Because the functional property of materials is based on the microscopic electronic states, quantum chemistry that reflects the property of the individual atom and molecule precisely must be effective. However, the computational time required is N3~4 (N: number of the bases functions) at Hartree-Fock (HF) level, and it becomes N5~7 at post HF level, and then applications to cohesion systems and materials are difficult even if we use a super parallel computer. Although quantum chemistry to precisely calculate molecular properties was accomplished and developed rapidly with the remarkable progress of the computers, the problem left is for the application to large-scale systems. Therefore, we developed Elongation (ELG) method as a tool for the large-scale complex system for which conventional method cannot handle.
The elongation method originally proposed by Imamura and Aoki in the early of 1990s; its idea came from the polymerization procedures in experiment. It has been developed for efficiently determining the electronic structure of polymers without considering any periodic boundary conditions. A target polymer is built up by adding a monomer unit to the active side of the starting cluster step by step. As there is no periodicity presumed, that is, in a general sense the adding monomers during the elongation steps can be random, and thus any random polymer can be theoretically synthesized. Contrast to some other approximation methods for large systems, the elongation is fully variational. It has been already demonstrated that the total energy obtained by the ELG method is in excellent agreement to those by the conventional method. The error of the elongation method is within 10-9 a.u./atom, showing its high accuracy compared to other methodologies. The main idea of the ELG method and its applications to various complex systems has been presented in Perspective .
In this talk, the efficiency and accuracy of our treatment is shown by applying it for large systems like nanotubes, DNA, and some complicated proteins like enzymes. We intended for one-dimensional polymers at first, but now it was generalized to two- and even three-dimensional (3D) systems with high speed calculations while giving results almost identical to those by conventional method. 3D-ELG method for materials and some new progresses will be also reported.
 A. Imamura, Y. Aoki, and K. Maekawa, J. Chem. Phys. 95 (1991) 5419.
 Y. Aoki and F. L. Gu, An elongation method for large systems toward bio-systems, Phys. Chem. Chem. Phys., 14(21), 7640-7668 (2012).