Elongation Method: Towards Linear Scaling for Electronic Structure of Random Polymers and other Quasilinear Materials

  • Feng Long GuEmail author
  • Bernard Kirtman
  • Yuriko Aoki
Part of the Challenges and Advances in Computational Chemistry and Physics book series (COCH, volume 13)


We present the linear scaling elongation method for Hartree-Fock and Kohn-Sham electronic structure calculations of either periodic or aperiodic quasi-one-dimensional systems. Linear scaling is achieved through two key computational features: (1) regional localization of molecular orbitals; and (2) a two-electron integral cutoff technique combined with quantum fast multipole evaluation of non-negligible long-range integrals. The accuracy and timing of the method is demonstrated for several systems of interest such as polyglycine and BN nanotubes. Future developments of both a technical and methodological nature are noted including the extension to higher dimensionality as well as higher level wave function treatments.


Elongation method Linear scaling Localization method Quasi-one-dimensional systems Cutoff technique 



This work was supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan.


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Center for Computational Quantum ChemistrySouth China Normal UniversityGuangzhouChina
  2. 2.Department of Chemistry and BiochemistryUniversity of CaliforniaSanta BarbaraUSA
  3. 3.Department of Material Sciences, Faculty of Engineering SciencesKyushu UniversityFukuokaJapan
  4. 4.Japan Science and Technology AgencyCRESTKawaguchiJapan

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