Inorganic Chemistry

Symmetry, d electrons and what the rest of the periodic table does

About this course

Inorganic chemistry built on symmetry: point groups and character tables and what they forbid, coordination complexes and isomerism, crystal and ligand field theory, colour and magnetism, substitution and electron transfer, the eighteen-electron rule and catalytic cycles, solids and band structure, and metals in biology.

What you will be able to do

  • Assign a point group and use a character table to decide what a spectrum can show
  • Describe coordination complexes, their ligands and their isomers
  • Explain colour, the spectrochemical series and spin state with crystal and ligand field theory
  • Reason about substitution, electron transfer and catalytic cycles with the eighteen-electron rule
  • Connect band structure in solids and metal centres in biology to the same bonding ideas

What this course covers

  • Crystal field splitting in octahedral complexes
  • Crystal field stabilization energy (CFSE)
  • Tetrahedral crystal field splitting and the 4/9 ratio
  • High-spin vs low-spin competition
  • Hydration enthalpy evidence and limits of the model
  • From molecular orbitals to energy bands
  • The Fermi level and metal vs. insulator classification
  • Why electron counting fails in metals
  • Band gap and exponential conductivity
  • Band gap as optical absorption edge
  • Mott insulators: band theory's failure for late transition metal oxides
  • Semiconductor doping and solar-cell material selection
  • Coordinate (dative) bond and Lewis acid-base framing
  • Denticity: counting donor atoms that can reach one metal
  • Nomenclature of coordination complexes
  • The chelate effect: magnitude and thermodynamic decomposition
  • Particle-count mechanism of the chelate entropy advantage
  • Ring-size correction and limits of the particle-count explanation
  • Audit of elements used in prior courses
  • Orbital capacity and the octet, 18-electron, and 32-electron rules
  • Oxidation state multiplicity and the hump across the first transition series
  • Variable coordination number and square-planar vs tetrahedral geometry
  • Color as a readout of D-orbital splitting energy
  • Cisplatin worked problem: counting isomers to determine geometry
  • Course roadmap and the unifying cause of D-block differences
  • Thermodynamics vs. kinetics independence
  • Water-exchange rate span: 18 orders of magnitude
  • Ionic radius fails to predict exchange rates
  • Measurement methods for water exchange
  • Crystal field activation energy and two non-overlapping rate classes
  • Charge as a coarse rate scale-setter
  • Jahn-Teller ions as the fastest labile exchangers
  • Inert vs. stable: kinetic and thermodynamic independence
  • Volume of activation and mechanism continuum
  • Electron transfer and the Franck-Condon reorganization barrier
  • Outer-sphere vs. inner-sphere electron transfer: Taub experiment
  • Kinetic design of metal-based drugs (cisplatin case)
  • Symmetry as operations with a test
  • Reduction of five operations to three families
  • Orthogonality and the determinant criterion
  • Counting operations from a CN axis
  • Mechanical procedure for finding symmetry operations
  • Limits of the verification procedure and point groups
  • Grouping operations into conjugacy classes
  • Closure and the group structure of symmetry operations
  • Chirality redefined via improper operations
  • CO₂ as a worked symmetry analysis
  • Biological metal selection: two necessary conditions
  • Epistemic status of the two-condition argument
  • Dating biological metal use to Earth's oxygenation
  • Hemoglobin cooperativity from spin state and ionic radius
  • Course dependency graph and its one leaf
  • Two master quantities: field splitting and electron repulsion
  • Carbonic anhydrase: why zinc (worked example)
  • Two counting conventions, one electron total
  • Why 18: nine valence orbitals and the octet analogy
  • 16-electron rule and square-planar geometry
  • Domain of the 18-electron rule: pi-acceptor ligands
  • Electron count as a predictor of reactivity
  • Isomers as rotation orbits
  • Naive division as a strict lower bound; when it works and why
  • Two independent counting routes: enumeration and Burnside's lemma
  • Chirality as the difference between rotation-orbit count and full-group-orbit count
  • Tris-bidentate complex: delta and lambda enantiomers
  • Ligand field MO construction via symmetry reduction
  • Delta as an antibonding gap, not electrostatic repulsion
  • Pi interactions and the spectrochemical series
  • Nephelauxetic effect as independent evidence of covalency
  • Crystal-field splitting versus visible photon energy
  • Central promise: explaining a real d-metal spectrum
  • Three inherited concepts as lecture foundation
  • A spectrum has two axes: energy and intensity
  • Deriving symmetry candidates from molecular geometry
  • Point-group flowchart and nomenclature
  • Agreement of two roots and the generator's structural blind spot
  • Chirality as a point-group name lookup
  • Grammar of six elementary organometallic steps
  • Signature collisions and limits of the grammar
  • Catalytic cycle closure and the turnover number
  • The 18-electron ceiling forbids step orderings
  • Phosphine inhibition as a predicted experimental consequence
  • What a catalyst can and cannot do — thermodynamics vs. barrier
  • Character as a basis-independent trace
  • Conjugacy classes and table structure
  • Counting constraints on table dimensions
  • The reduction formula
  • Counting molecular vibrations by symmetry
  • Linear molecules and the subgroup technique
  • Spin-only formula for magnetic moment
  • Gouy method for measuring magnetic susceptibility
  • Orbital contribution and its quenching
  • Jahn-Teller distortion confirmed by bond lengths
  • Spin-crossover: watching a spin state change
  • Integrating magnetism, bond length, and spectra as diagnostics
  • Selection rules from symmetry of integrals
  • Orthogonality and the diagonal selection rule
  • Infrared and Raman activity from character-table columns
  • Mutual exclusion rule and structural determination
  • Predicted versus observed band counts; degeneracy and category errors

Syllabus

  1. Symmetry and the Periodic Table

    1. L1 · The Rest of the Periodic Table
    2. L2 · Symmetry Operations
    3. L3 · Point Groups
    4. L4 · Character Tables
    5. L5 · What Symmetry Forbids

  2. Coordination Complexes

    1. L6 · Complexes and Ligands
    2. L7 · Isomerism in Complexes

  3. Bonding, Colour and Magnetism

    1. L8 · Crystal Field Theory
    2. L9 · Ligand Field Theory
    3. L10 · Colour and the Spectrochemical Series
    4. L11 · Magnetism and Spin State

  4. Reactivity and Organometallics

    1. L12 · Substitution and Electron Transfer
    2. L13 · The Eighteen-Electron Rule
    3. L14 · Catalytic Cycles

  5. Solids and Biology

    1. L15 · Solids and Band Structure
    2. L16 · Metals in Biology, and the Course as One Argument