Crystal Field Theory explains the properties of coordination compounds by treating ligands as point charges (or dipoles) that create an electrostatic field around the central metal ion. This field splits the otherwise degenerate d-orbitals into groups of different energies. In an octahedral complex: the 5 d-orbitals split into two groups: $e_g$ set ($d_{z^2}$ and $d_{x^2-y^2}$) — higher energy, pointing toward ligands. $t_{2g}$ set ($d_{xy}$, $d_{xz}$, $d_{yz}$) — lower energy, pointing between ligands. Crystal field splitting energy $\Delta_o$ (or $10Dq$) = energy difference between $e_g$ and $t_{2g}$. The magnitude of $\Delta_o$ depends on: the nature of the ligand (spectrochemical series), the nature of the metal ion (charge and size), the type of complex geometry (octahedral, tetrahedral, square planar). $\Delta_{tet} \approx 4/9 \Delta_{oct}$ for same metal-ligand combination. Square planar: $\Delta_{sp} \approx 1.3 \Delta_{oct}$.

The spectrochemical series ranks ligands by their ability to cause crystal field splitting. In order of increasing field strength (increasing $\Delta_o$): $I^- < Br^- < S^{2-} < SCN^- < Cl^- < NO_3^- < F^- < OH^- < ox^{2-} < H_2O < NCS^- < EDTA < NH_3 < en < bipy < phen < NO_2^- < CN^- < CO$. Mnemonic: "I Bring Sulphur, Such Chlorine, Naughty Frogs Often Help Normally Establish Amorous Encounters Before Passion Normally Can Come." (rough approximation). Strong field ligands (CO, CN⁻, NO₂⁻): produce large $\Delta_o$, absorb UV/short wavelength light, form low-spin complexes. Weak field ligands (halides, H₂O): produce small $\Delta_o$, absorb visible red/orange light, often form high-spin complexes. The spectrochemical series applies to both $\Delta_o$ prediction and predicting spin state (high vs low spin).

For d⁴ to d⁷ configurations, electrons can be distributed in two ways depending on whether $\Delta_o$ > or < $P$ (pairing energy). Strong field ($\Delta_o > P$): electrons prefer to pair in $t_{2g}$ → low spin complex (fewer unpaired electrons). Weak field ($\Delta_o < P$): electrons prefer to go to higher $e_g$ rather than pair → high spin complex (more unpaired electrons). Examples for Co³⁺ (d⁶): with CN⁻ (strong field): $t_{2g}^6 e_g^0$ — 0 unpaired electrons, low spin, diamagnetic. With H₂O: $t_{2g}^6 e_g^0$ (still low spin for Co³⁺ because $\Delta_o$ for Co³⁺ with most ligands is large). Fe³⁺ (d⁵) with CN⁻: low spin, 1 unpaired. With H₂O: high spin, 5 unpaired. Magnetic moment: $\mu = \sqrt{n(n+2)}$ BM where $n$ = unpaired electrons. Measuring magnetic moment tells us whether a complex is high spin or low spin.

Transition metal complexes are coloured because electrons absorb certain wavelengths of visible light to jump from $t_{2g}$ to $e_g$ (d-d transitions). The colour we observe is the complementary colour of the absorbed colour. Complementary colour pairs: red-green, orange-blue, yellow-violet. A complex that absorbs red light appears green. [Ti(H₂O)₆]³⁺ (Ti³⁺, d¹): absorbs at 510 nm (green) → appears violet/purple. [Cu(H₂O)₆]²⁺: absorbs at ~810 nm (near IR/red) → appears blue. [CrCl₃(H₂O)₃]: dark green. [Co(NH₃)₆]³⁺: yellow-orange (absorbs blue-violet). [Co(NH₃)₅Cl]²⁺: purple. Stronger field ligand → larger $\Delta_o$ → shorter $\lambda$ absorbed → colour shifts toward blue/violet end → complex appears more reddish/orange. Weak field ligand → longer $\lambda$ absorbed → absorbs in orange/red → complex appears blue/green.

