Surface Green’s function calculations: A nonrecursive scheme with an infinite number of principal layers

A novel computational method for a surface Green’s function matrix is introduced for the calculation of electrical current in molecular wires. The proposed nonrecursive approach includes an infinite number of principal layers and yields the second-order matrix equation for the transformed Green’s function matrix. The solution is found by the direct diagonalization of the auxiliary matrix without any iteration process. As soon as complex roots of the auxiliary matrix $(≃ĜS)$ are calculated, the gaps and the bands in the surface electronic structure are found. It is shown that the solution of a second-order matrix equation determines the spectral density matrix, that is, the density of states for noninteracting electrons. Single and double principal layer models are studied both analytically and numerically. The energy interval for nonvanishing spectral matrices is determined. This method is applicable to matrices of any rank.