Transition metal dichalcogenide materials MX2 (M = Mo;W;X = S; Se) are being thoroughly studied due to their novel two-dimensional structure, that is associated with exceptional optical and transport properties. From a computational point of view, Density Functional Theory simulations perform very well in these systems and are an indispensable tool to predict and complement experimental results. However, due to the time and length scales where even the most efficient DFT implementations can reach today, this methodology suffers of stringent limitations to deal with finite temperature simulations or electron-lattice coupling when studying excitation states: the unit cells required to study, for instance, systems with thermal fluctuations or large polarons would require a large computational power. Multi-scale techniques, like the recently proposed Second Principles Density Functional Theory, can go beyond these limitations but require the construction of tight-binding models for the systems under investigation. In this work, we compare two such methods to construct the bands of WSe2. In particular, we compare the result of (i) Wannier-based model construction with (ii) the band fitting method of Liu et al.,[1] where the top of the valence band and the bottom of the conduction band are modeled by three bands symmetrized to have mainly Tungsten dz2, dxy and dx2-y2character. Our results emphasize the differences between these two approaches and how band fitting model construction leads to an overestimation of the localization of the real-space basis in a tight-binding representation.

We develop a simple model to compute the energy-dependent decay factors of metal-induced gap states in metal/insulator interfaces considering the collective behavior of all the bulk complex bands in the gap of the insulator. The agreement between the penetration length obtained from the model (considering only bulk properties) and full first-principles simulations of the interface (including explicitly the interfaces) is good. The influence of the electrodes and the polarization of the insulator are analyzed. The method simplifies the process of screening materials to be used in Schootky barriers or in the design of giant tunneling electroresistance and magnetoresistance devices.