Symmetry of Polycentric Systems: The Polycentric Tensor Algebra for Molecules

Introduction....Pages 1-5
Summary of the Wigner-Racah algebra of non-simply-reducible point groups with non-ambivalent classes....Pages 6-16
Representations induced by polyhedral edges....Pages 17-21
Bicentric matrices....Pages 22-25
The matrix elements of s.-a. molecular orbitals....Pages 26-28
Polyhedral coefficients referring to edges....Pages 29-31
Triangular coefficients....Pages 32-35
Triangular invariants....Pages 36-38
Symmetry-adapted geminals and densities....Pages 39-40
Pseudo-tetrahedral coefficients....Pages 41-42
Two-particle interaction....Pages 43-46
Complete bases of irreducible representations....Pages 47-50
Transformation properties and structure of the multi-centre integrals....Pages 51-57
Multi-centre integrals and molecular symmetry....Pages 58-60
Ab initio determination of the polycentric invariants....Pages 61-64
Wolfsberg-Helmholtz and Mulliken approximations....Pages 65-67
Floating orbitals....Pages 68-70
Overlap- and structural matrices, orthonormalization....Pages 71-74
Many-electron systems....Pages 75-80
Sketch of the VB picture....Pages 81-85
Prospect of crystals....Pages 86-92
Case study: Tetrahedral structures....Pages 93-111
Case study: Matrix elements....Pages 112-120