Further enhancement of crude oil recovery in the enhanced recovery stage from calcite oil wells is a major global challenge for oil industry. Experimental results suggest that ions present in sea water, also called smart water, have a significant influence on the wettability alteration (less oil wet) of calcite surface. In this paper, by utilizing Density Functional Theory (DFT) and Quantum Molecular Dynamics (QMD) simulations, we investigate the effect of additive ions of sea water in oil recovery by using acetic acid as a model compound of crude oil molecules. We find that Na⁺ ions precipitate to the calcite surface and form Na acetate. The binding energy of Na acetate is larger than original oil molecule (acetic acid), which reduces oil recovery. On the other hand, Mg²⁺ and ions can also reach to the calcite surface in proximity and modify the calcite surface. The binding energy of oil molecule on modified calcite surface is smaller than on pure calcite surface, which enhances oil recovery. Our results might help in understanding interaction among oil, water and additives ions of smart water for further experimental investigations.