Framework groups

Stoichiometry C5H5N Framework group C2V[C2(NCH),SGV(C4H4)] Deg. of freedom 10... 

Although ZOLs have physical properties similar to those of their inorganic counterparts, they exhibit a higher hydrophobicity because of the presence of the organic framework group. This could be exemplarily shown for ZOL-A by the much higher adsorption capacity for n-hexane in comparison to its inorganic counterpart zeolite A.81... 

The pairs (P,R) are elements of a group, often called the framework group of... 

Note that in two different molecules a given common point symmetry operator R can be associated with two different permutation operators P and P depending on the nuclear arrangements. Consequently, the framework groups do contain more information on molecular shapes than point symmetry groups. 

Whereas framework groups are more informative than point symmetry groups, they are able to describe only a rather restricted aspect of molecular shape. Alternative group theoretical methods, notably, the Shape Group Methods (SGM) of molecular topology, are more suitable for a detailed shape characterization. The shape groups will be discussed in Chapter 5 of this book. 

Framework group CS[SG(C9H804)] Deg. of freedom 39 Full point group Largest Abelian subgroup Largest concise Abelian subgroup Standard CS NOp CS NOp Cl NOp orientation 2 2 1 ... 

When acid zeolite catalysts must be prepared, trivalent elements which can be in tetrahedral coordination are introduced to the synthesis media with silica. Then a structure with framework groups of the type ... 

Now consider the symmetry point group G (or, more precisely, the framework group ) of the above ML coordination compound. This group has IGI operations of which lf l are proper rotations so that IGI/I/ I = 2if the compound is achiral and IGI/I I = 1 if the compound is chiral (i.e., has no improper rotations). The n distinct permutations of the n sites in the coordination compound or cluster are divided into nM R right cosets which represent the permutational isomers since the permutations corresponding to the IWI proper rotations of a given isomer do not change the isomer but merely rotate it in space. This leads naturally to the concept of isomer count, I, namely,... 

This theorem has been proven using an earlier result of Pechukas along a steepest descent path the point symmetry group (as well as the framework group) of nuclear configurations may change only at a critical point, where it must have all those point symmetry elements (framework group elements, resp.) that are present at non-critical points of the path [5]. 

In order to describe a framework group the relevant symmetry point group is first found and described by its Schoen-flies symbol. The points in the framework are then described in terms of their positions relative to subspaces corresponding to the symmetry elements in the group. These subspaces can be classified by their dimensionalities as follows ... 

The property of chirality can be used to classify framework groups. An object is chiral if its symmetry group contains no improper rotations S (including Si = a and Si = i). Systems with symmetry groups containing one or more improper rotations are thus achiral. Framework groups can be classified in terms of their chirality as follows ... 

All of the planar framework groups can be polarized to give a framework group with half the number of operations. 

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