Symmetry, near-symmetry and energetics

Is there a connection between symmetry and energetics? Surveys of over 300000 local minima from nine different model systems reveal some correlation between the degree of symmetry and the mean energy. However, both theory and calculation suggest that the variance may be more important. Systems with higher symmetry, defined in terms of the spectrum of contributions to the total energy, are more likely to exhibit particularly low and high energy minima. This change in viewpoint may be sufficient to account for the widespread appearance of high symmetry.