Numerical generation of hyperspherical harmonics for tetra-atomic systems

A numerical generation method of hyperspherical harmonics for tetra-atomic systems, in terms of row-orthonormal hyperspherical coordinates—a hyper-radius and eight angles—is presented. The nine-dimensional coordinate space is split into three three-dimensional spaces, the physical rotation, kinematic rotation, and kinematic invariant spaces. The eight-angle principal-axes-of-inertia hyperspherical harmonics are expanded in Wigner rotation matrices for the physical and kinematic rotation angles. The remaining two-angle harmonics defined in kinematic invariant space are expanded in a basis of trigonometric functions, and the diagonalization of the kinetic energy operator in this basis provides highly accurate harmonics. This trigonometric basis is chosen to provide a mathematically exact and finite expansion for the harmonics. Individually, each basis function does not satisfy appropriate boundary conditions at the poles of the kinetic energy operator; however, the numerically generated linear combination of these functions which constitutes the harmonic does. The size of this basis is minimized using the symmetries of the system, in particular, internal symmetries, involving different sets of coordinates in nine-dimensional space corresponding to the same physical configuration

CDSE Quantum Dots and Luminescent/Magnetic Particles for Biological Applications

CdSe semiconductor nanocrystals (quantum dots--QDs) with diameters ranging between 1.5 and 8 nm exhibit strong, tunable luminescence [1-5]. They have been widely investigated for their size-dependent optoelectronic properties [6], and for their potential use in optical devices [7], biological labels [8] and sensors [9]. Luminescent quantum dots (QDs) show higher photostability and narrower emission peaks compared to organic fluorophores [8]. The objective of my project was to apply QDs magnetic/luminescent nanoparticle as biological labels in cells. Luminescent CdSe QDs emit bright visible light with high quantum yield and sharp emission peak. The CdSe QDs were capped with a ZnS layer. This increased their emission efficiency and photostability due to the larger band gap of ZnS. The QDs were transferred from organic solvent (e.g. chloroform, hexane) to water by exchanging the capping group (Trioctylphosphine Oxide—TOPO) with mercaptoacetic acid. To develop a separation and detection tool for cells, we combined γ-Fe2O3 magnetic particles with CdSe/ZnS QDs in core-shell composite. The composite nanoparticles showed strong fluorescence emission and high water solubility. Different antibodies were attached to the particles through EDAC coupling. The antibody-coated particles were used to successfully separate and detect breast cancer cells in blood cells