The data for n = 7


The potential
The picture and a description of the configuration
The Gram minimal eigenvalue projection
The Gram middle eigenvalue projection
The Gram largest eigenvalue projection
The Coulomb view
The points in Mathematica format

potential = 14.45297743


The configuration is a regular pentagonal bipyramid, i.e. a regular pentagon on the equator plus the two poles. The (1,5,1) bandology appears in the Gram projections while the Coulomb projection shows a (1,2,2,2) bandology. We note for n = 7 the algorithm takes considerably longer to converge than for the surrounding values of n. This was also observed by [EH].

[Graphics:n7pic.jpg]

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smallest eigenvalue Gram view

[Graphics:n7g1.jpg]

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second largest eigenvalue Gram view

[Graphics:n7g2.jpg]

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largest eigenvalue Gram view

[Graphics:n7g3.jpg]

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The Coulomb view

[Graphics:n7coul.jpg]

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The points

{{0,0,1.},{0.951057,0,0.309017},{-0.951054,0.00220967,0.309017}, {0.587784,-0.00191208,-0.809016},{-0.587786,-0.000297586,-0.809016}, {0.00122003,0.999999,-0.000989075},{-0.00122037,-0.999999,0.000987317}}

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Copyright by Neubauer, Schilling, Watkins and Zeitlin (1998).