Symmetry and Bonding in Inorganic Chemistry
Symmetry and bonding applies molecular symmetry and group theory to inorganic molecules, providing the framework that predicts molecular-orbital schemes, spectroscopic activity, and the electronic spectra of complexes.
Definition
Symmetry and bonding in inorganic chemistry is the application of molecular symmetry and group theory to determine point groups, construct molecular-orbital and bonding descriptions, and predict the vibrational and electronic spectra of inorganic molecules and complexes.
Scope
This area covers the systematic use of symmetry in inorganic chemistry: identifying symmetry elements and assigning molecules to point groups, using character tables and reducible representations to build symmetry-adapted orbitals, constructing molecular-orbital diagrams for inorganic molecules and complexes, and interpreting their electronic spectra through term symbols, Orgel and Tanabe–Sugano diagrams, and selection rules. It supplies the theoretical scaffolding used across coordination and main-group chemistry rather than the descriptive chemistry of any element block.
Sub-topics
Core questions
- How is a molecule's point group determined from its symmetry elements?
- How do character tables generate symmetry-adapted orbitals and molecular-orbital diagrams?
- Which vibrational and electronic transitions are allowed by symmetry?
- How do term symbols and Tanabe–Sugano diagrams explain the electronic spectra of complexes?
Key concepts
- Symmetry elements and operations
- Point groups and character tables
- Reducible and irreducible representations
- Symmetry-adapted linear combinations
- Selection rules for spectroscopy
- Term symbols and Tanabe–Sugano diagrams
Key theories
- Group theory and point-group classification
- The symmetry operations of a molecule form a mathematical group; assigning the molecule to a point group and using its character table organizes orbitals, vibrations, and spectroscopic selection rules.
- Symmetry-adapted linear combinations and MO diagrams
- Combining ligand orbitals into symmetry-adapted linear combinations that match metal orbitals of the same symmetry yields the molecular-orbital diagrams of complexes, generalizing crystal-field splitting to a covalent picture.
- Term symbols and Tanabe–Sugano analysis
- The free-ion terms of a d-electron configuration split in a ligand field; Tanabe–Sugano diagrams plot the resulting state energies versus field strength and quantitatively interpret the d–d absorption spectra of complexes.
Clinical relevance
Symmetry analysis is the everyday tool for interpreting infrared, Raman, and electronic spectra, assigning structures, and predicting the bonding and reactivity of inorganic molecules and catalysts.
History
The application of group theory to chemistry grew from the molecular-symmetry analyses of the 1930s and the crystal-field work of Bethe and Van Vleck. Tanabe and Sugano's 1954 energy-level diagrams and Orgel's interpretations connected symmetry to the spectra of complexes, and Cotton's textbook made the methods standard equipment for inorganic chemists.
Key figures
- F. Albert Cotton
- Hans Bethe
- Leslie Orgel
- Yukito Tanabe
Related topics
Seminal works
- tanabe1954
- cottongrouptheory1990
- weller2018
Frequently asked questions
- Why do chemists bother assigning a molecule to a point group?
- Once the point group is known, its character table immediately reveals which orbitals can combine, which vibrations are infrared or Raman active, and which electronic transitions are allowed, turning qualitative structure into quantitative spectroscopic predictions.
- What does a Tanabe–Sugano diagram tell you?
- It shows how the energies of the electronic states of a d-electron ion change as the ligand-field strength increases, letting chemists assign the absorption bands of a complex and extract the field-splitting and electron-repulsion parameters.