Determination of Chemical Shift Equivalence by Interchange Through Symmetry Operations

1 Determination of Chemical Shift Equivalence by Interchange Through Symmetry Operations 

There are three symmetry operations each involving a symmetry element rotation about a simple axis of symmetry (C ), reflection through a plane of symmetry (a), and inversion through a center of symmetry (i). More rigorously, symmetry operations may be described under two headings Cn and Sn. The latter is rotation 

Of course, an identity operation—a 360° rotation around a symmetry axis—is not valid. The symmetry elements are the axis, plane, and center. 

Before we describe the three common symmetry operations to effect interchange of nuclei within a molecule, we raise another question How do we know whether or not a symmetry operation has indeed resulted in interchange Simply enough Build two models of the molecule—one before the operation, one after the operation. If they are indistinguishable, interchange 

Of course, an identity operation—a 360° rotation around a symmetry axis—is not valid. 

The methylene protons of propanoic acid (Fig. 4.37, structure c) are exchangeable by reflection through the plane of symmetry in the plane of the paper. There are no other symmetry elements. The protons are enantiotopes of each other and have the same chemical shift only in an achiral environment. Drawings and models of the molecule are indistinguishable by inspection before and after the operation. 

Symmetry (/) A center of symmetry exists if a line drawn from each nucleus through the selected center encounters the same nucleus or group at the same distance on the other side of the center (Fig. 4.37, structure d). 

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