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Theoretical study on a robust control of molecular spin state by pi-figuration

Planned Research

Project Areapi-System Figuration: Control of Electron and Structural Dynamism for Innovative Functions
Project/Area Number 26102017
Research Category

Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area)

Allocation TypeSingle-year Grants
Review Section Science and Engineering
Research InstitutionTokyo Institute of Technology

Principal Investigator

Tada Tomofumi  東京工業大学, 元素戦略研究センター, 准教授 (40376512)

Co-Investigator(Kenkyū-buntansha) 南谷 英美  東京大学, 大学院工学系研究科(工学部), 講師 (00457003)
Project Period (FY) 2014-07-10 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥40,040,000 (Direct Cost: ¥30,800,000、Indirect Cost: ¥9,240,000)
Fiscal Year 2018: ¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000)
Fiscal Year 2017: ¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000)
Fiscal Year 2016: ¥6,110,000 (Direct Cost: ¥4,700,000、Indirect Cost: ¥1,410,000)
Fiscal Year 2015: ¥6,110,000 (Direct Cost: ¥4,700,000、Indirect Cost: ¥1,410,000)
Fiscal Year 2014: ¥16,640,000 (Direct Cost: ¥12,800,000、Indirect Cost: ¥3,840,000)
Keywords分子スピン / 量子輸送 / 第一原理計算 / 量子ビット / 単分子コンタクト / 量子輸送特性 / 量子ダイナミクス / 分子集積 / 分子集積体 / 分子接合 / π伝導チャネル / 量子情報 / 励起状態
Outline of Final Research Achievements

Quantum computational systems in which computations are carried out in a quantum way and thereby the computational performance is extremely higher than the present ones have been extensively investigated in both theoretical and experimental studies. For the realization of practical quantum systems, a large number of quantum bit, qubit, is required, and we proposed a self-assembled molecular system. The required properties for the molecule are robustness of spin protection and spin operation, and we succeeded in the theoretical proposal of such a molecule and our experimental collaborator succeeded in the synthesis of the molecule. First principles theoretical calculations and experimental observation revealed that the synthesized molecule holds the required properties.

Academic Significance and Societal Importance of the Research Achievements

量子コンピュータの可能性に注目が集まっている今日において、量子コンピュータの情報ユニットである量子ビットの数を現状のものから飛躍的に増大させることが必要とされている。本研究は、量子ビット数の飛躍的増大を実現するための方向性として、分子のもつ特性である表面上自己組織性に注目し、その集積化された構造により量子コンピューティングを達成しようとする研究である。表面上分子が量子ビットとして利用される際に必要とされる条件を明確化し、本研究にて具体的分子の設計と共同実験研究者による分子合成に至ったことは、今後における新しい方向性を打ち出した研究と位置付けることが出来る。

Report

(6 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Annual Research Report
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • 2014 Annual Research Report
  • Research Products

    (54 results)

All 2019 2018 2017 2016 2015 2014 Other

All Int'l Joint Research (3 results) Journal Article (19 results) (of which Int'l Joint Research: 6 results,  Peer Reviewed: 19 results,  Open Access: 8 results,  Acknowledgement Compliant: 9 results) Presentation (31 results) (of which Int'l Joint Research: 16 results,  Invited: 22 results) Book (1 results)

  • [Int'l Joint Research] Graz University of Technology(オーストリア)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Heidelberg University(ドイツ)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] The Hebrew University of Jerusalem(イスラエル)

    • Related Report
      2018 Annual Research Report
  • [Journal Article] Anionic Stannaferrocene and Its Unique Electronic State2019

    • Author(s)
      Saito Masaichi、Matsunaga Naoki、Hamada Jumpei、Furukawa Shunsuke、Tada Tomofumi、Herber Rolfe H.
    • Journal Title

      Chemistry Letters

      Volume: 48 Issue: 2 Pages: 163-165

    • DOI

      10.1246/cl.180880

    • NAID

      130007590723

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] First-Principles Study of the Adsorption Behavior of Triptycene Molecular Tripods on Au(111): Site-Selectivity and Unambiguous Molecular Orientation2019

