Using geometry optimization and DFT method at the B3LYP/6-31G* level for C20H10, an equilibrium geometry is identified to have the form of polyhedral hydrocarbon with five carbon-carbon single bonds linking two pentap...Using geometry optimization and DFT method at the B3LYP/6-31G* level for C20H10, an equilibrium geometry is identified to have the form of polyhedral hydrocarbon with five carbon-carbon single bonds linking two pentaprismane cages. Thus, C20H10 is a tri-cage molecule with three pentaprismane cages. Vibrational frequencies and infrared spectrum are computed at the same level. The heat of formation for this molecule has also been estimated in this paper.展开更多
In this article, we first study the trace for the heat kernel for the sub-Laplacian operator on the unit sphere in ? n+1. Then we survey some results on the spectral zeta function which is induced by the trace of the ...In this article, we first study the trace for the heat kernel for the sub-Laplacian operator on the unit sphere in ? n+1. Then we survey some results on the spectral zeta function which is induced by the trace of the heat kernel. In the second part of the paper, we discuss an isospectral problem in the CR setting.展开更多
基金This work was supported by the Natural Science Foundation of Shandong Province (Y2002G11)
文摘Using geometry optimization and DFT method at the B3LYP/6-31G* level for C20H10, an equilibrium geometry is identified to have the form of polyhedral hydrocarbon with five carbon-carbon single bonds linking two pentaprismane cages. Thus, C20H10 is a tri-cage molecule with three pentaprismane cages. Vibrational frequencies and infrared spectrum are computed at the same level. The heat of formation for this molecule has also been estimated in this paper.
基金supported by National Security Agency,United States Army Research Offfice and a Hong Kong RGC Competitive Earmarked Research (Grant No. 600607)
文摘In this article, we first study the trace for the heat kernel for the sub-Laplacian operator on the unit sphere in ? n+1. Then we survey some results on the spectral zeta function which is induced by the trace of the heat kernel. In the second part of the paper, we discuss an isospectral problem in the CR setting.
