Finite difference methods for ab initio electronic structure and quantum transport calculations of nanostructures

Publisher Summary This chapter discusses finite difference methods for ab initio electronic structure and quantum transport calculations of nanostructures. Among the numerical discretization methods used to solve the equations of densityfunctional theory (DFT), the most widely used are linear combination of atomic orbitals (LCAO) - usually Gaussian-type orbitals (GTO) -, plane-waves (PW) and finite differences (FD). Of these three methods, FD is the most recent and less common. It discusses the method with an application to calculations of electronic structure and conductance of carbon nano-tube on a metallic contact. It highlights ab initio Density Functional Theory models, where no parameters are fitted to experimental data. In addition, advanced numerical methods like those presented in this chapter are useful only if they allow treating real problems in solid state physics or physical chemistry. Besides the foreseen improvement in performance for calculations of large scale systems, localized orbital adapted to their chemical environment offer the possibility of novel computational applications.