    • Author(s)
      T. Tada, F. Ishiwari, Y. Shoji, T. Fukushima
    • Journal Title

      J. Phys. Chem. C

      Volume: 123 Issue: 7 Pages: 4401-4406

    • DOI

      10.1021/acs.jpcc.9b00869

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Triptycene Tripods for the Formation of Highly Uniform and Densely Packed Self-Assembled Monolayers with Controlled Molecular Orientation2019

    • Author(s)
      F. Ishiwari, G. Nascimbeni, E. Sauter, H. Tago, Y. Shoji, S. Fujii, M. Kiguchi, T. Tada, M. Zharnikov, E. Zojer, T. Fukushima
    • Journal Title

      J. Am. Chem. Soc.

      Volume: 141 Issue: 14 Pages: 5995-6005

    • DOI

      10.1021/jacs.9b00950

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Wave-packet multi-scale simulations based on a non-linear tight-binding Hamiltonian for carrier transport in π-conjugated polymers2018

    • Author(s)
      Tomofumi Tada
    • Journal Title

      Materials Chemistry Frontiers

      Volume: 印刷中 Issue: 7 Pages: 1351-1359

    • DOI

      10.1039/c7qm00591a

    • Related Report
      2018 Annual Research Report 2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] “Doping” of Polyyne with an Organometallic Fragment Leads to Highly Conductive Metallapolyyne Molecular Wire2018

    • Author(s)
      Tanaka Yuya、Kato Yuya、Tada Tomofumi、Fujii Shintaro、Kiguchi Manabu、Akita Munetaka
    • Journal Title

      Journal of the American Chemical Society

      Volume: 140 Issue: 32 Pages: 10080-10084

    • DOI

      10.1021/jacs.8b04484

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ring shape-dependent self-sorting of pillar[n]arenes assembled on a surface2018

    • Author(s)
      Ogoshi T, Takashima S, Inada N, Asakawa H, Fukuma T, Shoji Y, Kajitani T, Fukushima T, Tada T, Dotera T, Kakuta T, Yamagishi T
    • Journal Title

      Communications Chemistry

      Volume: 1 Issue: 1 Pages: 92-92

    • DOI

      10.1038/s42004-018-0094-z

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] CO-tip manipulation using repulsive interactions2018

    • Author(s)
      Nana K M Nazriq, E Minamitani, and T K Yamada
    • Journal Title

      Nanotechnology

      Volume: 29 Issue: 49 Pages: 495701-495701

    • DOI

      10.1088/1361-6528/aae0df

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A Stable, Soluble, and Crystalline Supramolecular System with a Triplet Ground State2017

    • Author(s)
      Tsukasa Futagoishi, Tomoko Aharen, Tatsuhisa Kato, Azusa Kato, Toshiyuki Ihara, Tomofumi Tada, Michihisa Murata, Atsushi Wakamiya, Hiroshi Kageyama, Yoshihiko Kanemitsu, and Yasujiro Murata
    • Journal Title

      Angew. Chem. Int. Ed.

      Volume: in press Issue: 15 Pages: 4261-4265

    • DOI

      10.1002/anie.201701212

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Triphosphasumanene Trisulfide: High Out-of-Plane Anisotropy and Janus-Type π-Surfaces2017

    • Author(s)
      Shunsuke Furukawa, Yuki Suda, Junji Kobayashi, Takayuki Kawashima, Tomofumi Tada, Shintaro Fujii, Manabu Kiguchi, Masaichi Saito
    • Journal Title

      Journal of the Americal Chemical Society

      Volume: 139 Issue: 16 Pages: 5787-5792

    • DOI

      10.1021/jacs.6b12119

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Theoretical prediction of phonon-mediated superconductivity with Tc about 25 K in Li-intercalated h-BN bilayer2017

    • Author(s)
      N. H. Shimada, E. Minamitani, S. Watanabe
    • Journal Title

      Appl. Phys. Express

      Volume: 10 Issue: 9 Pages: 0931011-4

    • DOI

      10.7567/apex.10.093101

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Single Molecule Quantum Dot as a Kondo Simulator2017

