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To have a fully ab initio description of the Moir\'e pattern in a transitionmetal dichalcogenide heterobilayer, we have carried out density functionaltheory calculations, taking accounts of both atomic registry in and the latticecorrugation out of the monolayers, on a MoTe2(9*9)/MoS2(10*10) system which hasa moderate size of superlattice larger than an exciton yet not large enough tojustify a continuum model treatment. We find that the local potential in themidplane of the bilayer displays a conspicuous Moir\'e pattern. It furtherleads us to reveal that the variation of the average local potential near Moatoms in both MoTe2 and MoS2 layers make intralayer Moir\'e potentials. Theyare the result of mutual modulation and correlate directly with the spatialvariation of the valence band maximum and conduction band minimum. Theinterlayer Moir\'e potential, defined as the difference between the twointralayer Moir\'e potentials, has a depth of 0.11 eV and changes roughly inproportion to the band gap variation in the Moir\'e cell, which has anamplitude of 0.04 eV. We find the lattice corrugation is significant in bothMoTe2 (0.30{\AA}) and MoS2 (0.77{\AA}) layers, yet its effect on the electronicproperties is marginal. The wrinkling of the MoTe2/MoS2 bilayer enhances thespatial variation of the local band gap by 5 meV, while its influence on theglobal band gap is within 1 meV. A simple intralayer band-coupling model isproposed to understand the correlation of Moir\'e potential and spatialvariation of the band gap.

Moir\'e potential, lattice corrugation, and band gap spatial variation in a twist-free MoS2/MoTe2 heterobilayer