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Solving the Non-BO Schroedinger equations and analytical potential energy surface

Research Project

Project/Area Number 17H04867
Research Category

Grant-in-Aid for Young Scientists (A)

Allocation TypeSingle-year Grants
Research Field Physical chemistry
Research InstitutionQuantum Chemistry Research Institute

Principal Investigator

Nakashima Hiroyuki  認定NPO法人量子化学研究協会, 研究所, 部門長 (80447911)

Project Period (FY) 2017-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥21,580,000 (Direct Cost: ¥16,600,000、Indirect Cost: ¥4,980,000)
Fiscal Year 2020: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2019: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2018: ¥6,240,000 (Direct Cost: ¥4,800,000、Indirect Cost: ¥1,440,000)
Fiscal Year 2017: ¥5,460,000 (Direct Cost: ¥4,200,000、Indirect Cost: ¥1,260,000)
Keywordsシュレーディンガー方程式 / 自由完員関数法 / 解析的ポテンシャル面 / 核の運動の量子効果 / Non-BOシュレーディンガー方程式 / 解析的ポテンシャルカーブ / ポテンシャル曲面
Outline of Final Research Achievements

The Born-Oppenheimer (BO) approximation is one of the most favorable assumptions ordinarily assumed in chemistry. In recent years, however, the significances of the nuclear quantum effects and the theoretical studies by non-Born-Oppenheimer (non-BO) calculations have been pointed out in various scientific fields. In the present study, we extended the free complement (FC) theory for solving the non-BO Schroedinger equations connected with the integral-free local Schroedinger equation method applicable to general atoms and molecules. We also developed the theory to obtain analytical potential energy surfaces from the non-BO wave functions. Thus, the present study indicated high potentialities for doing chemistry with exact non-BO solutions. We will further continue to develop the present theories to study more practical physical and chemical phenomena.

Academic Significance and Societal Importance of the Research Achievements

シュレーディンガー方程式は、原子・分子の微視的世界を支配する量子力学の基礎方程式であり、この方程式を正確に解くことができれば、あらゆる化学現象を予言することができる。原子・分子は、原子核と電子から構成されるが、ほとんどの化学研究では重い原子核を固定し電子のみ量子的に扱う。しかし、原子核も量子的に扱うnon-Born-Oppenheimer (non-BO)こそ、真に量子力学原理を反映する。本研究では、これまで皆無であったnon-BOシュレーディンガー方程式を解く計算理論と、得られた解を解析し化学反応に応用する方法を開拓した。未熟な段階であるが、今後の発展の礎を築くことができたと確信している。

Report

(5 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • Research Products

    (20 results)

All 2020 2019 2018 2017 Other

All Journal Article (8 results) (of which Peer Reviewed: 8 results) Presentation (11 results) (of which Int'l Joint Research: 4 results,  Invited: 4 results) Remarks (1 results)

  • [Journal Article] Solving the Schroedinger equation of the hydrogen molecule with the free-complement variational theory: essentially exact potential curves and vibrational levels of the ground and excited states of Π symmetry2020

    • Author(s)
      Yusaku I. Kurokawa, Hiroyuki Nakashima, Hiroshi Nakatsuji
    • Journal Title

      Physical Chemistry Chemical Physics

      Volume: 22 Issue: 24 Pages: 13489-13497

    • DOI

      10.1039/d0cp01492c

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Free complement sij-assisted rij theory: Variational calculation of the quintet state of a carbon atom2020

    • Author(s)
      Hiroyuki Nakashima and Hiroshi Nakatsuji
    • Journal Title

      Physical Review A

      Volume: 102 Issue: 5

    • DOI

      10.1103/physreva.102.052835

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Inverse Hamiltonian method assisted by the complex scaling technique for solving the Dirac-Coulomb equation: Helium isoelectronic atoms2020

    • Author(s)
      Hiroyuki Nakashima, Hiroshi Nakatsuji
    • Journal Title

      Chemical Physics Letters

      Volume: 749 Pages: 137447-137447

    • DOI

      10.1016/j.cplett.2020.137447

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Solving the Schroedinger equation of atoms and molecules using one- and two-electron integrals only2020

    • Author(s)
      Hiroshi Nakatsuji, Hiroyuki Nakashima, Yusaku I. Kurokawa
    • Journal Title

      Physical Review A

      Volume: 101 Issue: 6

    • DOI

      10.1103/physreva.101.062508

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Solving the Schroedinger equation with the free-complement chemical-formula theory: Variational study of the ground and excited states of Be and Li atoms2019

    • Author(s)
      Hiroshi Nakatsuji, Hiroyuki Nakashima
    • Journal Title

      The Journal of Chemical Physics

      Volume: 150 Issue: 4

    • DOI

      10.1063/1.5065565

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Solving the Schroedinger equation of atoms and molecules: Chemical-formula theory, free-complement chemical-formula theory, and intermediate variational theory2018

