## 1 Introduction  
Soon after the discovery of graphene by mechanical exfoliation, this technique was applied to the isolation of other families of van der Waals materials [1]. Among them, semiconducting transition metal dichalcogenides (TMD) are of special interest because they have a gap in the optical range of the energy spectrum, which is what makes them candidates for applications in photonics and optoelectronics [2; 3; 4]. The electronic properties of these materials are highly sensitive to external conditions such as strain, pressure or temperature. For instance, a direct-to-indirect gap and even a semiconducting-to-metal transition can be induced under specific conditions [5; 6; 7; 8; 9; 10]. They also present a strong spin-orbit coupling (SOC) that, due to the absence of inversion symmetry in single layer samples, lifts the spin degeneracy of the energy bands [11]. In time reversal-symmetric situations, inequivalent valleys have opposite spin splitting, leading to the so called spin-valley coupling [12; 13; 14], which has been observed experimentally [15; 16; 17; 18; 19; 20]. The coupling of the spin and valley degrees of freedom in semiconducting TMDs creates the possibility to manipulate them for future applications in spintronics and valleytronics nanodevices [21; 22; 23; 24].  
On the other hand, TMDs present a high stretchability. Moreover, external strain can be used to efficiently manipulate their electronic and optical properties [25]. Non-uniform strain profiles can be used to create _funnels of excitons_, which allows for capturing a broad light spectrum, concentrating carriers in specific regions of the samples [5; 26]. Strain engineering can be also used to exploit the piezoelectric properties of atomically thin layers of TMDs, converting mechanical to electrical energy [27].  
The rich orbital structure of the valence and conduction bands of semiconducting TMDs [28] complicates the construction of a tight-binding (TB) model for these systems. Such a TB model must be precise enough as to include all the pertinent orbitals of the relevant bands, but at the same time, simple enough as to be used without too much effort in calculations of optical and transport properties of these materials. The advantage of a tight-binding description with respect to first-principles methods is that it provides a simple starting point for the further inclusion of many-body electron-electron interaction, external strains, as well as of the dynamical effects of the electron-lattice interaction. Tight-binding approaches are often more convenient than ab initio methods for investigating systems involving a very large number of atoms [26], disordered and inhomogeneous samples [29], strained and/or bent samples [30; 31], materials nanostructured in large scales (nanoribbons [32; 33], ripples [34]) or in twisted multilayer materials. The aim of the present paper is twofold. Starting from the TB model for MoS\({}_{2}\) developed by [PERSON] et al. [35], we present a more accurate set of Slater-Koster parameters obtained from a more sophisticated fitting procedure, and we further generalize it to the other families of semiconducting TMDs, namely WS\({}_{2}\), MoSe\({}_{2}\) and WSe\({}_{2}\). Finally, we apply the obtained tight-binding models to calculate the optical conductivity of the four compounds.