Complex band structure, decay lengths, and Fermi level alignment in simple molecular electronic systems

The complex band structure of a periodic system is the conventional band structure extended to complex Bloch k vectors. The k vectors with an imaginary part describe spatially decaying wave functions and arise in, for example, the analysis of impurity and surface states. They also represent the quantum tunneling states which are vehicles of electron transport through a barrier such as a thin oxide layer or a molecule. We present a method for obtaining the complex band structure of a molecule which is composed of repeating units. The complex band structures of some simple organic molecules (n-alkanes, alkenes, and linked benzene rings) will be determined and used to analyze electron conduction through molecules (e.g., octanedithiol) connected between gold electrodes. The form of the complex band structure clearly elucidates the molecule length dependence of the tunneling current and also suggests the energy for alignment of the Fermi level.