    • Author(s)
      Hiroshi Nakatsuji, Hiroyuki Nakashima, and Yusaku I. Kurokawa
    • Journal Title

      The Journal of Chemical Physics

      Volume: 149 Issue: 11

    • DOI

      10.1063/1.5040376

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Solving the Schroedinger equation of atoms and molecules with the free-complement chemical-formula theory: First-row atoms and small molecules2018

    • Author(s)
      Hiroshi Nakatsuji, Hiroyuki Nakashima, and Yusaku I. Kurokawa
    • Journal Title

      The Journal of Chemical Physics

      Volume: 149 Issue: 11

    • DOI

      10.1063/1.5040377

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Solving the Schroedinger equation of hydrogen molecule with the free complement-local Schroedinger equation method: Potential energy curves of the ground and singly excited singlet and triplet states, Σ, Π, Δ, and Φ2018

    • Author(s)
      Hiroyuki Nakashima, Hiroshi Nakatsuji
    • Journal Title

      The Journal of Chemical Physics

      Volume: 149 Issue: 24

    • DOI

      10.1063/1.5060659

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Presentation] FC 理論による exact に至る計算のための Slater 型関数の積分法とプログラムの開発2019

    • Author(s)
      中嶋 浩之、黒川 悠索、中辻 博
    • Organizer
      第22回理論化学討論会(札幌)
    • Related Report
      2019 Annual Research Report
  • [Presentation] Slater型関数の積分プログラム開発とFC理論による原子の高精度計算2019

    • Author(s)
      中嶋 浩之、黒川 悠索、中辻 博
    • Organizer
      第13回分子科学討論会(名古屋)
    • Related Report
      2019 Annual Research Report
  • [Presentation] Implementation of Slater-type one-center atomic integrals for accurate variational calculations of small atoms by free complement theory2019

    • Author(s)
      Hiroyuki Nakashima, Hiroshi, Nakatsuji
    • Organizer
      The 9th Asia-Pacific Conference of Theoretical and Computational Chemistry (APCTCC9), Sydney, Australia
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] FC-CF理論に基づく簡単な分子の変分解とexact解の計算2018

    • Author(s)
      中嶋 浩之、黒川 悠索、中辻 博
    • Organizer
      第21回理論化学討論会(岡崎)
    • Related Report
      2018 Annual Research Report
  • [Presentation] Potential Energy Curves and Nature of Chemical Bonds Studied by the Free Complement Variational (FC-V) Theory2018

    • Author(s)
      Hiroyuki Nakashima, Yusaku I. Kurokawa, Hiroshi Nakatsuji
    • Organizer
      7th Japan-Czech-Slovak (JCS) Symposium, Prague, Czech
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] non-BO Solutions and Analytical Potential Energy Curves by Solving the Schroedinger Equations of a few Electron Diatomic Molecules2018

    • Author(s)
      Hiroyuki Nakashima, Hiroshi Nakatsuji
    • Organizer
      16th International Congress of Quantum Chemistry (16th-ICQC), Menton, France
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Free-Complement Chemical-Formula-Theory (FC-CFT) による簡単な分子の計算と金属間結合の研究2018

    • Author(s)
      中嶋 浩之、黒川 悠索、中辻 博
    • Organizer
      第12回分子科学討論会(福岡)
    • Related Report
      2018 Annual Research Report
  • [Presentation] Solving the Schroedinger Equations:Variational and Exact Calculations of Small Atoms and Molecules by the Free Complement Theory2018

    • Author(s)
      Hiroyuki Nakashima, Yusaku I. Kurokawa, and Hiroshi Nakatsuji
    • Organizer
      International WS on Quantum Chemistry/Quantum Chemical Calculations on Quantum Computers, Osaka City University, Osaka, Japan
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] FC-LSE法による原子・分子のシュレーディンガー解の計算 I.2017

    • Author(s)
      中嶋 浩之、黒川 悠索、中辻 博
    • Organizer
      第20回理論化学討論会(京都)
    • Related Report
      2017 Annual Research Report
  • [Presentation] 原子・分子のシュレーディンガー解データベースの構築:Exact Chemical Informaticsの開発に向けて2017

    • Author(s)
      中嶋 浩之、中辻 博
    • Organizer
      第11回分子科学討論会(仙台)
    • Related Report
      2017 Annual Research Report
  • [Presentation] Important and interesting message from the exact Non-BO solutions of the Schroedinger equationby the free-complement methodology2017

    • Author(s)
      Hiroyuki Nakashima and Hiroshi Nakatsuji
    • Organizer
      2nd International Symposium on Quantum Chemistry, KWANSEI GAKUIN University, Japan
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Remarks] 量子化学研究協会・研究所ホームページ

    • URL

      http://qcri.or.jp/

    • Related Report
      2020 Annual Research Report 2019 Annual Research Report

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Published: 2017-04-28   Modified: 2022-01-27  

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