Group theory for chemists pp 81-90 | Cite as

# Symmetry-adapted linear combinations

## Abstract

In Chapter 6, it was shown how to determine which irreducible representations were present in any reducible representation. For example, a set of bond vectors for a square-planar (**D**_{4h}) molecule reduced to A_{1g} + B_{1g} + E_{u}. What is the physical significance of this result? It means that, for this case, the four basis vectors can be used to form four *linear combinations* (that is, sums and/or differences) such that one combination has A_{1g} symmetry, one B_{1g} symmetry and two (together) E_{u} symmetry. Each of these corresponds to one vibrational mode of the molecule (see Chapter 8). Similar results are found for any set of *n* basis vectors or functions — it will be possible to form *n* **symmetry-adapted linear combination (SALCs)** of them, corresponding to the appropriate irreducible representations of the molecular point group.

### Keywords

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