Linear Scaling Methodology

  • Oleksandr LobodaEmail author
Part of the Carbon Nanostructures book series (CARBON)


In 1991 the elongation method, an efficient method for quantum mechanical calculations of large systems, was originally proposed by Imamura [1] during one of his stays in Heidelberg, Germany. Although in the early 1990s the concept of and need for order-N [O(N)] methods didn’t exist, Prof. Akira Imamura was thinking about “how to avoid direct SCF calculations for large biological systems (biopolymers composed of hundreds if not thousands of residues of amino acids or nucleic acid base pairs in proteins and DNA or RNA) by treating only the local interactions between a few neighbor residues in large systems.” While contemplating how to perform such calculations, he got the idea of “theoretically simulating the synthesis of polymers so as to mimic the chemical reactions which occur in nature during polymerization reactions to form peptides, proteins and polynucleotides.


Energy Matrix Elongation Process Freeze Orbital Freeze Region Fragment Molecular Orbital 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institute of Colloid and Water ChemistryKievUkraine

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