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We investigate the ${\rm H_3S}$ phase of sulphur hydride under high pressure$\simeq$ 200 GPa by means of {\it ab-initio} calculations within the frameworkof the density-functional theory (DFT) with the PBE0 hybridexchange-correlation ($E_{\rm xc}$) approximation. The choice of $E_{\rm xc}$has the largest effect on the calculated electron-phonon coupling (EPC) matrixelements; the high pressure equation of state and phonon frequencies are onlyslightly modified. Mode-dependent EPC correction factors are determined fromPBE0 using a frozen-phonon supercell approach, while standarddensity-functional perturbation theory is used to determine the EPC with PBEgeneralized-gradient approximation $E_{\rm xc}$. Our principle finding is thatthe calculated PBE0 $T_c$ is enhanced by 25\% compared to PBE. This is similarin magnitude, but in opposite direction, to the proposed suppression of $T_c$by anharmonic effects [Errea {\em et al., Phys. Rev. Lett.} {\bf 114}, 157004(2015)]. Our calculations demonstrate the importance of consideringexchange-correlation approximations for calculations of superconductingproperties for this class of materials.

Electron-phonon coupling and exchange-correlation effects in superconducting ${\rm H_3S}$ under high pressure