancer. Discovered in 1960, it initiated platinum-based chemotherapy. These applications demonstrate how complex stability principles translate to life-saving medical treatments.

Gadolinium(III) complexes are used as MRI contrast agents. They enhance the contrast between different tissues by shortening the relaxation times of nearby water protons. The complexes are typically chelated with DTPA or DOTA ligands to prevent toxicity. Gadolinium's large magnetic moment and slow electronic relaxation make it ideal for this application.

MRI operates on NMR principles where radio frequency energy causes protons to flip to higher energy states and precess, creating net magnetization oriented perpendicular to the main magnetic field. As protons return to baseline, they undergo T2 relaxation (losing transverse magnetization) and T1 relaxation (recovering longitudinal magnetization). Gadolinium, a paramagnetic lanthanide metal with atomic number 64, serves as the primary MRI contrast agent. Its electron configuration [Xe] 4f^7 5d^1 6s^2 provides unpaired electrons responsible for magnetic properties. When injected, gadolinium affects local magnetic fields, accelerating proton relaxation and producing stronger T1 signals that enhance image contrast.