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X-ray Atomic Orbital and Molecular Orbital Analyzes

Research Project

Project/Area Number 05453021
Research Category

Grant-in-Aid for General Scientific Research (B)

Allocation TypeSingle-year Grants
Research Field Physical chemistry
Research InstitutionNagoya Institute of Technology

Principal Investigator

TANAKA Kiyoaki  Nagoya Institute of Technology Chemistry Department Professor, 工学部, 教授 (00092560)

Co-Investigator(Kenkyū-buntansha) SHIDA Norihiro  Nagoya Institute of Technology Chemistry Department Lecturer, 工学部, 講師 (00226127)
尾中 証  名古屋工業大学, 工学部, 教授 (50024302)
Project Period (FY) 1993 – 1995
Project Status Completed (Fiscal Year 1995)
Budget Amount *help
¥6,700,000 (Direct Cost: ¥6,700,000)
Fiscal Year 1995: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1994: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1993: ¥5,500,000 (Direct Cost: ¥5,500,000)
KeywordsX-ray diffraction method / Electron density distribution / Atomic orbital / Molecular orbital / f-electron density distribution / Multiple diffraction / X線原子軌道解析法 / X線分子軌道解析法 / 多重反射 / X線原子軌道解析 / X線分子軌道解析 / 遷移金属錯体 / d軌道関数 / 4f電子 / ジフォルムヒドラジド / CeBb / 多重反射(同時反射) / Cu(diazacyclooctane)_2(NO_3)_2 / PtP_2 / NiP_2 / ジフォルモヒドラジド((NHCHO)_2)
Research Abstract

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

Report

(4 results)
  • 1995 Annual Research Report   Final Research Report Summary
  • 1994 Annual Research Report
  • 1993 Annual Research Report
  • Research Products

    (42 results)

All Other

All Publications (42 results)

  • [Publications] Kiyoaki Tanaka: "X-ray Analysis of Wavefunctions by the Least-squares Method In corporating Orthhonormality. II. Ground State of the Cu^<2+>Ion of Bis (1,5-diazacyclooctane) copper (II) Nitrate in a Low Symmetry Crystal Field." Acta Crystallogr.B49. 1001-1010 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Kiyoaki Tanaka: "Multiple-Diffraction Effect in Accurate Structure-Factor Measurements of PtP_2 Crystals" Acta Crystallogr.A50. 246-252 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 田中清明: "電子密度解析法の開発と遷移金属化学物結晶への応用" 日本結晶学会誌. 36. 307-319 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Kiyoaki Tanaka: "X-ray Atomic and Molecular Orbital Analysis and its Applications" Proceedings of The 24th Seminar on Science and Technology"Crystallo graphy". 31-40 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 田中清明: "X線精密結晶構造解析と化学反応" 日本結晶学会誌. 37. 35-41 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Kiyoaki Tanaka: "X-ray Molecular Orbital Analysis of Diformohydrazide" Mol. Cryst. Liq. Cryst.278. 111-116 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Wakatsu Nagai: "Structure and Fluores cence of Secondary Products Produced from the Cope-Knoevenagel Reaction of 2-Pheny lpropionldehyde with Methyl Cyanoacetate." J.Heterocyclic Chem.33. 123-128 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Kiyoaki Tanaka: "X-ray Analysis of 4f-Electron Density in CeB_6 Crystals at 165K" Proceedings German-Japanese Workshop on the Use of Ultra-short Wavelength Photons and γ-rays for High-Precision,High Resolution Analysis of Electronic States of Solids. 133-136 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Kiyoaki Tanaka: "4f-Electron Density Distribution in Crystals of CeB_6 at 165K and its Analysis based on the Crystal Field Theory." Acta Crystallogr.B52(in print). (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 志田典弘: "分子クラスターにおける生成と崩壊のダイナミックス" 数理科学. 396. 50-56 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Takeshita: "A Theoretical Study on the ionization if H_2S with Analysis if Vibrational Stucture of Photoelectron Spectra." Chem.Phys.(in print). (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 田中清明: "分子の化学-化学結合と分子集合体" 学術図書出版社, 220 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 日本結晶学会編: "結晶解析ハンドブック" 共立出版(刊行予定), (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Kiyoaki Tanaka: "X-ray Analysis of Wavefunctions by the Least-squares Method Incorporating Orthhonormality. II.Ground State of the Cu^<2+> Ion of Bis (1,5-diazacyclooctane) copper (II) Nitrate in a Low Symmetry Crystal Field." Acta Crystallogr.B49. 1001-1010 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Kiyoaki Tanaka, Shinji Kumazawa, Michiaki Tsubokawa, Sigeo Maruno & Ichimin Shirotani: "Multiple-Diffraction Effect in Accurate Structure-Factor Measurements of PtP_2 Crystals" Acta Crystallogr.A50. 246-252 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Kiyoaki Tanaka: "X-ray Atomic Orbital Analysis and Anharmonic Thermal Vibratin Analysis, and their Application to Transition Metal Complexex. (In Japanese)" J.Crystallogr.Soc Jpn. 36. 307-319 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Kiyoaki Tanaka: "X-ray Atomic and Molecular Orbital Analysis and its Applications" Proceedings of The 24th Semonar on Science and Technology "Crystallography". 31-40 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Kiyoaki Tanaka: "X-ray accurate Structure Analysis and Chemical Reactions (in Japanese)" J.Crystallogr.Soc.Jpn. 37. 35-41 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Kiyoaki Tanaka: "X-ray Molecular Orbital Analysis of Diformohydrazide" Mol.Cryst.Liq.Cryst. 278. 111-116 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Wakatsu Nagai, Yumiko Hirata, Masao Kawai & Kiyoaki Tanaka: "Structure and Fluorescence of Secondary Products Produced from the Cope-Knoevenagel Reaction of 2-Phenylpropionldehyde with Methyl Cyanoacetate." J.Heterocyclic Chem.33. 123-128 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Kiyoaki Tanaka & Yoshichika Onuki: "X-ray Analysis of 4f-Electron Density in CeB_6 Crystals at 165K" Proceedings German-Japanese Workshop on the Use of Ultra-short Wavelength Photons and gamma-rays for High-Precision, High Resolution Analysis of Electronic States of Solids. 133-136 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Kiyoaki Tanaka, Yoshio Kato & Yoshichila Onuki: "4f-Electron Density Distribution in Crystals of CeB_6 at 165K and its Analysis based on the Crystal Field Theory." Acta Crystallogr.B52 (in print). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Norihiro Shida: "Dynamics of evolution and corruption in molecular clusters (in Japanese)" Mathematical Sciences. 396. 50-56 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Takeshita & N.Shida: "A Theoretical Study on the ionization if H_2S with Analysis if Vibrational Structure of Photoelectron Spectra." Chem.Phys.(in print). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] W.Nagai: ""Structure and fluorescence of products from Cope-Knoevenagel reaction of 2-phenylpropion-aldehyde with methyl cyanoacetate"," J. Heterocy. Chem.(in print). (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] 田中清明: "X線精密構造解析と化学反応" 日本結晶学会誌. 37. 35-41 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 田中清明: "電子密度解析法の開発と遷移金属化合物結晶への応用" 日本結晶学会誌. 36. 307-319 (1994)

