Recent studies on excitons in two-dimensional materials have been widely conducted for their potential usages for novel electronic and optical devices. Especially, sophisticated manipulation techniques of quantum degrees of freedom of excitons are demanded. In this paper we propose a technique of forming an optical dipole trap for excitons in graphane, a two-dimensional wide gap semiconductor, based on first principles calculations. We develop a first principles method to evaluate the exciton transition dipole matrix and combine it with the density functional theory and GW+BSE calculations. We reveal that in graphane the huge exciton binding energy and the large dipole moments of Wannier-like excitons enable us to induce the dipole trap of the order of meV depth and $mu$m width. This work opens a new way to control light-exciton interacting systems based on a newly developed numerically robust ab initio calculations.
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