1,3-Dimethylimidazolium dimethylphosphate ([C(1)mim][DMP]) was observed experimentally to be able to eliminate the atmospheric azeotropic point of acetone and methanol, which is an important azeotrope generally encountered in furfural production and the Fischer-Tropsch process. Here, we employed ab initio calculation to understand the underlying mechanism of [C(1)mim][DMP] in eliminating the azeotropic point of acetone and methanol. Structure, energy and interaction in binary-, ternary-and quaternary-clusters composed of methanol, acetone, [C(1)mim](+) or/and [DMP](-) were calculated. The sigma-hole, AIM and NBO analyses were performed to understand intermolecular interaction with electron density, electron occupancy, charge transfer and molecular orbital interaction. Hydrogen bond interaction plays a key role in azeotropic point elimination; due to the much stronger hydrogen bond interaction between methanol and [C(1)mim][DMP] than that between acetone and [C(1)mim][DMP], [C(1)mim][DMP] prefers to interact with methanol rather than acetone, and the original interaction between methanol and acetone is separated by [C(1)mim][DMP]. The hydrogen bond is from the orbital interaction between O lone-pair-electron orbitals of the hydrogen bond acceptor and sigma* (C-H) or sigma* (O-H) anti-bonding orbitals of the hydrogen bond donor, where remarkable electron or charge transfer occurs. These theoretical calculation results are in agreement with the experimental observation that [C(1)mim][DMP] eliminates the azeotropic point of methanol and acetone. This work shows that ab initio calculation may be employed to rationalize the design or synthesis of ionic liquids for separating azeotropes.