Symmetry of Polycentric Systems

The Polycentric Tensor Algebra for Molecules

Summary of the Wigner-Racah algebra of non-simply-reducible point groups with non-ambivalent classes.
Representations induced by polyhedral edges.
Bicentric matrices.
The matrix elements of s.
a. molecular orbitals.
Polyhedral coefficients referring to edges.
Triangular coefficients.
Triangular invariants.
Symmetry-adapted geminals and densities.
Pseudo-tetrahedral coefficients.
Two-particle interaction.
Complete bases of irreducible representations.
Transformation properties and structure of the multi-centre integrals.
Multi-centre integrals and molecular symmetry.
Ab initio determination of the polycentric invariants.
Wolfsberg-Helmholtz and Mulliken approximations.
Floating orbitals.
Overlap- and structural matrices, orthonormalization.
Many-electron systems.
Sketch of the VB picture.
Prospect of crystals.
Case study: Tetrahedral structures.
Case study: Matrix elements.