Shape analysis of carbon nanotube junctions
Using the eigenvectors of the Laplacian matrix of the graph describing the topology of a nanotube junction we have developed a shape analysis. The X, Y, Z relaxed Descartes coordinates of the atoms were calculated as a linear combination of the eigenvectors. We have obtained that the partial sums generated thre-dimensional structures only if they contained all the three bi-lobal eigenvectors of the Laplacian. We have found partial sums that produced satisfactory initial coordinates for molecular mechanics calculations.