Coordination Chemistry

Coordination compounds contain a central metal ion (usually a transition metal) bonded to surrounding molecules or ions called ligands through coordinate covalent bonds. In these bonds, both electrons come from the ligand, which acts as a Lewis base donating an electron pair to the metal (Lewis acid).

The metal ion plus its attached ligands form the coordination sphere, enclosed in square brackets in formulas. Species outside the brackets are counter ions, not directly bonded to the metal. The coordination number is the total number of donor atoms bonded to the metal — common values are 2, 4, and 6, producing linear, tetrahedral or square planar, and octahedral geometries respectively.

Monodentate ligands (e.g., NH₃, Cl⁻, H₂O) bind through a single donor atom. For these ligands the coordination number equals the number of ligands attached.

Polydentate ligands bind to a metal through two or more donor atoms simultaneously. Bidentate ligands such as ethylenediamine (en, H₂NCH₂CH₂NH₂) have two donor atoms; for example, [Co(en)₃]³⁺ has three bidentate ligands giving a coordination number of six.

A complex formed with a polydentate ligand is called a chelate (from the Greek for “claw”). Chelates are generally more stable than analogous complexes with monodentate ligands because dissociation requires breaking multiple bonds simultaneously.

The hexadentate ligand EDTA binds through six donor atoms and is widely used in water softening, food preservation, and medicine. In chelation therapy, drugs such as dimercaptosuccinic acid (DMSA) form water-soluble chelates with toxic heavy metals (arsenic, mercury, lead), allowing the kidneys to excrete them.

Werner nomenclature follows systematic rules for naming coordination compounds:

1. In ionic compounds, name the cation before the anion.
2. Name ligands alphabetically before the metal. Anionic ligands add -o to the root (chlorido, hydroxido, cyano). Neutral ligands use their molecule name, with four exceptions: H₂O = aqua, NH₃ = ammine, CO = carbonyl, NO = nitrosyl.
3. Use Greek prefixes (di-, tri-, tetra-, penta-, hexa-) for multiple identical ligands. If the ligand name itself contains a prefix, use bis-, tris-, tetrakis- with the ligand in parentheses.
4. State the metal name followed by its oxidation state in Roman numerals. When the complex is an anion, the metal name takes the suffix -ate (ferrate for iron, cuprate for copper, plumbate for lead).

Example: [Co(NH₃)₄Cl₂]Cl is tetraamminedichloridocobalt(III) chloride. The oxidation state of cobalt is +3 because the complex ion has a +1 charge: +1 = Co + 0 + 2(−1).

The coordination number of a complex largely determines its geometry. The three most common arrangements are:

• Octahedral (coordination number 6): six ligands arranged at 90° angles around the metal, e.g., [Co(H₂O)₆]²⁺.
• Tetrahedral (coordination number 4): four ligands at 109.5° angles, common for d⁰ or d¹⁰ metals with low oxidation states, e.g., [Zn(CN)₄]²⁻.
• Square planar (coordination number 4): four ligands in a flat arrangement at 90°, typical for d⁸ metals such as Pt²⁺ and Ni²⁺, e.g., [Pt(NH₃)₂Cl₂].

Less common geometries include linear (coordination number 2, e.g., [Ag(NH₃)₂]⁺), trigonal bipyramidal and square pyramidal (coordination number 5). Unlike main-group compounds, nonbonding d electrons do not influence the arrangement of ligands.

Coordination compounds can exist as isomers — species with the same formula but different structures or spatial arrangements.

Geometric isomers (cis/trans) occur when two identical ligands can occupy adjacent positions (cis) or opposite positions (trans). For example, [Co(NH₃)₄Cl₂]⁺ has a violet cis isomer and a green trans isomer, demonstrating that spatial arrangement affects physical properties including color, polarity, and solubility.

Optical isomers (enantiomers) are non-superimposable mirror images, analogous to left and right hands. Complexes such as [M(en)₃]ⁿ⁺ are chiral and rotate plane-polarized light in opposite directions.

Other isomer types include linkage isomers (same ligand bound through different atoms, e.g., –SCN vs. –NCS) and ionization isomers (exchange of an ion between the coordination sphere and the counter ion).

Crystal field theory (CFT) explains the electronic structure, color, and magnetic behavior of coordination complexes. It treats metal–ligand interactions as purely electrostatic: ligand electron pairs repel the metal’s d electrons, causing the five d orbitals to split into groups of different energy.

In an octahedral complex, ligands approach along the axes, repelling the e_g orbitals (d_z² and d_x²−y²) more than the t_2g orbitals (d_xy, d_xz, d_yz). The energy gap between these sets is called Δ_oct.

The spectrochemical series ranks ligand tendencies from smaller to larger crystal-field splitting for otherwise comparable complexes. Use the Spectrochemical Series and Spin States reference for the complete general-chemistry ordering. The actual Δ_oct also depends on the metal ion, oxidation state, d-block row, geometry, and full ligand environment.

For octahedral d⁴–d⁷ complexes, compare Δ_oct with the pairing energy P. If Δ_oct > P, electrons pair in t_2g before occupying e_g, giving a low-spin complex. If Δ_oct < P, electrons occupy e_g before pairing, giving a high-spin complex.

Crystal field theory extends beyond octahedral complexes, and each geometry has its own splitting pattern.