    • Author(s)
      R. Hiraoka, E. Minamitani, R. Arafune, N. Tsukahara, S. Watanabe, M. Kawai, N. Takagi
    • Journal Title

      Nature Communications

      Volume: 8 Issue: 1 Pages: 16012-16012

    • DOI

      10.1038/ncomms16012

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Atomic-scale characterization of the interfacial phonon in graphene/SiC2017

    • Author(s)
      E. Minamitani, R. Arafune, T. Frederiksen, T. Suzuki, S. M. F. Shahed, T. Kobayashi, N. Endo, H. Fukidome, S. Watanabe, T. Komeda,
    • Journal Title

      Phys. Rev. B

      Volume: 96 Issue: 15 Pages: 155431-155431

    • DOI

      10.1103/physrevb.96.155431

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Resolving metal-molecule interfaces at single-molecule junctions2016

    • Author(s)
      Y. Komoto, S. Fujii, H. Nakamura, T. Tada, T. Nishino, M. Kiguchi
    • Journal Title

      Sci. Rep.

      Volume: 6 Issue: 1 Pages: 26606-26606

    • DOI

      10.1038/srep26606

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Rashba Splitting in Image Potential State Investigated Using Circular Dichroism Two-Photon Photoemission Spectroscopy2016

    • Author(s)
      T. Nakazawa, N. Takagi, M. Kawai, H. Ishida, R. Arafune
    • Journal Title

      Physical Review B

      Volume: 117 Issue: 20 Pages: 205402-205402

    • DOI

      10.1103/physrevb.94.205402

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Surface phonon excitation on clean metal surfaces in scanning tunneling microscopy2016

    • Author(s)
      E. Minamitani, R. Arafune, N. Tsukahara, Y. Ohda, S. Watanabe, M. Kawai, H. Ueba, N. Takagi
    • Journal Title

      Physical Review B

      Volume: 93 Issue: 8 Pages: 085411-085411

    • DOI

      10.1103/physrevb.93.085411

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Organometallic Molecular Wires as Versatile Modules for Energy-Level Alignment of the Metal-Molecule-Metal Junction2016

    • Author(s)
      K. Sugimoto, Y. Tanaka, S. Fujii, T. Tada, M. Kiguchi, M. Akita
    • Journal Title

      Chemical Communications

      Volume: 52 Issue: 34 Pages: 5796-5799

    • DOI

      10.1039/c6cc01705c

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Rectifying electron-transport properties through stacks of aromatic molecules inserted into a self-assembled cage2015

    • Author(s)
      S. Fujii, T. Tada, Y. Komoto, T. Osuga, T. Murase, M. Fujita, M. Kiguchi
    • Journal Title

      J. Am. Chem. Soc.

      Volume: 137 Issue: 18 Pages: 5939-5947

    • DOI

      10.1021/jacs.5b00086

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Spatially extended underscreened Kondo state from collective molecular spin2015

    • Author(s)
      Emi Minamitani, Ying-Shuang Fu, Qi-Kun Xue, Yousoo Kim, Satoshi Watanabe
    • Journal Title

      Physical Review B

      Volume: 92 Issue: 7 Pages: 075144-075144

    • DOI

      10.1103/physrevb.92.075144

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Molecular design of electron transport with orbital rule: toward conductance-decay free molecular junctions2015

    • Author(s)
      T. Tada and K. Yoshizawa
    • Journal Title

      Phys. Chem. Chem. Phys.

