# Chapters

- Page ID
- 281952

- 1.1: Symmetry Elements
- Symmetry elements of the molecule are geometric entities: an imaginary point, axis or plane in space, which symmetry operations: rotation, reflection or inversion, are performed. Their recognition leads to the application of symmetry to molecular properties and can also be used to predict or explain many of a molecule’s chemical properties. Symmetry elements and symmetry operations are two fundamental concepts in group theory.

- 1.4: Representations
- A representation is a set of matrices, each of which corresponds to a symmetry operation and combine in the same way that the symmetry operators in the group combine. Symmetry operators can be presented in matrices, this allows us to understand the relationship between symmetry operators through calculation from matrices. In order to understand representations, knowing matrix notions for symmetry operations is essential.

- 1.6: SALCs and the projection operator technique
- SALCs refers to Symmetry Adapted Linear Combinations, which are generated via use of the projection operator technique. This technique is a mathematical method which outputs a function called a SALC that models the orbitals of the atoms of interest. These SALCs are mathematical representations and therefore bare no physical meaning. They are commonly used in the generation of molecular orbitals.

- 1.15: Vibrational Spectroscopy of Linear Molecules
- Groups with axial symmetry are also known as continuous groups due to the infinite amount of rotations and reflections that leave the molecule invariant. Due to the sheer number of symmetry operations, determining irreducible representations is not feasible. There is one aspect of group theory that can be taken advantage of and these are the group, subgroup relationships.

- 1.19: Electron Counting and the 18 Electron Rule
- The 18 Electron Rule is a useful tool to predict the structure and reactivity of organometallic complexes. It describes the tendency of the central metal to achieve the noble gas configuration in its valence shell, and is somewhat analogous to the octet rule in a simplified rationale. Exceptions to this rule exist, depending on the energy and character of atomic and molecular orbitals.