Using first-principles simulation, the correlation between structure, phonon spectra, thermal expansion, and thermomechanics of single-layer ${\mathrm{MoS}}_2$ is established. The laminar structure results in the low-dimension ZA mode with a parabolic dispersion and negative Grüneisen constants ($\gamma$), while the nonorthogonal covalent Mo–S bonds (or intralayer thickness) result in the interatom and interdirection vibrational hybridizations, which tend to increase $\gamma$. There is a negative-positive crossover in thermal expansion coefficient at 20 K, because of the competition between the modes with negative and positive $\gamma$. Although the phononic activation at finite temperatures has a stiffening effect on the bulk modulus, the dominant effect from thermal expansion softens the lattice upon heating. The intralayer thickness results in the similarity between the thermal expansions of SL and bulk ${\mathrm{MoS}}_2$. Our numerical results explicitly support that the experimentally measured thermal shifts of the Raman modes are dominated by multiphonon scattering, but not thermal expansion.

We report a hierarchical first-principles investigation on the entangled effects of lattice dimensionality and bond characteristics in the lattice dynamics of silicene and germanene. It is found that bond bending (stretching) negatively (positively) contributes to Grüneisen constant $\gamma$, which results in the negative acoustic (positive optical) $\gamma$. The layer thickening (bond weakening) caused by chemical functionalization tends to increase (decrease) the acoustic (optical) $\gamma$, due to the increased (decreased) bond-stretching effect. The excitation of the negative-$\gamma$ modes results in negative thermal expansion, while mode excitation and thermal expansion compete with each other in thermomechanics. The sensitive structural and electronic responses of silicene and germanene to functionalization help us to derive a generic physical picture for two-dimensional lattice dynamics.