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Number of signals and symmetry in flexible systems

Rule:

In the case of impossibility to fit different conformations by any symmetry operation, the protons involved show different chemical shifts.

In general you will observe this behaviour if you have CH2 groups and at least one asymmetric carbon atom together in one molecule.
Example: Within the compound

2D Formel      3D Formel

with one asymmetric carbon atom (C*) it is impossible to fit the conformations:

Schema

with any symmetry operation. Each moment of the free rotation there interact different chemical environments with both methylene protons H(1) und H(2). Both methylene protons show their individual signal, as demonstrated within the experimental spectrum.

And now back to more fundamental problems
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