Theoretical calculations of vibrational modes in endohedral metallofullerenes: La@C82 and Sc2@C84

Density functional theory at the B3LYP level is applied to representative mono- and dime-tallofullerenes, La@C₈₂ and Sc₂@C₈₄, to calculate the metal-cage vibrational modes that are currently of considerable interest in far-infrared and Raman spectroscopic studies. The La based vibrations calculated for La@C₈₂ are in good agreement with those assigned experimentally. The vibrational frequencies are little changed upon reduction and oxidation. The Sc based vibrations calculated for Sc₂@C₈₄ are also compared with the available experimental data. In addition, the structures of the isomers of Sc₂@C₈₄ are discussed. Electrostatic interactions play an important role in endohedral metallofullerenes.     

TOMOGRAPHY FORMULA FOR BIOCHEMICAL IMAGING OF THIN TISSUE WITH DIFFUSE-PHOTON DENSITY WAVES

Using the transport theory to describe the near infrared light propagating in tissue with finite parallel-plane geometry, and taking the zero-boundary condition, we obtain the analytical expression of average photon density and Green's function incorporating the boundary effects in the homogeneous tissure. Making use of perturbation theory we also obtain the analytical expression of scattered wave induced by the heterogeneity, and present the 2-dimensional spatial transform of scattered wave with respect to transverse coordinate. If the information of heterogeneity on depth and thickness is available, diffraction tomography formula is presented to save the time of image reconstruction; if the information is unknown, we suggest to obtain the inhomogeneous function from the one-dimensional integral equation of 2-dimensional spatial transform of scattered wave applying the direct matrix method or iterative method for image reconstruction. This approach avoids directly solving three-dimensional integral equation of scattered wave. In our proposed approach the strong points of the direct matrix method, iterative method, and diffraction tomography are fully combined.