The distortive effect of π electrons in conjugated systems in two and three dimensions is modelled, following Heilbronner, by varying Hückel bond parameters subject to retention of a constant sum around each graph vertex. For this simplified model a symmetry theorem gives the numbers and types of distortion modes that lead away from the σ optimal geometry. General results are given for linear and cyclic polyenes, linear and cyclic acenes, and carbon prisms. Connections between Heilbronner modes, eigenvectors of the bond polarisability matrix and the frontier-orbital rule for symmetry lowering are established. An application to the C60 fullerene shows that the seven most distortive of its 24 symmetry-distinct π modes are well modelled by the set of seven non-totally symmetric Heilbronner modes, and confirms that this system lies below the threshold for spontaneous distortion to non-icosahedral symmetry.
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