Molybdenum disulfide, MoS₂, has recently gained considerable attention as a layered material where neighboring layers are only weakly interacting and can easily slide against each other. Therefore, mechanical exfoliation allows the fabrication of single and multi-layers and opens the possibility to generate atomically thin crystals with outstanding properties. In contrast to graphene, it has an optical gap of ~1.9 eV. This makes it a prominent candidate for transistor and opto-electronic applications. Single-layer MoS₂ exhibits remarkably different physical properties compared to bulk MoS₂ due to the absence of interlayer hybridization. For instance, while the band gap of bulk and multi-layer MoS₂ is indirect, it becomes direct with decreasing number of layers.

In this review, we analyze from a theoretical point of view the electronic, optical, and vibrational properties of single-layer, few-layer and bulk MoS₂. In particular, we focus on the effects of spin–orbit interaction, number of layers, and applied tensile strain on the vibrational and optical properties. We examine the results obtained by different methodologies, mainly ab initio approaches. We also discuss which approximations are suitable for MoS₂ and layered materials. The effect of external strain on the band gap of single-layer MoS₂ and the crossover from indirect to direct band gap is investigated. We analyze the excitonic effects on the absorption spectra. The main features, such as the double peak at the absorption threshold and the high-energy exciton are presented. Furthermore, we report on the the phonon dispersion relations of single-layer, few-layer and bulk MoS₂. Based on the latter, we explain the behavior of the Raman-active $A_{1g}$ and $E_{2g}^1$ modes as a function of the number of layers. Finally, we compare theoretical and experimental results of Raman, photoluminescence, and optical-absorption spectroscopy.

二硫化钼MoS ₂作为一种层状材料最近受到了广泛的关注，其中相邻层之间的相互作用很弱并且很容易彼此滑动。因此，机械剥离允许制造单层和多层，并打开了产生具有出色性能的原子薄晶体的可能性。与石墨烯相比，它的光学间隙约为1.9 eV。这使其成为晶体管和光电应用的杰出候选人。由于没有层间杂交，所以单层MoS ₂与本体MoS ₂相比，物理性能显着不同。例如，块状和多层MoS ₂的带隙 是间接的，它随着层数的减少而变成直接的。

在这篇综述中，我们从理论的角度分析了单层，少层和块状MoS ₂的电子，光学和振动特性。特别是，我们关注自旋-轨道相互作用，层数以及所施加的拉伸应变对振动和光学特性的影响。我们检查了通过不同方法（主要是从头开始的方法）获得的结果。我们还将讨论哪种近似适用于MoS ₂和分层材料。外部应变对单层MoS ₂带隙的影响研究了从间接带隙到直接带隙的交叉。我们分析了激子对吸收光谱的影响。提出了主要特征，如吸收阈值处的双峰和高能激子。此外，我们报道了单层，少层和块状MoS ₂的声子色散关系。基于后者，我们解释了拉曼活性的行为。${\mathrm{一个}}_{\mathrm{1个}G}$ 和 $E_{\mathrm{2个}G}^{\mathrm{1个}}$模式是层数的函数。最后，我们比较了拉曼光谱，光致发光光谱和光学吸收光谱的理论和实验结果。