Submatrix inversion approach to the ab initio Green's function method for electrical transport

In order to theoretically examine electrical transport, including the effects of semi-core orbitals, we propose a submatrix inversion approach within the framework of Green's function method. The efficiency and reliability of the proposed approach is investigated for a model system of a Au-6 linear chain between Au(001) surfaces using the BPW91 functional and a modified LANL2MB basis set. For the energy integration of Green's function, the large integral window ranging from -116 eV to EF (=-5.0 eV) is successfully converted into three small windows [-116 eV, -106 eV], [-67 eV, -55 eV], and [-15 eV, EF]. The computation time of the submatrix inversion approach is faster by about 40% than that for the full-matrix inversion. At the same time, excellent agreement of the computational results between the submatrix and full-matrix inversion is achieved. Further, we propose a new quantity that is useful to determine an appropriate submatrix size.