Theoretical Chemistry Accounts

, Volume 130, Issue 4–6, pp 711–724 | Cite as

(Hyper)polarizability density analysis for open-shell molecular systems based on natural orbitals and occupation numbers

  • Masayoshi NakanoEmail author
  • Hitoshi Fukui
  • Takuya Minami
  • Kyohei Yoneda
  • Yasuteru Shigeta
  • Ryohei Kishi
  • Benoît Champagne
  • Edith Botek
  • Takashi Kubo
  • Koji Ohta
  • Kenji Kamada
Regular Article


We have developed a method for analyzing the (hyper)polarizabilities of open-shell molecular systems. This method employs the (hyper)polarizability densities based on the natural orbitals and occupation numbers, which enables us to analyze the contributions of odd electrons having various open-shell (diradical) characters. Within broken-symmetry, i.e., spin-unrestricted, single-determinant molecular orbital and density functional theory approaches, we can also remove the spin contamination effects on these quantities through spin projection. To do that, an approximate spin projected method has been elaborated and applied to the analysis of the (hyper)polarizability of multi-radical systems. As examples, typical open-shell singlet systems, 1,3-dipoles and rectangular graphene nanoflakes, are examined.


Hyperpolarizability Open-shell molecule Diradical Natural orbital Broken-symmetry method Spin projection 



This work was supported by Grant-in-Aid for Scientific Research (Nos. 21350011 and 20655003) and “Japan-Belgium Cooperative Program” (J091102006) from Japan Society for the Promotion of Science (JSPS), and the global COE (center of excellence) program “Global Education and Research Center for Bio-Environmental Chemistry” of Osaka University. Theoretical calculations were partly performed using Research Center for Computational Science, Okazaki, Japan. E.B. thanks the Interuniversity Attraction Pole on “Functional Supramolecular Systems” (IUAP No. P6-27) for her postdoctoral grant. This work has also been supported by the Academy Louvain (ARC “Extended-π-Conjugated Molecular Tinkertoys for Optoelectronics, and Spintronics”) and by the Belgian Government (IUAP No P06-27 “Functional Supramolecular Systems”).


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Masayoshi Nakano
    • 1
    Email author
  • Hitoshi Fukui
    • 1
  • Takuya Minami
    • 1
  • Kyohei Yoneda
    • 1
  • Yasuteru Shigeta
    • 1
  • Ryohei Kishi
    • 1
  • Benoît Champagne
    • 2
  • Edith Botek
    • 2
  • Takashi Kubo
    • 3
  • Koji Ohta
    • 4
  • Kenji Kamada
    • 4
  1. 1.Department of Materials Engineering Science, Graduate School of Engineering ScienceOsaka UniversityToyonakaJapan
  2. 2.Laboratoire de Chimie Théorique, Facultés Universitaires Notre-Dame de la Paix (FUNDP)NamurBelgium
  3. 3.Department of Chemistry, Graduate School of ScienceOsaka UniversityToyonakaJapan
  4. 4.Research Institute for Ubiquitous Energy DevicesNational Institute of Advanced Industrial Science and Technology (AIST)IkedaJapan

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