An elongation method for large systems toward bio-systems.

The elongation method, proposed in the early 1990s, originally for theoretical synthesis of aperiodic polymers, has been reviewed. The details of derivation of the localization scheme adopted by the elongation method are described along with the elongation processes. The reliability and efficiency of the elongation method have been proven by applying it to various models of bio-systems, such as gramicidin A, collagen, DNA, etc. By means of orbital shift, the elongation method has been successfully applied to delocalized π-conjugated systems. The so-called orbital shift works in such a way that during the elongation process, some strongly delocalized frozen orbitals are assigned as active orbitals and joined with the interaction of the attacking monomer. By this treatment, it has been demonstrated that the total energies and non-linear optical properties determined by the elongation method are more accurate even for bio-systems and delocalized systems like fused porphyrin wires. The elongation method has been further developed for treating any three-dimensional (3D) systems and its applicability is confirmed by applying it to entangled insulin models whose terminal is capped by both neutral and zwitterionic sequences.