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A new solution method to perform the pi-orbital axis vector analysis was developed in this paper. The model of circular cone was built and the solution equations of the pyramidalization angle were obtained based on the model and the space analytic geometry. Our method merely requires the atomic coordinates of the conjugated central atom and the three attached atoms. Moreover, systematic calculations on the pyramidalization angles of fullerenes and carbon nanotubes were performed using the method we developed. The relationship of pyramidalization angle and the stability for the carbon cages and tubes was also discussed.
A new solution method to perform the pi-orbital axis vector analysis was developed in this paper. The model of circular cone was built and the solution equations of the pyramidalization angles were obtained based on the model and the space analytic geometry. the atomic coordinates of the conjugated central atom and the three attached atoms. Moreover, systematic calculations on the pyramidalization angles of fullerenes and carbon nanotubes were performed using the method we developed. The relationship of pyramidalization angle and the stability for the carbon cages and tubes was also discussed.