      Volume: 17 Issue: 48 Pages: 32099-32110

    • DOI

      10.1039/c5cp05423k

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Presentation] Theoretical studies on a single molecular spin contact for quantum information processing2019

    • Author(s)
      Tomofumi Tada
    • Organizer
      Nature conference
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 準局在状態間トンネル伝導に関する理論的研究2019

    • Author(s)
      多田 朋史
    • Organizer
      日本化学会第99春季年会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 電子相関とスピン軌道相互作用が織りなす多様な吸着分子磁性2019

    • Author(s)
      南谷 英美
    • Organizer
      日本物理学会第74回年次大会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 非弾性分光で探る表面界面の素励起:理論的側面を中心に2019

    • Author(s)
      南谷 英美
    • Organizer
      第17回SPring-8ユーザー協同体顕微ナノ材料科学研究会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 酸素内包フラーレン型分子におけるゼロ磁場分裂の第一原理計算2019

    • Author(s)
      山田秀祐・二子石師・村田靖次郎・多田朋史
    • Organizer
      日本化学会第99春季年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Theoretical study on electron transport through organometallic molecular wires2018

    • Author(s)
      Tomofumi Tada
    • Organizer
      International Conference on Coordination Chemistry 2018 (ICCC2018)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 第一原理計算による電子フォノン相互作用解析とその応用2018

    • Author(s)
      南谷 英美
    • Organizer
      第二回フォノンエンジニアリング研究会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Full Atomistic Kinetic Monte Carlo with Direct Counting Approach for Ion Dynamics in Electrochemical Cells2018

    • Author(s)
      Tomofumi Tada
    • Organizer
      233rd ECS Meeting
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 単分子コンダクタンスの分子鎖長依存性に関する解析的分子軌道を用いた理論解析2018

    • Author(s)
      菅野志優,多田朋史
    • Organizer
      日本化学会新領域ナノスケール分子デバイス第7 回若手セミナー
    • Related Report
      2017 Annual Research Report
  • [Presentation] 第一原理計算及びモンテカルロシミュレーションを用いたπスタック分子吸着における分子配向の基板依存性の理論的検討2018

    • Author(s)
      西山航平,多田朋史
    • Organizer
      日本化学会新領域ナノスケール分子デバイス第7 回若手セミナー
    • Related Report
      2017 Annual Research Report
  • [Presentation] Controlling the competition between Kondo effect and spin-orbit interaction in a single molecule by atomic manipulation2018

    • Author(s)
      E. Minamitani, R. Hiraoka, R. Arafune, N. Tsukahara, S. Watanabe, M. Kawai and N. Takagi
    • Organizer
      DPG March meeting
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Atomic-Scale Investigation of the Interfacial Phonon at Graphene/SiC2017

    • Author(s)
      Emi Minamitani
    • Organizer
      5th Ito International Research Conference, RIKEN Central Anniversary & Surface and Interface Spectroscopy 2017
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 単一スピン制御のための単分子コンタクトの理論的研究2017

    • Author(s)
      多田 朋史
    • Organizer
      日本化学会
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] 吸着分子におけるスピン物性の理論2016

    • Author(s)
      南谷 英美
    • Organizer
      応用物理学会
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Recent Topics on Orbital Rule for Single Molecular Conductance2016

    • Author(s)
      Tomofumi Tada
    • Organizer
      Fujihara Seminar-70
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Theoretical Study on a Single Molecular Spin Control and Detection for Quantum Information Processing2016

    • Author(s)
      Tomofumi Tada
    • Organizer
      OCUIC-2016 Molecular Spins and Quantum Technology
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Multiscale simulation for carrier mobility of micro-meter scale pi-conjugated molecular wire2016

    • Author(s)
      Tomofumi Tada
    • Organizer
      24th-International Colloquium on Scanning Probe Microscopy (ICSPM24)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Competition between spin-orbit interaction and Kondo effect in Fe-phthalocyanine molecule on Au(111)2016

    • Author(s)
      Emi Minamitani
    • Organizer
      Pre-conference of ICMM2016
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Hybrid density functional study on electron transport though π-stack molecular junctions for high conductance2015

    • Author(s)
      T. Tada
    • Organizer
      PacifiCHEM2015
    • Place of Presentation
      Hawaii Convention Center
    • Year and Date
      2015-12-13
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] イオン輸送と電子輸送に関する 第一原理計算からの マルチスケールシミュレーション2015

    • Author(s)
      多田朋史
    • Organizer
      High Performance Computing Chemistry (HPCC) -2015-
    • Place of Presentation
      理化学研究所 計算科学研究機構
    • Year and Date
      2015-12-01
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] 有機高分子ワイヤーの量子波束散乱シミュレーションの現状と今後について2015

