First-principles Calculation Method for Electronic Structures of Nanostructures Intervening between Semi-infinite Electrodes

A method which solves the Kohn-Sham equation directly on grid points in the real space has recently been introduced[5-10], which avoids many of these problems. Within this method, boundary conditions are not constrained to be periodic, which permits the use of nonperiodic boundary conditions for clusters and a combination of periodic and nonperiodic boundary conditions for surfaces. Furthermore, in order to realize the order-N (O(N)) calculation, the orbitals constrained to be localized in finite regions of the real space can be employed instead of wave functions extending over supercells, and then, by making efficient use of the advantages of such localized orbitals, one can calculate the ground-state electronic structure of a nanostructure sandwiched between two infinitely continuing crystalline electrodes (see Fig. 1 for an example).