Counting d electrons first. Every CFT analysis starts from the metal ion's d-electron count: write the free-metal configuration, then remove electrons 4s before 3d (even though 3d fills after 4s during Aufbau). Example: Fe = [Ar]4s²3d⁶ → Fe³⁺ = [Ar]3d⁵; Cu = [Ar]4s¹3d¹⁰ → Cu²⁺ = [Ar]3d⁹.

Tetrahedral complexes invert the octahedral pattern. With four ligands at alternate corners of a cube, no d orbital points directly at a ligand. The e set (d_z², d_x²−y²) lies lower and the t₂ set (d_xy, d_xz, d_yz) lies higher — the reverse of octahedral. Because the overlap is weaker, the gap is small: Δ_tet = (4/9)Δ_oct. That small gap is below the pairing energy in ordinary general-chemistry cases, so tetrahedral complexes are treated as high spin.

Square-planar complexes (d⁸) split into four levels. Removing the two z-axis ligands from an octahedron stabilizes d_z² and strongly destabilizes d_x²−y², which points straight at the four in-plane ligands. From highest to lowest: d_x²−y² > d_xy > d_z² > d_xz/d_yz (degenerate). A d⁸ ion (Pt²⁺, Pd²⁺, or some Ni²⁺ complexes) can fill the four lower orbitals with all 8 electrons and leave d_x²−y² empty, making the square-planar complex diamagnetic.

When high-spin/low-spin is not meaningful. The HS/LS distinction exists only where field strength changes the filling. For d³ octahedral (three electrons singly filling t_2g) and d⁸ octahedral (t_2g full, two unpaired in e_g), the filling is identical at any field strength. Likewise d¹, d⁹, and d¹⁰ each have only one possible arrangement. For these counts, state the configuration and magnetism, and note that the HS/LS label does not apply.

Mixed ligands require evidence. There is no rule that the strongest ligand present sets the field strength for the entire complex. If a mixed-ligand d⁴–d⁷ octahedral problem supplies neither a Δ_oct/P comparison nor experimental spin information, its spin state may be underdetermined.

Transition metal complexes are often vividly colored because they absorb visible light with energy matching Δ_oct. An absorbed photon promotes an electron from the t_2g to the e_g set. The color you see is complementary to the absorbed wavelength — for example, [Cu(NH₃)₄]²⁺ absorbs orange-red light and appears blue.

Strong-field ligands produce large Δ_oct values, so these complexes absorb higher-energy violet or blue light and appear yellow, orange, or red. Weak-field ligands yield small Δ_oct, absorbing lower-energy red or orange light, making the complex appear blue or green. Complexes with d⁰ or d¹⁰ configurations (no possible d–d transitions) are usually colorless.

CFT also explains magnetic behavior. Complexes with unpaired electrons are paramagnetic (attracted to a magnetic field), while those with all electrons paired are diamagnetic. The measured magnetic moment reveals the number of unpaired electrons, confirming whether a complex is high-spin or low-spin.

Use this workflow to keep naming, geometry, and electronic reasoning consistent:

1. Identify the coordination sphere and any counterions first.
2. Determine oxidation state from ligand charges and overall complex charge.
3. Name ligands alphabetically (ignoring multiplicative prefixes for alphabetization), then metal with oxidation state.
4. Check geometry from coordination number, then evaluate possible isomerism.
5. Use ligand-field strength to reason about splitting magnitude, spin state, color, and magnetism.

Frequent errors: losing charge balance when assigning oxidation state, mixing ligand naming conventions, and treating color predictions as exact wavelength calculations rather than qualitative d-orbital splitting outcomes. A final consistency check is whether nomenclature, oxidation state, and electron count all tell the same chemical story.

Because a colored complex absorbs visible light at the energy of its d–d transition (the Δ_oct gap), the amount of light it absorbs can be measured and used to find how much complex is present. This quantitative relationship is the Beer-Lambert law (also called Beer's law):

A = εbc

The three quantities on the right each have a specific meaning:

• Absorbance (A) is a dimensionless (unitless) measure of how much light the sample absorbs at a chosen wavelength. A larger A means more light absorbed.
• Molar absorptivity (ε), also called the molar extinction coefficient, measures how strongly one mole-per-liter of the absorbing species absorbs at that wavelength. It has units of M⁻¹·cm⁻¹ (equivalently L·mol⁻¹·cm⁻¹) and is specific to both the species and the wavelength chosen — a different wavelength gives a different ε.
• Path length (b), sometimes written ℓ, is the distance the light travels through the sample, measured in centimeters (cm). A standard cuvette has b = 1 cm.
• Concentration (c) is the molar concentration of the absorbing species in mol/L (M).

Because A is dimensionless and b is in cm and c is in M, the units of ε (M⁻¹cm⁻¹) are exactly what is needed to cancel cm and M, leaving A unitless.

The law can be rearranged to solve for whichever quantity is unknown when the other three are known:

• Concentration: c = A / (εb)
• Molar absorptivity: ε = A / (bc)
• Path length: b = A / (εc)

The ratio (comparison) form. When the same species is measured at the same wavelength in the same cuvette, ε and b are constant, so absorbance is directly proportional to concentration (A ∝ c). Comparing two solutions then lets ε and b cancel entirely:

A₁ / A₂ = c₁ / c₂

This is the fastest route to an unknown concentration from a known standard: c₂ = c₁ × (A₂ / A₁), with no need to know ε or b. If a sample is diluted before measuring, first apply the dilution law (M₁V₁ = M₂V₂) to get the diluted concentration that the spectrophotometer actually sees, then use A = εbc on that diluted concentration to extract ε.