X-ray Atomic Orbital and Molecular Orbital Analyzes

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A least-squares method incorporating orthonormal relationships between orbital functions were formulated. This is equivalent to the idempotency condition for orbitals occupied by integer number, which is less than 2, of electrons. The first aim of the present research is to obtain atomic orbitals (AO) or molecular orbitals (MO) by analyzing electron density distribution (EDD) measured by X-ray diffraction method with this method. The second aim is to measure so accurate structure factors that EDD in crystals composed of heavy atoms such as rare-earth elements can be obtained reliably.The least-squares method was successfully applied aand 3d-orbital functions of Cu^<2+> in a low symmetry field were obtained. Therefore AO can be obtained by the analysis of X-ray structure factors. We call the method as X-ray AO analysis. The similar research for obtaining MO,which is called as X-ray MO analysis, is still being investigated because unexpectedly long computation time is necessary. However … More following three basic problems has been solved and it is feasible to accomplish X-ray MO analysis. First, in a simple organic compounds scattering factors of two-center electrons is larger than their experimental error for many reflections enough for the least-squares analysis. Second, ttemperature factors for two-center electrons are successfully formulated, giving reasonable R-factors. Third basic Gaussian-type functions which is proper for X-ray MO analysis was found, which reduce the inconsistency of electron density near atomic nuclei significantly.As X-ray analysis of EDD develops more accurate measurement is required. Multiple diffraction effect was found to occur so frequently that intensity perturbations due to it easily exceeded 1% of measured structure factors for PtP_2 crystals. Therefore it was avoided during the measurement with a 4 cirde diffractometer. Intensities were also measured in stable temperature region of toold nitrogen gas stream of the Oxford cryostat. These improvementts were achieved in the present research. As s result of it 4f-electron density distribution in CeB_6 was measured clearly at 165K and it was analyzed based on the crystal field theory by X-ray AO analysis. This to our knowledge is the first successful quantitative analysis of felectrons. The studies on EDD in crystals composed of heavy atoms showed a remarkable progress. Less