Compact expression for the angular dependence of tight-binding Hamiltonian matrix elements

We present a general, compact expression for the angular dependence of tight-binding Hamiltonian matrix elements in the two-center approximation. In addition, a general expression for the on-site spin-orbit Hamiltonian matrix elements is given. The expressions are valid for all angular momentum quantum numbers, have a simple structure, and are well suited for numerical calculations.

Figure 1

Definition of coordinate systems and Euler angles for the coupled atoms.