Symmetry-Adapted Bases of Matrix Spaces Applied to Quantum Chemistry

Abstract

Generalized normalized irreducible tensorial matrices (GNITM) are obtained by symmetry-adapting the matrix basis of a matrix space that is invariant to reducible representations of a unitary group. Like previously defined normalized irreducible tensorial matrices (NITM), the GNITM are orthonormal under the trace and transform irreducibly under G. The GNITM are useful for constructing matrices having specific behavior under G. In particular, an Hamiltonian matrix is invariant under the symmetry group of the corresponding physical system and is expressed as a linear combination of invariant GNITM. The orbital model of ammonia is treated as an example.

Finite Group Theory for Large Systems. 2. Generating Relations and Irreducible Representations for the Icosahedral Point Group, h

“…Nevertheless, group theoretical analysis facilitates calculations that otherwise might be impossible. Applying the full power of group theory to these systems requires symmetry-adapted bases and the projection operators that produce them. − A consistent set of irreducible representations for ℐ h are obtained here by the methods described by this author in reference 1. As a simple example, in section V these methods are applied to the Hückel treatment of the smallest fullerene, C 20 .…”