By Charles M. Quinn, Patrick Fowler, David Redmond
, Pages vii-viii
1 - working directions for the crowd idea Calculator
, Pages 1-28
2 - Geometry, orbits and decorations
, Pages 29-66
3 - of orbits utilizing neighborhood capabilities: Reducible characters for s, p, d, … neighborhood services; crucial polynomial features as foundation units for the irreducible representations of the purpose teams; the
, Pages 67-131
4 - Symmetrized powers and their applications
, Pages 133-149
Appendix 1 - The icosahedral harmonics
, Pages 151-162
Appendix 2 - Quantum Chemistry on an EXCEL® spreadsheet
, Pages 163-175
Appendix three - pattern enter documents for the ApianusII.exe and FunctionPlot.exe programmes at the CDROM
, Pages 177-183
, Page 185
, Pages 187-188
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Additional resources for Computational Quantum Chemistry II. The Group Theory Calculator
Archimedean polyhedra have equivalent vertex figures on all vertices. All faces remain planar and equilateral, but are of two or three distinct kinds. 38 The Group Theory Calculator A more unified perspective can be developed by starting with the polyhedra derived from the regular orbits in the two parent groups, cubic (Oh) and icosahedral (Ih). The various Archimedean and Platonic solids then follow by a process of collapsing vertices of these regular-orbit polyhedra. Each polyhedron appears as the realization of an orbit of Oh/Ih or a subgroup.
6 Orbits and Polyhedra in Ih Point Symmetry The character table for the Ih point group is Ih E 12C5 12C 2 20C3 15C2 Ag 1 1 1 1 Tlg 3 r 1-r 0 T2g 3 1-r r 0 Gg 4 -1 -1 1 Hg 5 0 0 Au 1 1 1 1 1 Tlu 3 r 1- r 0 T2u 3 1- r r Gu 4 -1 -1 Hu 5 0 0 1 2 S 1 0 12S~0 20S6 15o 1 1 1 1 -1 3 1-r r 0 -1 -1 3 r 1-r 0 -1 0 4 -1 -1 1 1 5 0 0 -1 -1 -1 -1 -1 - 1 -3 r - 1 -r 0 - 1 -3 -r 1 0 -4 1 1 1 -5 0 0 -1 -1 1 i r - 1 1 0 1 -1 0 1 0 1 -1 1 0 -1 wherein r, the golden section of classical antiquity, is of value (1 + ~/5)/2.
19c the decoration pattern is arranged to divide the 120 vertices into sets of 6 about the 20 poles of these axes on the unit sphere. Again, uniform contraction of these subsets of vertices onto these positions on the unit sphere generates the fifth Platonic solid, the dodecahedron, and the site symmetry each vertex is C3v. There are 15 two-fold axes in an object of Ih point symmetry. 19c. The 30-vertex cage of the icosidodecahedron to result on contraction of these local sets onto the pole positions on the unit sphere.
Computational Quantum Chemistry II. The Group Theory Calculator by Charles M. Quinn, Patrick Fowler, David Redmond