CFSE = extra stability gained from crystal field splitting. For octahedral complex: $t_{2g}$ electrons each contribute $-0.4\Delta_o$ (they are 0.4$\Delta_o$ below the barycentre). $e_g$ electrons each contribute $+0.6\Delta_o$. CFSE = $(-0.4 \times n_{t_{2g}} + 0.6 \times n_{e_g})\Delta_o$. For d⁶ low spin (Co³⁺ with CN⁻): $t_{2g}^6 e_g^0$: CFSE = $(-0.4 \times 6)\Delta_o = -2.4\Delta_o$. For d⁵ high spin (Fe³⁺ with H₂O): $t_{2g}^3 e_g^2$: CFSE = $(-0.4 \times 3 + 0.6 \times 2)\Delta_o = 0$ (no stabilization). This explains: why d⁰, d⁵ (high spin), d¹⁰ complexes have zero CFSE and are less stable than d³, d⁶ (low spin), d⁸ complexes. Anomalies in stability constants, lattice energies of transition metal compounds, and Irving-Williams series are explained by CFSE.

Coordination number (CN) = number of ligand donor atoms bonded to metal. CN 2: linear (e.g., [Ag(NH₃)₂]⁺, [Cu(CN)₂]⁻). CN 4: tetrahedral (weaker field, large ligands) or square planar (d⁸ ions like Pt²⁺, Pd²⁺, Ni²⁺ with strong field, Au³⁺). CN 6: octahedral (most common). CN 5: trigonal bipyramidal or square pyramidal. VSEPR alone cannot explain coordination geometry — electronic configuration of metal and ligand field strength matter. d⁸ metals (Ni²⁺, Pd²⁺, Pt²⁺, Au³⁺) form square planar complexes because the large crystal field splitting in square planar geometry stabilizes all 8 d-electrons in 4 orbitals below the highest-energy one (which remains empty), giving large CFSE advantage. This is why Pt²⁺ forms square planar but Ni²⁺ can form either, depending on ligand field strength.

Rules: name cation first, anion second. For complex ion: ligands named alphabetically, then metal with oxidation state in parentheses. Anionic ligands: -o suffix (Cl⁻=chlorido, CN⁻=cyanido, OH⁻=hydroxido, O²⁻=oxido, H⁻=hydrido, F⁻=fluorido). Neutral ligands: name as is except: H₂O=aqua, NH₃=ammine, CO=carbonyl, NO=nitrosyl. Prefixes: di-, tri-, tetra-, penta-, hexa- (for simple); bis-, tris-, tetrakis-, pentakis- (for complex/branched ligands). Anionic complexes: -ate suffix on metal (e.g., ferrate, chromate, cobaltate, platinate). Examples: [Co(NH₃)₅Cl]Cl₂ = pentaamminechloridocobalt(III) chloride. K₄[Fe(CN)₆] = potassium hexacyanidoferrate(II). [Cr(en)₃]³⁺ = tris(ethane-1,2-diamine)chromium(III) ion. Na₂[Pt(Cl)₄] = sodium tetrachloridoplatinate(II).

Structural isomers: (1) Ionisation isomers: different ions in coordination sphere vs outside. [Co(NH₃)₅Br]SO₄ vs [Co(NH₃)₅SO₄]Br. (2) Hydrate/solvate isomers: water inside or outside coordination sphere. [Cr(H₂O)₆]Cl₃ vs [CrCl(H₂O)₅]Cl₂·H₂O vs [CrCl₂(H₂O)₄]Cl·2H₂O. All have formula CrCl₃·6H₂O. (3) Linkage isomers: ambidentate ligands (SCN⁻ or NCS⁻, NO₂⁻ or ONO⁻) coordinated through different atoms. [Co(NO₂)(NH₃)₅]²⁺ (N-bonded, nitro) vs [Co(ONO)(NH₃)₅]²⁺ (O-bonded, nitrito). (4) Coordination position isomers. Stereoisomers: (5) Geometric (cis-trans): [PtCl₂(NH₃)₂] — cisplatin (cis) vs transplatin. (6) Optical isomers: non-superimposable mirror images (enantiomers). [Co(en)₃]³⁺, [CoCl₂(en)₂]⁺ (cis only). Optical isomers have same physical properties but rotate plane-polarized light in opposite directions (+d and −l or R and S).