    • Related Report
      1995 Annual Research Report
  • [Publications] K.Tanaka: "Multiple diffraction effect in accurate structure factor measurement of PtP_2 crystals" Acta Crystallogr.,. A50. 246-252 (1994)

    • Related Report
      1995 Annual Research Report
  • [Publications] K.Tanaka: "X-ray analysis of wavefunctions by the least-squares method incorporating orthonormality. II. Ground state of the Cu^<2+> ion of bis(1, 5-diazacyclooctane)copper(II)nitrate in a low symmetry field" Acta Crystallogr.B49. 632-636 (1993)

    • Related Report
      1995 Annual Research Report
  • [Publications] S.Yamazaki: "A structural study of facet and off-facet parts of rare-earth garnets, Gd_3Sc_2Al_3O_<12>, Gd_3Sc_2Ga_3O_<12> and La_3Lu_2Ga_3O_<12>" J. Solid State Chem.108. 94-98 (1993)

    • Related Report
      1995 Annual Research Report
  • [Publications] E.N.Maslen: "A synchrotron radiation study of potassium zinc fluoride perovskite" Acta Crystallogr.B49. 632-636 (1993)

    • Related Report
      1995 Annual Research Report
  • [Publications] K.Takeshita: "A theoretical study on the ionization of H_2S with analysis of vibrational structure of photoelectron spectra" Chem. Phys.in print

    • Related Report
      1995 Annual Research Report
  • [Publications] 志田典弘: "小さな稀ガス分子クラスターのダイナミックス" 物性研究. (発表予定).

    • Related Report
      1995 Annual Research Report
  • [Publications] 志田典弘: "分子クラスターの生成と崩壊のダイナミックス" 数理科学. 5月号(発表予定).

    • Related Report
      1995 Annual Research Report
  • [Publications] E.N.MASLEN 他5名: "“Asynchrotron radiation study of potassium zinc fluoride perovskite"." Acta Crystallogr.B49. 632-636 (1993)

    • Related Report
      1994 Annual Research Report
  • [Publications] K.TANAKA: "“X-ray Analysis of Wavefunctions by the Least-squares Method Incorporating Orthonomality II.Ground state of the Cu^<2+>ion of bis(1,5-deazacyclooctane)copper(II)nitrate in alow symmetry field"." AcTa Crystallogr.B49. 1001-1010 (1993)

    • Related Report
      1994 Annual Research Report
  • [Publications] K.TANAKA 他4名: "“Multiple diffraction effect in accurate structure factor measurements of PtP_2 crystals"" AcTa Crystallogr.A50. 246-252 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] 田中 清明: "電子密度解析法の開発と遷移金属化合物結晶への応用" 日本結晶学会誌. 36. 307-319 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] K.TANAKA 他5名: "“A synchrotron radiation study of potassium zinc fluoride perovskite"." Acta Crystallogr.B49. 632-636 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] K.TANAKA: "“X-ray Analysis of Wavefunctions by the Least-squares Method Incorporating Orthonormality.II.Ground state of the Cu^<2+> ion of bis(1,5-diazacyclooctane)copper(II) nitrate in a low symmetry field."" Acta Crystallogr.B49. 1001-1010 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] K.TANAKA 他6名: "“A Structural study of facet and off-facet parts of rare-earth garnets,Gd_3Sc_2Al_3O_<12>,Gd_3Sc_2Ga_3O_<12> and La_3Lu_2Ga_3O_<12>."" J.Solid State Chem.108. 94-98 (1994)

    • Related Report
      1993 Annual Research Report
  • [Publications] K.TANAKA 他4名: "“Multiple diffraction effect in accurate structure factor measurements of PtP_2 crystals"" Acta Crystallogr.A50(in print). (1994)

    • Related Report
      1993 Annual Research Report

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Published: 1993-04-01   Modified: 2016-04-21  

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