    • Author(s)
      多田朋史
    • Organizer
      数理構造保存を接点とした数学・HPC・実科学のクロスオーバー
    • Place of Presentation
      電気通信大学
    • Year and Date
      2015-11-24
    • Related Report
      2015 Annual Research Report
  • [Presentation] Nobel Kondo effects in single molecules on metal surfaces2015

    • Author(s)
      Emi Minamitani
    • Organizer
      Studying the Function of Soft Molecular Systems by the Concerted Use of Theory and Experiment The 12th Workshop
    • Place of Presentation
      National Institute for Material Sciences (NIMS)
    • Year and Date
      2015-10-01
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Wave packet scattering simulations for spin dependent transport in molecular-spin junctions2015

    • Author(s)
      T. Tada
    • Organizer
      CT-NanoSim2015
    • Place of Presentation
      Tsukuba Univ.
    • Year and Date
      2015-09-17
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] DFT+NRG studies on the spatially extended Kondo effect in MnPc/Pb(111)2015

    • Author(s)
      Emi Minamitani, Yingshuang Fu, Qikun Xue, Yousoo Kim, Satoshi Watanabe
    • Organizer
      Psi-k
    • Place of Presentation
      SAN SEBASTIAN
    • Year and Date
      2015-09-06
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 電子伝導とイオン伝導に関する第一原理計算からのマルチスケールシミュレーション2015

    • Author(s)
      多田朋史
    • Organizer
      第28期CAMMフォーラム
    • Place of Presentation
      アイビーホール, 東京
    • Year and Date
      2015-05-15
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] πスタック単分子架橋系の量子輸送計算2015

    • Author(s)
      多田朋史
    • Organizer
      日本化学会第95春季年会
    • Place of Presentation
      日大船橋キャンパス
    • Year and Date
      2015-03-26
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Underscreened Kondo state of collective molecular spin in Mn-Phthalocyanine on Pb(111)2014

    • Author(s)
      E. Minamitani, Y. Fu, Q.-K. Xue, Y. Kim, and S. Watanabe
    • Organizer
      International Symposium on Computics: Quantum Simulation and Design
    • Place of Presentation
      Tokyo, Japan
    • Year and Date
      2014-12-01
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research
  • [Presentation] π造形科学:電子と構造のダイナミズム制御による新機能創出2014

    • Author(s)
      多田朋史, 福島孝典
    • Organizer
      第8回物性科学領域横断研究会
    • Place of Presentation
      大阪大学豊中キャンパス
    • Year and Date
      2014-11-21
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] DFT+NRG studies on novel Kondo effects in single molecules on metal surfaces2014

    • Author(s)
      Emi Minamitani
    • Organizer
      The 17th Asian Workshop on First-Principles Electronic Structure Calculations
    • Place of Presentation
      Seoul, Korea
    • Year and Date
      2014-11-03
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Underscreened Kondo effect of the collective spin state in Mn-phthalocyanine on Pb(111)2014

    • Author(s)
      E. Minamitani, Y. Fu, Q.-K. Xue, Y. Kim, and S. Watanabe
    • Organizer
      ISSS-7 (The 7th International Symposium on Surface Science)
    • Place of Presentation
      Matsue, Japan
    • Year and Date
      2014-11-02
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Kondo effects in single molecules on metal surfaces2014

    • Author(s)
      Emi Minamitani
    • Organizer
      Spintronics and Magnetochemistry on the Atomic and Molecular Level
    • Place of Presentation
      Ascona, Switzerland
    • Year and Date
      2014-10-27
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research / Invited
  • [Book] Single‐Molecule Electronics ‐ An Introduction to Synthesis, Measurement, and Theory, Ch.7: Orbital rule for electron transport of molecular junctions2016

    • Author(s)
      Tomofumi Tada
    • Total Pages
      24
    • Publisher
      Springer
    • Related Report
      2015 Annual Research Report

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Published: 2014-11-20   Modified: 2020-03-30  

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