Configuration anomalies: Cr = [Ar]3$d^{5}$ 4$s^{1}$ (half-filled d, exchange energy); Cu = [Ar]3$d^{10}$ 4$s^{1}$ (fully-filled d, symmetry). Both sacrifice one 4s electron for d-subshell stability.

Properties of transition metals: Variable oxidation states (both ns and (n−1)d electrons participate); coloured ions (d–d transition in partially filled d-orbitals); paramagnetism (unpaired d-electrons); catalytic activity (variable OS + surface adsorption); coordination compound formation (empty d-orbitals accept lone pairs).

$KMnO_{4}$ products: Acidic → $Mn^{2+}$ (colourless, +7→+2, 5$e^{-}$); Neutral → $MnO_{2}$ (brown, +7→+4, 3$e^{-}$); Basic → $MnO_{4}^{2-}$ (green, +7→+6, 1$e^{-}$). Electrons gained follow 5-3-1 pattern from acid to base.

$K_{2}Cr_{2}O_{7}$: In acidic medium, $Cr_{2}O_{7}^{2-}$ (orange) → $Cr^{3+}$ (green). Chromate-dichromate equilibrium: $CrO_{4}^{2-}$ (yellow, basic) ⇌ $Cr_{2}O_{7}^{2-}$ (orange, acidic).

Lanthanoid contraction: Gradual decrease in $Ln^{3+}$ ionic radii from La to Lu due to poor 4f shielding. Consequence: 4d and 5d congeners (Zr/Hf, Nb/Ta, Mo/W) are nearly identical in size.

Spectrochemical series (weak → strong): $I^{-}$ < $Br^{-}$ < $Cl^{-}$ < $F^{-}$ < $OH^{-}$ < $H_{2}O$ < $NH_{3}$ < en < $NO_{2}^{-}$ < $CN^{-}$ < CO. Strong field ($CN^{-}$, CO) → large $\Delta o$ → pairing → low spin → diamagnetic. Weak field ($Cl^{-}$, $F^{-}$) → small $\Delta o$ → no pairing → high spin → paramagnetic.

CFT — octahedral vs tetrahedral: Octahedral: t_{2}g < eg, $\Delta o$. Tetrahedral: e < t_{2} (inverted), $\Delta t$ = 4/9 $\Delta o$. Tetrahedral complexes are almost always high spin due to small $\Delta t$.

Magnetic moment: $\mu = \sqrt{n(n+2)}\text{ BM}$. n = 0 → diamagnetic; n = 1 → 1.73 BM; n = 5 → 5.92 BM (maximum for first-row transition metals).

Werner's theory: Primary valence = oxidation state (ionisable). Secondary valence = coordination number (non-ionisable, directional, defines geometry).

Isomerism types: Geometrical (cis/trans in $MA_{2}B_{2}$ square planar or $MA_{4}B_{2}$ octahedral); optical (tris-chelate, no symmetry plane); linkage (ambidentate ligands: $NO_{2}^{-}$, S$CN^{-}$); ionisation (ligand ⇌ counter-ion exchange).

Biological coordination compounds: Haemoglobin ($Fe^{2+}$), chlorophyll ($Mg^{2+}$), vitamin $B_{12}$ ($Co^{3+}$), carbonic anhydrase ($Zn^{2+}$), cisplatin ($Pt^{2+}$, anticancer).

IUPAC naming rule: List ligands alphabetically → metal with Roman numeral charge → complex anion suffix -ate → name cation before anion.