Interchange through symmetry operations

Interpretation of NMR spectra depends on the concept of chemical-shift equivalence, an understanding of which depends on stereochemical concepts these are reviewed with special emphasis on interchange through symmetry operations within the molecule, and through rapid structural changes. 

Determination of Chemical Shift Equivalence by Interchange Through Symmetry Operations... 

First, it is apparent that reflection through the xz plane, indicated by transforms H into H". More precisely, we could say that H and H" are interchanged by reflection. Because the z-axis contains a C2 rotation axis, rotation about the z-axis of the molecule by 180° will take H into H" and H" into H, but with the "halves" of each interchanged with respect to the yz plane. The same result would follow from reflection through the xz plane followed by reflection through the yz plane. Therefore, we can represent this series of symmetry operations in the following way ... 

The immediate question is are selected nuclei in a molecule chemical shift equivalent, or are they not If they are, they are placed in the same set. The answer can be framed as succinctly as the question Nuclei are chemical shift equivalent if they are interchangeable through any symmetry operation or by a rapid process. This broad definition assumes an achiral environment (solvent or reagent) in the NMR experiment the common solvents are achiral (Section 3.17). 

No Interchangeability by a Symmetry Operation If geminal protons (CH2) in a molecule cannot be interchanged through a symmetry element,... 

Here is worth making also the difference between the equivalence points (which can be interchanged through a symmetry operation existing in structure) and the identical points (witch are identical overlapped through a symmetry operation). 

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